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R/daily_response.R
In dendroTools: Linear and Nonlinear Methods for Analyzing Daily and Monthly Dendroclimatological Data
Defines functions
daily_response
Documented in
daily_response
#' daily_response
#'
#' Function calculates all possible values of a selected statistical metric
#' between one or more response variables and daily sequences of environmental
#' data. Calculations are based on moving window which is defined with two
#' arguments: window width and a location in a matrix of daily sequences of
#' environmental data. Window width could be fixed (use fixed_width) or
#' variable width (use lower_limit and upper_limit arguments). In this case,
#' all window widths between lower and upper limit will be used. All calculated
#' metrics are stored in a matrix. The location of stored calculated metric
#' in the matrix is indicating a window width (row names) and a location in a
#' matrix of daily sequences of environmental data (column names).
#'
#' @param response a data frame with tree-ring proxy variables as columns and
#' (optional) years as row names. Row.names should be matched with those from a
#' env_data data frame. If not, set row_names_subset = TRUE.
#' @param env_data a data frame of daily sequences of environmental data as
#' columns and years as row names. Each row represents a year and
#' each column represents a day of a year. Row.names should be matched with
#' those from a response data frame. If not, set row_names_subset = TRUE.
#' Alternatively, env_data could be a tidy data with three columns,
#' i.e. Year, DOY and third column representing values of mean temperatures,
#' sum of precipitation etc. If tidy data is passed to the function, set the argument
#' tidy_env_data to TRUE.
#' @param method a character string specifying which method to use. Current
#' possibilities are "cor" (default), "lm" and "brnn".
#' @param cor_method a character string indicating which correlation
#' coefficient is to be computed. One of "pearson" (default), "kendall", or
#' "spearman".
#' @param metric a character string specifying which metric to use. Current
#' possibilities are "r.squared" and "adj.r.squared". If method = "cor",
#' metric is not relevant.
#' @param lower_limit lower limit of window width
#' @param upper_limit upper limit of window width
#' @param fixed_width fixed width used for calculation. If fixed_width is
#' assigned a value, upper_limit and lower_limit will be ignored
#' @param previous_year if set to TRUE, env_data and response variables will be
#' rearranged in a way, that also previous year will be used for calculations of
#' selected statistical metric.
#' @param neurons positive integer that indicates the number of neurons used
#' for brnn method
#' @param brnn_smooth if set to TRUE, a smoothing algorithm is applied that
#' removes unrealistic calculations which are a result of neural net failure.
#' @param remove_insignificant if set to TRUE, removes all correlations bellow
#' the significant threshold level, based on a selected alpha. For "lm" and
#' "brnn" method, squared correlation is used as a threshold
#' @param alpha significance level used to remove insignificant calculations.
#' @param row_names_subset if set to TRUE, row.names are used to subset
#' env_data and response data frames. Only years from both data frames are
#' kept.
#' @param PCA_transformation if set to TRUE, all variables in the response
#' data frame will be transformed using PCA transformation.
#' @param log_preprocess if set to TRUE, variables will be transformed with
#' logarithmic transformation before used in PCA
#' @param components_selection character string specifying how to select the Principal
#' Components used as predictors.
#' There are three options: "automatic", "manual" and "plot_selection". If
#' argument is set to automatic, all scores with eigenvalues above 1 will be
#' selected. This threshold could be changed by changing the
#' eigenvalues_threshold argument. If parameter is set to "manual", user should
#' set the number of components with N_components argument. If components
#' selection is set to "plot_selection", Scree plot will be shown and a user must
#' manually enter the number of components to be used as predictors.
#' @param eigenvalues_threshold threshold for automatic selection of Principal Components
#' @param N_components number of Principal Components used as predictors
#' @param aggregate_function character string specifying how the daily data
#' should be aggregated. The default is 'mean', the other options are 'median',
#' 'sum', 'min' and 'max'
#' @param temporal_stability_check character string, specifying, how temporal stability
#' between the optimal selection and response variable(s) will be analysed. Current
#' possibilities are "sequential", "progressive" and "running_window". Sequential check
#' will split data into k splits and calculate selected metric for each split. Progressive
#' check will split data into k splits, calculate metric for the first split and then
#' progressively add 1 split at a time and calculate selected metric. For running window,
#' select the length of running window with the k_running_window argument.
#' @param k_running_window the length of running window for temporal stability check.
#' Applicable only if temporal_stability argument is set to running window.
#' @param k integer, number of breaks (splits) for temporal stability and cross validation
#' analysis.
#' @param cross_validation_type character string, specifying, how to perform cross validation
#' between the optimal selection and response variables. If the argument is set to "blocked",
#' years will not be shuffled. If the argument is set to "randomized", years will be shuffled.
#' @param subset_years a subset of years to be analyzed. Should be given in the form of
#' subset_years = c(1980, 2005)
#' @param plot_specific_window integer representing window width to be displayed
#' for plot_specific
#' @param ylimits limit of the y axes for plot_extreme and plot_specific. It should be
#' given in the form of: ylimits = c(0,1)
#' @param seed optional seed argument for reproducible results
#' @param tidy_env_data if set to TRUE, env_data should be inserted as a data frame with three
#' columns: "Year", "DOY", "Precipitation/Temperature/etc."
#' @param reference_window character string, the reference_window argument describes,
#' how each calculation is referred. There are three different options: 'start'
#' (default), 'end' and 'middle'. If the reference_window argument is set to 'start',
#' then each calculation is related to the starting day of window. If the
#' reference_window argument is set to 'middle', each calculation is related to the
#' middle day of window calculation. If the reference_window argument is set to
#' 'end', then each calculation is related to the ending day of window calculation.
#' For example, if we consider correlations with window from DOY 15 to DOY 35. If
#' reference window is set to 'start', then this calculation will be related to the
#' DOY 15. If the reference window is set to 'end', then this calculation will be
#' related to the DOY 35. If the reference_window is set to 'middle', then this
#' calculation is related to DOY 25.
#' The optimal selection, which describes the optimal consecutive days that returns
#' the highest calculated metric and is obtained by the $plot_extreme output, is the
#' same for all three reference windows.
#' @param boot logical, if TRUE, bootstrap procedure will be used to calculate
#' estimates correlation coefficients, R squared or adjusted R squared metrices
#' @param boot_n The number of bootstrap replicates
#' @param boot_ci_type A character string representing the type of bootstrap intervals
#' required. The value should be any subset of the values c("norm","basic", "stud",
#' "perc", "bca").
#' @param boot_conf_int A scalar or vector containing the confidence level(s) of
#' the required interval(s)
#' @param day_interval a vector of two values: lower and upper time interval of
#' days that will be used to calculate statistical metrics. Negative values indicate
#' previous growing season days. This argument overwrites the calculation
#' limits defined by lower_limit and upper_limit arguments.
#' @param dc_method a character string to determine the method to detrend climate
#' (environmental) data. Possible values are c("Spline", "ModNegExp", "Mean",
#' "Friedman", "ModHugershoff"). Defaults to "none" (see dplR R package).
#' @param dc_nyrs a number giving the rigidity of the smoothing spline, defaults
#' to 0.67 of series length if nyrs is NULL (see dplR R package).
#' @param dc_f a number between 0 and 1 giving the frequency response or wavelength
#' cutoff. Defaults to 0.5 (see dplR R package).
#' @param dc_pos.slope a logical flag. Will allow for a positive slope to be used
#' in method "ModNegExp" and "ModHugershoff". If FALSE the line will be horizontal
#' (see dplR R package).
#' @param dc_constrain.nls a character string which controls the constraints of
#' the "ModNegExp" model and the "ModHugershoff" (see dplR R package).
#' @param dc_span a numeric value controlling method "Friedman", or "cv" (default)
#' for automatic choice by cross-validation (see dplR R package).
#' @param dc_bass a numeric value controlling the smoothness of the fitted curve
#' in method "Friedman" (see dplR R package).
#' @param dc_difference a logical flag. Compute residuals by subtraction if TRUE,
#' otherwise use division (see dplR R package).
#' @param cor_na_use an optional character string giving a method for computing
#' covariances in the presence of missing values for correlation coefficients.
#' This must be (an abbreviation of) one of the strings "everything" (default),
#' "all.obs", "complete.obs", "na.or.complete", or "pairwise.complete.obs". See
#' also the documentation for the base cor() function.
#'
#' @return a list with 17 elements:
#' \enumerate{
#' \item $calculations - a matrix with calculated metrics
#' \item $method - the character string of a method
#' \item $metric - the character string indicating the metric used for calculations
#' \item $analysed_period - the character string specifying the analysed period based on the information from row names. If there are no row names, this argument is given as NA
#' \item $optimized_return - data frame with two columns, response variable and aggregated (averaged) daily data that return the optimal results. This data.frame could be directly used to calibrate a model for climate reconstruction
#' \item $optimized_return_all - a data frame with aggregated daily data, that returned the optimal result for the entire env_data (and not only subset of analysed years)
#' \item $transfer_function - a ggplot object: scatter plot of optimized return and a transfer line of the selected method
#' \item $temporal_stability - a data frame with calculations of selected metric for different temporal subsets
#' \item $cross_validation - a data frame with cross validation results
#' \item $plot_heatmap - ggplot2 object: a heatmap of calculated metrics
#' \item $plot_extreme - ggplot2 object: line plot of a row with the highest value in a matrix of calculated metrics
#' \item $plot_specific - ggplot2 object: line plot of a row with a selected window width in a matrix of calculated metrics
#' \item $PCA_output - princomp object: the result output of the PCA analysis
#' \item $type - the character string describing type of analysis: daily or monthly
#' \item $reference_window - character string, which reference window was used for calculations
#' \item $boot_lower - matrix with lower limit of confidence intervals of bootstrap calculations
#' \item $boot_upper - matrix with upper limit of confidence intervals of bootstrap calculations
#' \item $aggregated_climate - matrix with all aggregated climate series
#'}
#' @export
#'
#' @examples
#' \donttest{
#' # Load the dendroTools R package
#' library(dendroTools)
#'
#' # Load data
#' data(data_MVA)
#' data(data_TRW)
#' data(data_TRW_1)
#' data(example_proxies_individual)
#' data(example_proxies_1)
#' data(LJ_daily_temperatures)
#'
#' # 1 Example with fixed width. Lower and upper limits are ignored.
#' example_daily_response <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures,
#' method = "cor", fixed_width = 40, cor_method = "spearman",
#' row_names_subset = TRUE, previous_year = TRUE,
#' remove_insignificant = TRUE,
#' alpha = 0.0000000000000005, aggregate_function = 'mean',
#' reference_window = "start")
#'
#' summary(example_daily_response)
#' plot(example_daily_response, type = 1)
#' plot(example_daily_response, type = 2)
#'
#' # 2 Example for past and present. Use subset_years argument.
#' example_MVA_early <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures, cor_method = "kendall",
#' method = "cor", lower_limit = 21, upper_limit = 90,
#' row_names_subset = TRUE, previous_year = TRUE,
#' remove_insignificant = TRUE, alpha = 0.05,
#' plot_specific_window = 60, subset_years = c(1940, 1980),
#' aggregate_function = 'sum')
#'
#' example_MVA_late <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures,
#' method = "cor", lower_limit = 21, upper_limit = 60,
#' row_names_subset = TRUE, previous_year = TRUE,
#' remove_insignificant = TRUE, alpha = 0.05,
#' plot_specific_window = 60, subset_years = c(1981, 2010),
#' aggregate_function = 'sum')
#'
#' plot(example_MVA_early, type = 1)
#' plot(example_MVA_late, type = 1)
#' plot(example_MVA_early, type = 2)
#' plot(example_MVA_late, type = 2)
#'
#' # 3 Example PCA
#' example_PCA <- daily_response(response = example_proxies_individual,
#' env_data = LJ_daily_temperatures, method = "lm",
#' lower_limit = 21, upper_limit = 180,
#' row_names_subset = TRUE, remove_insignificant = TRUE,
#' alpha = 0.01, PCA_transformation = TRUE,
#' components_selection = "manual", N_components = 2)
#'
#' summary(example_PCA$PCA_output)
#' summary(example_PCA)
#' plot(example_PCA, type = 2)
#'
#' # 4 Example negative correlations
#' example_neg_cor <- daily_response(response = data_TRW_1,
#' env_data = LJ_daily_temperatures, previous_year = TRUE,
#' method = "cor", lower_limit = 21, upper_limit = 90,
#' row_names_subset = TRUE, remove_insignificant = TRUE,
#' alpha = 0.05)
#'
#' summary(example_neg_cor)
#' plot(example_neg_cor, type = 1)
#' plot(example_neg_cor, type = 2)
#' example_neg_cor$temporal_stability
#'
#' # 5 Example of multiproxy analysis
#' summary(example_proxies_1)
#' cor(example_proxies_1)
#'
#' example_multiproxy <- daily_response(response = example_proxies_1,
#' env_data = LJ_daily_temperatures,
#' method = "lm", metric = "adj.r.squared",
#' lower_limit = 21, upper_limit = 180,
#' row_names_subset = TRUE, previous_year = FALSE,
#' remove_insignificant = TRUE, alpha = 0.05)
#'
#' plot(example_multiproxy, type = 1)
#'
#' # 6 Example to test the temporal stability
#' example_MVA_ts <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures, method = "brnn",
#' lower_limit = 100, metric = "adj.r.squared", upper_limit = 180,
#' row_names_subset = TRUE, remove_insignificant = TRUE, alpha = 0.05,
#' temporal_stability_check = "running_window", k_running_window = 10)
#'
#' example_MVA_ts$temporal_stability
#'
#' # 7 Example with nonlinear brnn estimation
#' example_brnn <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures, method = "brnn", boot = FALSE,
#' lower_limit = 100, metric = "adj.r.squared", upper_limit = 101,
#' row_names_subset = TRUE, remove_insignificant = TRUE, boot_n = 10)
#'
#' summary(example_brnn)
#' }
daily_response <- function(response, env_data, method = "cor",
metric = "r.squared", cor_method = "pearson",
lower_limit = 30, upper_limit = 90, fixed_width = 0,
previous_year = FALSE, neurons = 1,
brnn_smooth = TRUE, remove_insignificant = FALSE,
alpha = .05, row_names_subset = FALSE,
PCA_transformation = FALSE, log_preprocess = TRUE,
components_selection = 'automatic',
eigenvalues_threshold = 1,
N_components = 2, aggregate_function = 'mean',
temporal_stability_check = "sequential", k = 2,
k_running_window = 30, cross_validation_type = "blocked",
subset_years = NULL, plot_specific_window = NULL,
ylimits = NULL, seed = NULL, tidy_env_data = FALSE,
reference_window = 'start', boot = FALSE, boot_n = 1000,
boot_ci_type = "norm", boot_conf_int = 0.95,
day_interval = ifelse(c(previous_year == TRUE,
previous_year == TRUE),
c(-1, 366), c(1, 366)),
dc_method = NULL,
dc_nyrs = NULL,
dc_f = 0.5,
dc_pos.slope = FALSE,
dc_constrain.nls = c("never", "when.fail", "always"),
dc_span = "cv",
dc_bass = 0,
dc_difference = FALSE,
cor_na_use = "everything"
) {
##############################################################################
# 1 day interval is organized
offset_start <- day_interval[1]
offset_end <- day_interval[2]
# if both are positive but previous_year = TRUE
if (offset_start > 0 & offset_end > 0 & previous_year == TRUE){
previous_year <- FALSE
warning(paste0("Previous year is not included in selected day_interval. ",
"The argument previous_year is set to FALSE"))
}
# if both are negative negative
if (offset_start < 0 & offset_end < 0){
offset_start <- abs(offset_start)
offset_end <- abs(offset_end)
# If previous_year is FALSE, we set it to TRUE
if (previous_year == FALSE){
previous_year = TRUE
warning(paste0("Previous year is included in day_interval. ",
"The argument previous_year is set to TRUE"))
}
# if only offset_start is negative
} else if (offset_start < 0 & offset_end > 0){
offset_end <- offset_end + 366
offset_start <- abs(offset_start)
# If previous_year is FALSE, we set it to TRUE
if (previous_year == FALSE){
previous_year = TRUE
warning(paste0("Previous year is included in day_interval. ",
"The argument previous_year is set to TRUE"))
}
}
# Calculate the max_window allowed
max_window <- offset_end - offset_start + 1
# If max_window is greater then upper_limit, it must be reduced
if (upper_limit > max_window){
upper_limit <- max_window
if (fixed_width == 0){
warning(paste0("The upper_limit is outside your day_interval and",
" therefore reduced to the maximum allowed: ",max_window,"."))
}
}
# Now, if upper_limit > max_window, we make them the same
if (lower_limit > max_window){
lower_limit <- max_window
if (fixed_width == 0){
warning(paste0("The lower_limit is outside your day_interval and",
" therefore reduced to the minimum allowed: ",max_window,"."))
}
}
# Also correction for fixed_window approach
if (fixed_width > max_window){
stop(paste0("The selected fixed_width is outside your day_interval.",
" Decrease the fixed_width argument to at least: ",max_window,"."))
}
if (previous_year == FALSE){
offset_end <- 366 - offset_end
} else {
offset_end <- 732 - offset_end
}
##############################################################################
if (fixed_width != 0){
lower_limit = 30
upper_limit = 200
}
if (!is.null(seed)) {
set.seed(seed)
}
# Defining global variables
median <- NULL
proxy <- NULL
optimized_return <- NULL
transfer_f <- NULL
journal_theme <- NULL
CV <- NULL
Period <- NULL
Years <- NULL
yearABC <- NULL
RMSE <- NULL
RE <- NULL
CE <- NULL
DE <- NULL
d <- NULL
temporal_matrix_lower <- NULL
temporal_matrix_upper <- NULL
# If there is a column name samp.depth in response data frame, warning is given
if ("samp.depth" %in% colnames(response)){
samp.depth_index <- grep("samp.depth", colnames(response))
response <- response[, -samp.depth_index,F]
warning("Removed the samp.depth from response data frame")
}
# If there is more than 2 columns in response data frame, give a warning
if (ncol(response) > 1){
warning(paste0("Your response data frame has more than 1 column! Are you doing a multiproxy research?",
" If so, OK. If not, check your response data frame!"))
}
# If env_data is given in tidy version, transformation is needed
if (tidy_env_data == TRUE){
n_col_tidy_DF <- ncol(env_data)
colnames_tidy_DF <- colnames(env_data)
if (ncol(env_data) != 3){
stop(paste("env_data was inserted in tidy version (tidy_env_data is set to TRUE).",
"env_data should have 3 columns, but it has", n_col_tidy_DF, "instead!"))
}
if (colnames_tidy_DF[1] != "Year"){
stop(paste("env_data was inserted in tidy version (tidy_env_data is set to TRUE).",
"The first column name of the env_data should be 'Year', but it is",
colnames_tidy_DF[1], "instead!"))
}
if (colnames_tidy_DF[2] != "DOY"){
stop(paste("env_data was inserted in tidy version (tidy_env_data is set to TRUE).",
"The second column name of the env_data should be 'DOY', but it is",
colnames_tidy_DF[2], "instead!"))
}
value_variable = colnames(env_data)[3]
env_data <- dcast(env_data, Year~DOY, value.var = value_variable)
env_data <- years_to_rownames(env_data, "Year")
}
# PART 1 - general data arrangements, warnings and stops
# Both bojects (response and env_data) are converted to data frames
response <- data.frame(response)
env_data <- data.frame(env_data)
# Here we save the original env and response data that will be used later
response_original <- response
env_data_original <- env_data
# For metric calculations, both objects need to have the same length,
# with the exception, when row_names_subset is set to TRUE
# Stop message in case both data frames do not have the same length
if (nrow(response) != nrow(env_data) & row_names_subset == FALSE)
stop("Length of env_data and response records differ")
# Stop in case of method == "cor" and ncol(proxies) > 1
# Correlations could be calculated only for one variable
if (method == "cor" & ncol(response) > 1)
stop(paste("More than 1 variable in response data frame not suitable ",
"for 'cor' method. Use 'lm' or 'brnn'"))
#######################################################
# Rules for previous_year = FALSE
if (previous_year == FALSE){
# Stop message if fixed_width is not between 0 and 366
if (fixed_width < 0 | fixed_width > 366)
stop("fixed_width should be between 1 and 366")
if (lower_limit > upper_limit)
stop("lower_limit can not be higher than upper_limit!")
if (lower_limit > 366 | lower_limit < 1)
stop("lower_limit out of bounds! It should be between 1 and 366")
if (upper_limit > 366 | upper_limit < 1)
stop("upper_limit out of bounds! It should be between 1 and 366")
# Rules for previous_year = TRUE
} else if (previous_year == TRUE){
# Stop message if fixed_width is not between 0 and 366
if (fixed_width < 0 | fixed_width > 732)
stop("fixed_width should be between 1 and 732")
if (lower_limit > upper_limit)
stop("lower_limit can not be higher than upper_limit!")
if (lower_limit > 732 | lower_limit < 1)
stop("lower_limit out of bounds! It should be between 1 and 366")
if (upper_limit > 732 | upper_limit < 1)
stop("upper_limit out of bounds! It should be between 1 and 366")
}
# Make sure the selected method is appropriate
if (!is.null(dc_method)){
if (!(dc_method %in% c("Spline", "ModNegExp", "Mean", "Friedman", "ModHugershoff"))){
stop(paste0('dc_method should be one of "Spline", "ModNegExp", "Mean", "Friedman", "ModHugershoff",
but instead it is:',dc_method))
}
}
# Warn users in case of missing values (selected threshold is 270 days)
env_temp <- env_data[row.names(env_data) %in% row.names(response),]
# Subset of years
if (!is.null(subset_years)){
lower_subset <- subset_years[1]
upper_subset <- subset_years[2]
subset_seq <- seq(lower_subset, upper_subset)
env_temp <- subset(env_temp, row.names(env_temp) %in% subset_seq)
}
na_problem <- data.frame(na_sum = rowSums(is.na(env_temp)))
na_problem <- na_problem[na_problem$na_sum > 270, , F]
problematic_years <- paste0(row.names(na_problem), sep = "", collapse=", ")
if (nrow(na_problem) > 0){
warning(paste0("Problematic years with missing values are present: ", problematic_years))
}
# Data manipulation
# If use.previous == TRUE, env_data data has to be rearranged accordingly
if (previous_year == TRUE) {
# FIRST, both data frames need to be arranged, the most recent year is the first one
env_data$yearABC <- row.names(env_data)
env_data <- dplyr::arrange(env_data, desc(yearABC))
env_data <- years_to_rownames(env_data, "yearABC")
env_data_previous <- env_data[-1, , F]
env_data_current <- env_data[-nrow(env_data), ,F]
row_names_current <- row.names(env_data_current)
env_data <- cbind(env_data_previous, env_data_current)
env_data <- data.frame(env_data)
row.names(env_data) <- row_names_current
env_data_original <- env_data
# response$yearABC <- row.names(response)
# response <- dplyr::arrange(response, desc(yearABC))
# response <- years_to_rownames(response, "yearABC")
# response <- data.frame(response[-nrow(response),,F ])
# response <- data.frame(response)
# response_original <- response
}
# If row_names_subset == TRUE, data is subseted and ordered based on matching
# row.names. Additionally, number of characters in row.names is checked.
# There should be at least three characters (assuming years before 100 will
# never be analysed, there is no such environmental data available)
if (row_names_subset == TRUE & nchar(row.names(env_data)[1]) >= 3){
ncol_response <- ncol(response)
colnames_response <- colnames(response)
env_data$yearABC <- row.names(env_data)
response$yearABC <- row.names(response)
temporal_data <- merge(response, env_data, by = "yearABC")
response <- data.frame(temporal_data[, c(2:(1 + ncol_response))],
row.names = temporal_data$yearABC)
colnames(response) <- colnames_response
env_data <- data.frame(temporal_data[, c((1 + ncol_response + 1):
ncol(temporal_data))],
row.names = temporal_data$yearABC)
}
# if row.names of env_data and the response data frames are not equal,
# warning is given.
if (sum(row.names(env_data) == row.names(response)) != nrow(env_data)) {
warning("row.names between env_data and response do not match!")
}
# If row_names_subset == TRUE, but row.names does not appear to be years,
# error is given.
if (row_names_subset == TRUE & nchar(row.names(env_data)[1]) < 3){
stop(paste("row.names does not appear to be years!",
"At least three characters needed!"))
}
# If PCA_transformation = TRUE, PCA is performed
if (PCA_transformation == TRUE) {
# Logarithmic transformation before PCA
if (log_preprocess == TRUE) {
if (sum(response <= 0) > 1){
stop("your response data contains negative observations. Please set the argument log_preprocess to FALSE")
}
response <- data.frame(log(response))
}
PCA_result <- princomp(response, cor = TRUE)
if (components_selection == 'automatic'){
subset_vector <- PCA_result$sdev > eigenvalues_threshold
response <- as.data.frame(PCA_result$scores[, subset_vector])
}
if (components_selection == 'manual'){
response <- as.data.frame(PCA_result$scores[, 1:N_components])
}
if (components_selection == 'plot_selection'){
plot(PCA_result, type = 'l')
fun <- function(){
N_PC <- readline("What number of PC scores should be used as predictors? ")
return(N_PC)
}
N_PC <- fun()
response <- as.data.frame(PCA_result$scores[, 1:as.numeric(N_PC)])
}
number_PC <- ncol(response)
df_names <- paste( "PC_", seq(1:number_PC), sep = "")
colnames(response) <- df_names
} else (PCA_result <- "No PCA result avalialbe !")
# Subset of years
if (!is.null(subset_years)){
lower_subset <- subset_years[1]
upper_subset <- subset_years[2]
if (lower_subset > upper_subset){
stop("Change the order of elements in the subset_years argument! First element should be lower than the second!")
}
subset_seq <- seq(lower_subset, upper_subset)
if (any(!(subset_seq %in% row.names(response)))){
stop(paste0("Undefined columns selected. Subset years don't exist",
" in the response data frame. Change the subset_years argument"))
}
if (any(!(subset_seq %in% row.names(env_data)))){
stop(paste0("Undefined columns selected. Subset years don't exist",
" in the env_data data frame. Change the subset_years argument"))
}
response <- subset(response, row.names(response) %in% subset_seq)
env_data <- subset(env_data, row.names(env_data) %in% subset_seq)
}
# NA values are not allowed and must be removed from response data.frame
if (sum(is.na(response)) > 0){
prob_year <- row.names(response[is.na(response), , drop = F])
stop(paste0("NA is not allowed in response data frame. ",
"Problematic year is ", prob_year))
}
# PART 2 - Based on the selected function arguments, different chunks of code
# will be used. For demonstration:
# A) Chunks are used if fixed.withd != 0
# A.1 method == "cor"
# A.2 method == "lm"
# A.3 method == "brnn"
# B) Chunks are used if fixed.withd == 0
# B.1 method == "cor"
# B.2 method == "lm"
# B.3 method == "brnn"
# this is a list for climate and and holder for saving mm
list_climate <- list()
mm <- 1
# A.1 method = "cor"
if (fixed_width != 0 & method == "cor") {
# This is an empty matrix, currently filled with NA's
# Latter, calculations will be stored in this matrix
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = 1,
ncol = (ncol(env_data) - fixed_width) + 1)
} else if (reference_window == 'end') {
temporal_matrix <- matrix(NA, nrow = 1, ncol = (ncol(env_data)))
} else if (reference_window == 'middle') {
temporal_matrix <- matrix(NA, nrow = 1,
ncol = round2((ncol(env_data) - fixed_width +
1 + fixed_width/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (fixed_width != max_window){
pb <- txtProgressBar(min = 0, max = (ncol(env_data) - fixed_width - offset_end - offset_start + 1),
style = 3)
}
b = 0
# An iterating loop. In each itteration x is calculated and represents
# response (dependent) variable. X is a moving average. Window width of
# a moving window is fixed_width. Next, statistical metric is calculated
# based on a selected method (cor, lm or brnn). Calculation is stored in
# temporal matrix.
for (j in (0 + offset_start -1): (ncol(env_data) - max((fixed_width + offset_end), offset_end))) {
b = b + 1
if (aggregate_function == 'median'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , median, na.rm = TRUE)
}
} else if (aggregate_function == 'sum'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , sum, na.rm = TRUE)
}
} else if (aggregate_function == 'mean'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- rowMeans(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]), na.rm = TRUE)
}
} else if (aggregate_function == 'min'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , min, na.rm = TRUE) }
} else if (aggregate_function == 'max'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , max, na.rm = TRUE)
}
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + fixed_width)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_correlation <- cor(response[, 1], x[, 1], method = cor_method)
temporal_lower <- NA
temporal_upper <- NA
} else if (boot == TRUE){
temp_df_boot <- cbind(response[, 1], x[, 1])
calc <- boot(temp_df_boot, boot_f_cor, cor.type = cor_method, R = boot_n)
temporal_correlation <- colMeans(calc$t)[1]
ci_int <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type), silent = TRUE)
if (class(ci_int)[[1]] == "try-error"){
temporal_lower <- NA
temporal_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_lower <- ci_int$norm[2]
temporal_upper <- ci_int$norm[3]
} else if (boot_ci_type == "perc"){
temporal_lower <- ci_int$perc[4]
temporal_upper <- ci_int$perc[5]
} else if (boot_ci_type == "stud") {
temporal_lower <- ci_int$student[4]
temporal_upper <- ci_int$student[5]
} else if (boot_ci_type == "basic") {
temporal_lower <- ci_int$basic[4]
temporal_upper <- ci_int$basic[5]
} else if (boot_ci_type == "bca") {
temporal_lower <- ci_int$bca[4]
temporal_upper <- ci_int$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
print(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
# Each calculation is printed. Reason: usually it takes several minutes
# to go through all loops and therefore, users might think that R is
# not responding. But if each calculation is printed, user could be
# confident, that R is responding.
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_correlation
temporal_matrix_lower[1, j + 1] <- temporal_lower
temporal_matrix_upper[1, j + 1] <- temporal_upper
} else if (reference_window == 'end'){
temporal_matrix[1, j + fixed_width] <- temporal_correlation
temporal_matrix_lower[1, j + fixed_width] <- temporal_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_correlation
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_upper
}
if (fixed_width != max_window){setTxtProgressBar(pb, b)}
}
if (fixed_width != max_window){close(pb)}
# temporal_matrix is given rownames and colnames. Rownames represent a
# window width used fot calculations. Colnames represent the position of
# moving window in a original env_data data frame.
row.names(temporal_matrix) <- fixed_width
row.names(temporal_matrix_lower) <- fixed_width
row.names(temporal_matrix_upper) <- fixed_width
temporal_colnames <- as.vector(seq(from = 1,
to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# A.2 method == "lm"
# For a description see A.1
if (fixed_width != 0 & method == "lm") {
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = 1,
ncol = (ncol(env_data) - fixed_width) + 1)
} else if (reference_window == 'end') {
temporal_matrix <- matrix(NA, nrow = 1, ncol = (ncol(env_data)))
} else if (reference_window == 'middle') {
temporal_matrix <- matrix(NA, nrow = 1,
ncol = round2((ncol(env_data) - fixed_width +
1 + fixed_width/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (fixed_width != max_window){
pb <- txtProgressBar(min = 0, max = (ncol(env_data) - fixed_width - offset_end - offset_start + 1),
style = 3)}
b = 0
for (j in (0 + offset_start -1): (ncol(env_data) - max((fixed_width + offset_end), offset_end))) {
b = b + 1
if (aggregate_function == 'median'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(env_data[1:nrow(env_data),
(1 + j) : (j + fixed_width)],1 , median, na.rm = TRUE)
}
} else if (aggregate_function == 'sum'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j) : (j + fixed_width)]
} else {
x <- apply(env_data[1:nrow(env_data),
(1 + j) : (j + fixed_width)],1 , median, na.rm = TRUE)
}
} else if (aggregate_function == 'mean'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- rowMeans(env_data[1:nrow(env_data),
(1 + j) : (j + fixed_width)], na.rm = TRUE)
}
} else if (aggregate_function == 'min'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j) : (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j) : (j + fixed_width)]),1 , min, na.rm = TRUE) }
} else if (aggregate_function == 'max'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , max, na.rm = TRUE)
}
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + fixed_width)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_df <- data.frame(cbind(x, response))
temporal_model <- lm(x ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
temporal_r_squared <- temporal_summary$r.squared
temporal_adj_r_squared <- temporal_summary$adj.r.squared
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else if (boot == TRUE){
temporal_df <- data.frame(cbind(x, response))
calc <- boot(data = temporal_df, statistic = boot_f_lm, R = boot_n, lm.formula = "x ~ .")
temporal_r_squared <- colMeans(calc$t)[1]
temporal_adj_r_squared <- colMeans(calc$t)[2]
ci_int_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 1), silent = TRUE)
ci_int_adj_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 2), silent = TRUE)
if (class(ci_int_r_squared)[[1]] == "try-error"){
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_r_squared_lower <- ci_int_r_squared$norm[2]
temporal_r_squared_upper <- ci_int_r_squared$norm[3]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$norm[2]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$norm[3]
} else if (boot_ci_type == "perc"){
temporal_r_squared_lower <- ci_int_r_squared$perc[4]
temporal_r_squared_upper <- ci_int_r_squared$perc[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$perc[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$perc[5]
} else if (boot_ci_type == "stud") {
temporal_r_squared_lower <- ci_int_r_squared$studen[4]
temporal_r_squared_upper <- ci_int_r_squared$studen[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$studen[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$studen[5]
} else if (boot_ci_type == "basic") {
temporal_r_squared_lower <- ci_int_r_squared$basic[4]
temporal_r_squared_upper <- ci_int_r_squared$basic[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$basic[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$basic[5]
} else if (boot_ci_type == "bca") {
temporal_r_squared_lower <- ci_int_r_squared$bca[4]
temporal_r_squared_upper <- ci_int_r_squared$bca[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$bca[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
stop(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (metric == "r.squared"){
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_r_squared
temporal_matrix_lower[1, j + 1] <- temporal_r_squared_lower
temporal_matrix_upper[1, j + 1] <- temporal_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[1, j + fixed_width] <- temporal_r_squared
temporal_matrix_lower[1, j + fixed_width] <- temporal_r_squared_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared_upper
}
}
if (metric == "adj.r.squared"){
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_adj_r_squared
temporal_matrix_lower[1, j + 1] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, j + 1] <- temporal_adj_r_squared_upper
} else if (reference_window == 'end'){
temporal_matrix[1, j + fixed_width] <- temporal_adj_r_squared
temporal_matrix_lower[1, j + fixed_width] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_adj_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared_upper
}
}
if (fixed_width != max_window){setTxtProgressBar(pb, b)}
}
if (fixed_width != max_window){close(pb)}
row.names(temporal_matrix) <- fixed_width
row.names(temporal_matrix_lower) <- fixed_width
row.names(temporal_matrix_upper) <- fixed_width
temporal_colnames <- as.vector(seq(from = 1,
to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# A.3 method == "brnn"
# For a description see A.1
if (fixed_width != 0 & method == "brnn") {
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = 1,
ncol = (ncol(env_data) - fixed_width) + 1)
} else if (reference_window == 'end') {
temporal_matrix <- matrix(NA, nrow = 1, ncol = (ncol(env_data)))
} else if (reference_window == 'middle') {
temporal_matrix <- matrix(NA, nrow = 1,
ncol = round2((ncol(env_data) - fixed_width +
1 + fixed_width/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (fixed_width != max_window){
pb <- txtProgressBar(min = 0, max = (ncol(env_data) - fixed_width - offset_end - offset_start + 1),
style = 3)}
b = 0
for (j in (0 + offset_start -1): (ncol(env_data) - max((fixed_width + offset_end), offset_end))) {
b = b + 1
if (aggregate_function == 'median'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)],1 , median, na.rm = TRUE)
}
} else if (aggregate_function == 'sum'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)],1 , sum, na.rm = TRUE)
}
} else if (aggregate_function == 'mean') {
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- rowMeans(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)], na.rm = TRUE)
}
} else if (aggregate_function == 'min'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , min, na.rm = TRUE) }
} else if (aggregate_function == 'max'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , max, na.rm = TRUE)}
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + fixed_width)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_df <- data.frame(cbind(x, response))
capture.output(temporal_model <- try(brnn(x ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6),
silent = TRUE))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
if (class(temporal_model)[[1]] != "try-error"){
temporal_r_squared <- 1 - (sum((x[, 1] - temporal_predictions) ^ 2) /
sum((x[, 1] - mean(x[, 1])) ^ 2))
temporal_adj_r_squared <- 1 - ((1 - temporal_r_squared) *
((nrow(x) - 1)) /
(nrow(x) -
ncol(as.data.frame(temporal_df))
- 1 + 1))
}
temporal_r_squared_lower <- NA
temporal_r_squared_upper <- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else if (boot == TRUE){
temporal_df <- data.frame(cbind(x, response))
calc <- boot(data = temporal_df, statistic = boot_f_brnn, R = boot_n, brnn.formula = "x ~ .", neurons = neurons)
temporal_r_squared <- colMeans(calc$t)[1]
temporal_adj_r_squared <- colMeans(calc$t)[2]
ci_int_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 1), silent = TRUE)
ci_int_adj_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 2), silent = TRUE)
if (class(ci_int_r_squared)[[1]] == "try-error"){
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_r_squared_lower <- ci_int_r_squared$norm[2]
temporal_r_squared_upper <- ci_int_r_squared$norm[3]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$norm[2]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$norm[3]
} else if (boot_ci_type == "perc"){
temporal_r_squared_lower <- ci_int_r_squared$perc[4]
temporal_r_squared_upper <- ci_int_r_squared$perc[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$perc[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$perc[5]
} else if (boot_ci_type == "stud") {
temporal_r_squared_lower <- ci_int_r_squared$studen[4]
temporal_r_squared_upper <- ci_int_r_squared$studen[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$studen[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$studen[5]
} else if (boot_ci_type == "basic") {
temporal_r_squared_lower <- ci_int_r_squared$basic[4]
temporal_r_squared_upper <- ci_int_r_squared$basic[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$basic[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$basic[5]
} else if (boot_ci_type == "bca") {
temporal_r_squared_lower <- ci_int_r_squared$bca[4]
temporal_r_squared_upper <- ci_int_r_squared$bca[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$bca[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
stop(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (metric == "r.squared"){
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_r_squared
temporal_matrix_lower[1, j + 1] <- temporal_r_squared_lower
temporal_matrix_upper[1, j + 1] <- temporal_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[1, j + fixed_width] <- temporal_r_squared
temporal_matrix_lower[1, j + fixed_width] <- temporal_r_squared_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared_upper
}
}
if (metric == "adj.r.squared"){
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_adj_r_squared
temporal_matrix_lower[1, j + 1] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, j + 1] <- temporal_adj_r_squared_upper
} else if (reference_window == 'end'){
temporal_matrix[1, j + fixed_width] <- temporal_adj_r_squared
temporal_matrix_lower[1, j + fixed_width] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_adj_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared_upper
}
}
if (fixed_width != max_window){setTxtProgressBar(pb, b)}
}
if (fixed_width != max_window){close(pb)}
row.names(temporal_matrix) <- fixed_width
row.names(temporal_matrix_lower) <- fixed_width
row.names(temporal_matrix_upper) <- fixed_width
temporal_colnames <- as.vector(seq(from = 1,
to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# B fixed_width == 0, in this case, lower_limit and upper_limit arguments
# will be used to define window width of a moving window.
# B.1 method == "cor"
if (fixed_width == 0 & method == "cor") {
# This is an empty matrix, currently filled with NA's
# Latter, calculations will be stored in this matrix
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data) - lower_limit) + 1)
} else if (reference_window == 'end'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data)))
} else if (reference_window == 'middle'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = round2((ncol(env_data) - lower_limit +
1 + lower_limit/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
# An iterating double loop: 1 outer loop) iterating from lower_limit :
# upper_limit defines windo.width used for a moving window. 2) inner loop
# defines the starting position of a moving window.
# In each itteration, x is calculated and represents a response (dependent)
# variable. x is a moving average, based on rowMeans/apply function.
# Next, statistical metric is calculated based on a selected method (cor,
# lm or brnn). Calculation is stored in temporal matrix in a proper place.
# The position of stored calculation is informative later used for
# indiciating optimal values.
if (upper_limit != lower_limit){
pb <- txtProgressBar(min = 0, max = (upper_limit - lower_limit), style = 3)
}
b = 0
for (K in lower_limit:upper_limit) {
b = b + 1
for (j in (0 + offset_start -1): (ncol(env_data) - max((K + offset_end), offset_end))) {
if (aggregate_function == 'median'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , median, na.rm = TRUE)
} else if (aggregate_function == 'sum'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , sum, na.rm = TRUE)
} else if (aggregate_function == 'mean'){
x <- rowMeans(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]), na.rm = TRUE)
} else if(aggregate_function == 'min'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , min, na.rm = TRUE)
} else if (aggregate_function == 'max'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , max, na.rm = TRUE)
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + K)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_correlation <- cor(response[, 1], x[, 1], method = cor_method, use = cor_na_use)
temporal_lower <- NA
temporal_upper <- NA
} else if (boot == TRUE){
temp_df_boot <- cbind(response[, 1], x[, 1])
calc <- boot(temp_df_boot, boot_f_cor, cor.type = cor_method, R = boot_n)
temporal_correlation <- colMeans(calc$t)[1]
ci_int <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type), silent = TRUE)
if (class(ci_int)[[1]] == "try-error"){
temporal_lower <- NA
temporal_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_lower <- ci_int$norm[2]
temporal_upper <- ci_int$norm[3]
} else if (boot_ci_type == "perc"){
temporal_lower <- ci_int$perc[4]
temporal_upper <- ci_int$perc[5]
} else if (boot_ci_type == "stud") {
temporal_lower <- ci_int$student[4]
temporal_upper <- ci_int$student[5]
} else if (boot_ci_type == "basic") {
temporal_lower <- ci_int$basic[4]
temporal_upper <- ci_int$basic[5]
} else if (boot_ci_type == "bca") {
temporal_lower <- ci_int$bca[4]
temporal_upper <- ci_int$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
print(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_correlation
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_upper
} else if (reference_window == 'end'){
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_correlation
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_correlation
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_upper
}
}
if (upper_limit != lower_limit){setTxtProgressBar(pb, b)}
}
if (upper_limit != lower_limit){close(pb)}
# temporal_matrix is given rownames and colnames. Rownames represent a
# window width used fot calculations. Colnames represent the position of
# moving window in a original env_data data frame.
temporal_rownames <- as.vector(seq(from = lower_limit, to = upper_limit,
by = 1))
row.names(temporal_matrix) <- temporal_rownames
row.names(temporal_matrix_lower) <- temporal_rownames
row.names(temporal_matrix_upper) <- temporal_rownames
temporal_colnames <- as.vector(seq(from = 1,
to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# B.2 method == "lm"
# For a description see B.1
if (fixed_width == 0 & method == "lm") {
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data) - lower_limit) + 1)
} else if (reference_window == 'end'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data)))
} else if (reference_window == 'middle'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = round2((ncol(env_data) - lower_limit +
1 + lower_limit/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (upper_limit != lower_limit){
pb <- txtProgressBar(min = 0, max = (upper_limit - lower_limit), style = 3)
}
b = 0
for (K in lower_limit:upper_limit) {
b = b + 1
for (j in (0 + offset_start -1): (ncol(env_data) - max((K + offset_end), offset_end))) {
if (aggregate_function == 'median'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , median, na.rm = TRUE)
} else if (aggregate_function == 'sum'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , sum, na.rm = TRUE)
} else if (aggregate_function == 'mean'){
x <- rowMeans(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]), na.rm = TRUE)
} else if(aggregate_function == 'min'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , min, na.rm = TRUE)
} else if (aggregate_function == 'max'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , max, na.rm = TRUE)
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + K)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_df <- data.frame(cbind(x, response))
temporal_model <- lm(x ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
temporal_r_squared <- temporal_summary$r.squared
temporal_adj_r_squared <- temporal_summary$adj.r.squared
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else if (boot == TRUE){
temporal_df <- data.frame(cbind(x, response))
calc <- boot(data = temporal_df, statistic = boot_f_lm, R = boot_n, lm.formula = "x ~ .")
temporal_r_squared <- colMeans(calc$t)[1]
temporal_adj_r_squared <- colMeans(calc$t)[2]
ci_int_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 1), silent = TRUE)
ci_int_adj_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 2), silent = TRUE)
if (class(ci_int_r_squared)[[1]] == "try-error"){
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_r_squared_lower <- ci_int_r_squared$norm[2]
temporal_r_squared_upper <- ci_int_r_squared$norm[3]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$norm[2]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$norm[3]
} else if (boot_ci_type == "perc"){
temporal_r_squared_lower <- ci_int_r_squared$perc[4]
temporal_r_squared_upper <- ci_int_r_squared$perc[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$perc[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$perc[5]
} else if (boot_ci_type == "stud") {
temporal_r_squared_lower <- ci_int_r_squared$studen[4]
temporal_r_squared_upper <- ci_int_r_squared$studen[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$studen[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$studen[5]
} else if (boot_ci_type == "basic") {
temporal_r_squared_lower <- ci_int_r_squared$basic[4]
temporal_r_squared_upper <- ci_int_r_squared$basic[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$basic[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$basic[5]
} else if (boot_ci_type == "bca") {
temporal_r_squared_lower <- ci_int_r_squared$bca[4]
temporal_r_squared_upper <- ci_int_r_squared$bca[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$bca[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
stop(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (metric == "r.squared"){
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared_upper
}
}
if (metric == "adj.r.squared"){
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared_upper
}
}
}
if (upper_limit != lower_limit){setTxtProgressBar(pb, b)}
}
if (upper_limit != lower_limit){close(pb)}
temporal_rownames <- as.vector(seq(from = lower_limit, to = upper_limit, by = 1))
row.names(temporal_matrix) <- temporal_rownames
row.names(temporal_matrix_lower) <- temporal_rownames
row.names(temporal_matrix_upper) <- temporal_rownames
temporal_colnames <- as.vector(seq(from = 1, to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# B.3 method == "brnn"
# For a description see B.1
if (fixed_width == 0 & method == "brnn") {
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data) - lower_limit) + 1)
} else if (reference_window == 'end'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data)))
} else if (reference_window == 'middle'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = round2((ncol(env_data) - lower_limit +
1 + lower_limit/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (upper_limit != lower_limit){
pb <- txtProgressBar(min = 0, max = (upper_limit - lower_limit), style = 3)
}
b = 0
for (K in lower_limit:upper_limit) {
b = b + 1
for (j in (0 + offset_start -1): (ncol(env_data) - max((K + offset_end), offset_end))) {
if (aggregate_function == 'median'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , median, na.rm = TRUE)
} else if (aggregate_function == 'sum'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , sum, na.rm = TRUE)
} else if (aggregate_function == 'mean'){
x <- rowMeans(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]), na.rm = TRUE)
} else if(aggregate_function == 'min'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , min, na.rm = TRUE)
} else if (aggregate_function == 'max'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , max, na.rm = TRUE)
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + K)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_df <- data.frame(cbind(x, response))
capture.output(temporal_model <- try(brnn(x ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6),
silent = TRUE))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
if (class(temporal_model)[[1]] != "try-error"){
temporal_r_squared <- 1 - (sum((x[, 1] - temporal_predictions) ^ 2) /
sum((x[, 1] - mean(x[, 1])) ^ 2))
temporal_adj_r_squared <- 1 - ((1 - temporal_r_squared) *
((nrow(x) - 1)) /
(nrow(x) -
ncol(as.data.frame(temporal_df))
- 1 + 1))
} else {
temporal_r_squared <- NA
temporal_adj_r_squared <- NA
}
temporal_r_squared_lower <- NA
temporal_r_squared_upper <- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else if (boot == TRUE){
temporal_df <- data.frame(cbind(x, response))
calc <- boot(data = temporal_df, statistic = boot_f_brnn, R = boot_n, brnn.formula = "x ~ .", neurons = neurons)
temporal_r_squared <- colMeans(calc$t)[1]
temporal_adj_r_squared <- colMeans(calc$t)[2]
ci_int_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 1), silent = TRUE)
ci_int_adj_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 2), silent = TRUE)
if (class(ci_int_r_squared)[[1]] == "try-error"){
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_r_squared_lower <- ci_int_r_squared$norm[2]
temporal_r_squared_upper <- ci_int_r_squared$norm[3]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$norm[2]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$norm[3]
} else if (boot_ci_type == "perc"){
temporal_r_squared_lower <- ci_int_r_squared$perc[4]
temporal_r_squared_upper <- ci_int_r_squared$perc[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$perc[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$perc[5]
} else if (boot_ci_type == "stud") {
temporal_r_squared_lower <- ci_int_r_squared$studen[4]
temporal_r_squared_upper <- ci_int_r_squared$studen[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$studen[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$studen[5]
} else if (boot_ci_type == "basic") {
temporal_r_squared_lower <- ci_int_r_squared$basic[4]
temporal_r_squared_upper <- ci_int_r_squared$basic[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$basic[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$basic[5]
} else if (boot_ci_type == "bca") {
temporal_r_squared_lower <- ci_int_r_squared$bca[4]
temporal_r_squared_upper <- ci_int_r_squared$bca[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$bca[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
stop(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (metric == "r.squared"){
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared_upper
}
}
if (metric == "adj.r.squared"){
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared_upper
}
}
}
if (upper_limit != lower_limit){setTxtProgressBar(pb, b)}
}
if (upper_limit != lower_limit){close(pb)}
temporal_rownames <- as.vector(seq(from = lower_limit, to = upper_limit, by = 1))
row.names(temporal_matrix) <- temporal_rownames
row.names(temporal_matrix_lower) <- temporal_rownames
row.names(temporal_matrix_upper) <- temporal_rownames
temporal_colnames <- as.vector(seq(from = 1, to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# PART 3: smoothing function, if brnn method is used. It turnes out, that
# brnn sometimes (1 - 3 % of calculations) fails to construct a realistic
# result. In those cases, much lower r.squared (or adj.r.squared) are
# calculated. smooth_matrix function removes unrealistic calculations and
# replace them with mean of values in a window 3 x 3. Maximum value
# is not affected by any means.
# [i - 1, j - 1], [i - 1, j], [i - 1, j + 1]
# [ i, j - 1], [ i, j], [ i, j + 1]
# [i + 1, j - 1], [i + 1, j], [i + 1, j + 1]
if (method == "brnn" & brnn_smooth == TRUE){
temporal_matrix <- smooth_matrix(temporal_matrix, factor_drop = 0.7,
repeats = 2)
}
# To enhance the visualisation, insignificant values
# are removed if remove_insignificant == TRUE
if (remove_insignificant == TRUE){
critical_threshold_cor <- critical_r(nrow(response), alpha = alpha)
critical_threshold_cor2 <- critical_threshold_cor ^ 2
# 1 Method is correlation
if (method == "cor") {
temporal_matrix[abs(temporal_matrix) < abs(critical_threshold_cor)] <- NA
# 2 lm and brnn method
} else if (method == "lm" | method == "brnn") {
temporal_matrix[abs(temporal_matrix) < abs(critical_threshold_cor2)] <- NA
}
}
if(is.finite(mean(temporal_matrix, na.rm = TRUE)) == FALSE){
warning("All calculations are insignificant! Please change the alpha argument.")
final_list <- list(calculations = temporal_matrix,
method = method,
metric = cor_method,
analysed_period = NA,
optimized_return = NA,
optimized_return_all = NA,
transfer_function = NA, temporal_stability = NA,
cross_validation = NA,
plot_heatmap = NA,
plot_extreme = NA,
plot_specific = NA,
PCA_output = NA,
type = "daily",
reference_window = reference_window,
boot_lower = temporal_matrix_lower,
boot_upper = temporal_matrix_upper,
aggregated_climate = NA )
class(final_list) <- 'dmrs'
return(final_list)
} else {
########################################################################
# PART 4: Final list is being created and returned as a function output#
########################################################################
# The first three elements of the final list are already created: calculated
# values, method and metric used.
# Here we create the fourth element: the optimal sequence of days that
# returns the best selected statistical metric. We name it optimal_return.
# In case of negative correlations, different strategy is applied.
# For more detailed description see plot_extreme()
if(is.finite(mean(temporal_matrix, na.rm = TRUE)) == FALSE){
stop("All calculations are insignificant! Change the alpha argument!")
}
overall_max <- max(temporal_matrix, na.rm = TRUE)
overall_min <- min(temporal_matrix, na.rm = TRUE)
# absolute vales of overall_maximum and overall_minimum are compared and
# one of the following two if functions is used
# There are unimportant warnings produced:
# no non-missing arguments to max; returning -Inf
if ((abs(overall_max) >= abs(overall_min)) == TRUE) {
# maximum value is located. Row indeces are needed to query information
# about the window width used to calculate the maximum. Column name is
# needed to query the starting day.
max_result <- suppressWarnings(which.max(apply(temporal_matrix,
MARGIN = 2, max,
na.rm = TRUE)))
plot_column <- max_result
max_index <- which.max(temporal_matrix[, names(max_result)])
row_index <- row.names(temporal_matrix)[max_index]
}
if ((abs(overall_max) < abs(overall_min)) == TRUE) {
min_result <- suppressWarnings(which.min(apply(temporal_matrix,
MARGIN = 2, min,
na.rm = TRUE)))
plot_column <- min_result
min_index <- which.min(temporal_matrix[, names(min_result)])
row_index <- row.names(temporal_matrix)[min_index]
}
# The fourth return element is being created: rowMeans/ apply of optimal sequence:
# So, here we consider more options, based on the reference_winow
# option 1: reference window = "start"
if (reference_window == 'start'){
if (aggregate_function == 'median'){
dataf <- data.frame(apply(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf <- data.frame(apply(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf <- data.frame(rowMeans(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),
na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf <- data.frame(apply(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf <- data.frame(apply(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
# if detrending was applied, should also be applied here
if (!is.null(dc_method)){
dataf <- dplR::detrend(dataf, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
dataf_full <- cbind(response, dataf)
colnames(dataf_full)[ncol(dataf_full)] <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
## Once again, the same procedure, to get the optimal sequence, but this time for whole data, not only
# for the analysed period.
if (aggregate_function == 'median'){
dataf_original <- data.frame(apply(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf_original <- data.frame(apply(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf_original <- data.frame(rowMeans(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),
na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf_original <- data.frame(apply(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf_original <- data.frame(apply(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
dataf_full_original <- dataf_original
if (!is.null(dc_method)){
dataf_full_original <- dplR::detrend(dataf_full_original, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
colnames(dataf_full_original) <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
# Additional check: (we should get the same metric as before in the loop)
if (method == "lm" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$r.squared
}
if (method == "lm" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$adj.r.squared
}
if (method == "brnn" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model,
temporal_df), silent = TRUE)
optimized_result <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
}
if (method == "brnn" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ .,
data = temporal_df, neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
temporal_r_squared <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
optimized_result <- 1 - ((1 - temporal_r_squared) *
((nrow(temporal_df) - 1)) /
(nrow(temporal_df) -
ncol(as.data.frame(response[, 1])) - 1))
}
if (method == "cor"){
optimized_result <- cor(dataf, response, method = cor_method, use = cor_na_use)
}
# Just give a nicer colmname
colnames(dataf) <- "Optimized return"
}
# Option 2: reference window = "end"
if (reference_window == 'end'){
if (aggregate_function == 'median'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , mean, na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , max, na.rm = TRUE))
} else {
stop(paste0("gate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
# if detrending was applied, should also be applied here
if (!is.null(dc_method)){
dataf <- dplR::detrend(dataf, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
dataf_full <- cbind(response, dataf)
colnames(dataf_full)[ncol(dataf_full)] <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
## Once again, the same procedure, to get the optimal sequence, but this time for whole data, not only
# for the analysed period.
if (aggregate_function == 'median'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , mean, na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median or sum."))
}
dataf_full_original <- dataf_original
if (!is.null(dc_method)){
dataf_full_original <- dplR::detrend(dataf_full_original, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
colnames(dataf_full_original) <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
# Additional check: (we should get the same metric as before in the loop)
if (method == "lm" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$r.squared
}
if (method == "lm" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$adj.r.squared
}
if (method == "brnn" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model,
temporal_df), silent = TRUE)
optimized_result <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
}
if (method == "brnn" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ .,
data = temporal_df, neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
temporal_r_squared <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
optimized_result <- 1 - ((1 - temporal_r_squared) *
((nrow(temporal_df) - 1)) /
(nrow(temporal_df) -
ncol(as.data.frame(response[, 1])) - 1))
}
if (method == "cor"){
optimized_result <- cor(dataf, response, method = cor_method, use = cor_na_use)
}
# Just give a nicer colname
colnames(dataf) <- "Optimized return"
}
# option 3: reference window = "middle"
if (reference_window == 'middle'){
if (as.numeric(row_index)%%2 == 0){
adjustment_1 = 0
adjustment_2 = 1
} else {
adjustment_1 = 1
adjustment_2 = 2
}
if (aggregate_function == 'median'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , mean, na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
# if detrending was applied, should also be applied here
if (!is.null(dc_method)){
dataf <- dplR::detrend(dataf, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
dataf_full <- cbind(response, dataf)
colnames(dataf_full)[ncol(dataf_full)] <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
## Once again, the same procedure, to get the optimal sequence, but this time for whole data, not only
# for the analysed period.
if (aggregate_function == 'median'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , mean, na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min, max."))
}
dataf_full_original <- dataf_original
if (!is.null(dc_method)){
dataf_full_original <- dplR::detrend(dataf_full_original, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
colnames(dataf_full_original) <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
# Additional check: (we should get the same metric as before in the loop)
if (method == "lm" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$r.squared
}
if (method == "lm" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$adj.r.squared
}
if (method == "brnn" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model,
temporal_df), silent = TRUE)
optimized_result <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
}
if (method == "brnn" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ .,
data = temporal_df, neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
temporal_r_squared <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
optimized_result <- 1 - ((1 - temporal_r_squared) *
((nrow(temporal_df) - 1)) /
(nrow(temporal_df) -
ncol(as.data.frame(response[, 1])) - 1))
}
if (method == "cor"){
optimized_result <- cor(dataf, response, method = cor_method, use = cor_na_use)
}
# Just give a nicer colname
colnames(dataf) <- "Optimized return"
}
##############################################################################
# If detrending was used, it also needs to be applied on optimized return
# Element 5
# Here we create the fifth element of the final list: Analysed period in the
# form of min(year) - max(year), e.g. 1950 - 2015
min_env_data <- min(as.numeric(row.names(env_data)))
min_response <- min(as.numeric(row.names(response)))
max_env_data <- max(as.numeric(row.names(env_data)))
max_response <- max(as.numeric(row.names(response)))
min_together <- min(min_env_data, min_response)
max_together <- min(max_env_data, max_response)
analysed_period <- paste(as.character(min_together),
as.character(max_together),
sep = " - ")
if (nchar(analysed_period) < 9) {
analysed_period <- NA
}
# Here, the transfer function is being created
transfer_data = data.frame(proxy = response[,1], optimized_return =dataf[,1])
lm_model = lm(optimized_return ~ proxy, data = transfer_data)
capture.output(brnn_model <- try(brnn(optimized_return ~ proxy, data = transfer_data, neurons = neurons), silent = TRUE))
full_range = data.frame(proxy = seq(from = min(response[,1]), to = max(response[,1]), length.out = 100))
if (method == "lm" | method == "cor"){
full_range$transfer_f = predict(lm_model, full_range)
}
if (method == "brnn"){
full_range$transfer_f = predict.brnn(brnn_model, full_range)
}
# String for titles
if (method == "cor"){
title_string <- "Correlation Coefficients"
} else if (method == "lm"){
title_string <- "Linear Regression"
} else if (method == "brnn"){
title_string <- "ANN With Bayesian Regularization"
} else (print("The selection of method is not correct"))
# The definition of theme
journal_theme <- theme_bw() +
theme(axis.text = element_text(size = 16, face = "bold"),
axis.title = element_text(size = 18), text = element_text(size = 18),
plot.title = element_text(size = 16, face = "bold"))
p1 <- ggplot(transfer_data, aes(proxy, optimized_return)) +
geom_point() +
geom_line(aes(proxy, transfer_f), full_range) +
journal_theme +
ggtitle(paste("Analysed Period:", analysed_period, "\nMethod:", title_string))
analysed_period
# If there is more than one independent variable in the model,
# transfer function is not given, since we should return a 3d model
if (ncol(response) > 1){
p1 <- "No transfer function is created for two or more response variables"
}
#######################################################################
############## The temporal stability of optimized_return #############
#######################################################################
dataset = data.frame(optimized_return = dataf[,1], proxy = response)
empty_list = list()
empty_list_period = list()
empty_list_significance = list()
temporal_stability <- data.frame()
# 1. Progressive stability check
if (temporal_stability_check == "progressive"){
foldi <- seq(1:k)
#foldi <- paste("fold_", foldi)
folds <- cut(seq(1, nrow(dataset)), breaks = k, labels = FALSE)
for (m in 1:k){
#Segement your data by fold using the which() function
trainIndexes <- which(folds <= m, arr.ind = TRUE)
dataset_temp <- dataset[trainIndexes, ]
MAKS <- max(as.numeric(row.names(dataset_temp)))
MIN <- min(as.numeric(row.names(dataset_temp)))
empty_list_period[[m]] <- paste(MIN, "-", MAKS)
if (method == "cor"){
calculation <- cor(dataset_temp[,1], dataset_temp[,2], method = cor_method, use = cor_na_use)
sig <- cor.test(dataset_temp[,1], dataset_temp[,2], method = cor_method, exact=F)$p.value
empty_list_significance[[m]] <- sig
empty_list[[m]] <- calculation
colname = "correlation"
} else if (method == "lm" & metric == "r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
colname = "r.squared"
empty_list[[m]] <- summary(MLR)$r.squared
empty_list_significance[[m]] <- NA
} else if (method == "lm" & metric == "adj.r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
empty_list[[m]] <- summary(MLR)$adj.r.squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else if (method == "brnn" & metric == "r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
empty_list[[m]] <- r_squared
empty_list_significance[[m]] <- NA
colname = "r.squared"
} else {
empty_list[[m]] <- NA
colname = "r.squared"
empty_list_significance[[m]] <- NA
}
} else if (method == "brnn" & metric == "adj.r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
adj_r_squared <- 1 - ((1 - r_squared) * ((nrow(dataset_temp) - 1)) /
(nrow(dataset_temp) - ncol(as.data.frame(response[, 1])) - 1))
empty_list[[m]] <- adj_r_squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else {
empty_list[[m]] <- NA
colname = "adj.r.squared"
}
}
}
m1 <- do.call(rbind, empty_list)
m2 <- do.call(rbind, empty_list_period)
m3 <- do.call(rbind, empty_list_significance)
temporal_stability <- data.frame(cbind(m2, format(round(m1, 3), nsmall = 3), format(round(m3, 4), nsmall = 3)))
colnames(temporal_stability) <-c("Period", colname, "p value")
temporal_stability
}
# 2. Sequential stability check
if (temporal_stability_check == "sequential"){
foldi <- seq(1:k)
#foldi <- paste("fold_", foldi)
folds <- cut(seq(1, nrow(dataset)), breaks = k, labels = FALSE)
for (m in 1:k){
#Segement your data by fold using the which() function
trainIndexes <- which(folds == m, arr.ind = TRUE)
dataset_temp <- dataset[trainIndexes, ]
MAKS <- max(as.numeric(row.names(dataset_temp)))
MIN <- min(as.numeric(row.names(dataset_temp)))
empty_list_period[[m]] <- paste(MIN, "-", MAKS)
if (method == "cor"){
calculation <- cor(dataset_temp[,1], dataset_temp[,2], method = cor_method, use = cor_na_use)
sig <- cor.test(dataset_temp[,1], dataset_temp[,2], method = cor_method, exact=F)$p.value
empty_list[[m]] <- calculation
empty_list_significance[[m]] <- sig
colname = "correlation"
} else if (method == "lm" & metric == "r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
colname = "r.squared"
empty_list[[m]] <- summary(MLR)$r.squared
empty_list_significance[[m]] <- NA
} else if (method == "lm" & metric == "adj.r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
empty_list[[m]] <- summary(MLR)$adj.r.squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else if (method == "brnn" & metric == "r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
empty_list[[m]] <- r_squared
empty_list_significance[[m]] <- NA
colname = "r.squared"
} else {
empty_list[[m]] <- NA
colname = "r.squared"
empty_list_significance[[m]] <- NA
}
} else if (method == "brnn" & metric == "adj.r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
adj_r_squared <- 1 - ((1 - r_squared) * ((nrow(dataset_temp) - 1)) /
(nrow(dataset_temp) - ncol(as.data.frame(response[, 1])) - 1))
empty_list[[m]] <- adj_r_squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else {
empty_list[[m]] <- NA
colname = "adj.r.squared"
empty_list_significance[[m]] <- NA
}
}
}
m1 <- do.call(rbind, empty_list)
m2 <- do.call(rbind, empty_list_period)
m3 <- do.call(rbind, empty_list_significance)
temporal_stability <- data.frame(cbind(m2, format(round(m1, 3), nsmall = 3), format(round(m3, 4), nsmall = 3)))
colnames(temporal_stability) <-c("Period", colname, "p value")
temporal_stability
}
# 3. running_window
if (temporal_stability_check == "running_window"){
k_end <- nrow(dataset)
place_list <- 1
empty_list_datasets <- list()
empty_list_period <- list()
empty_list <- list()
empty_list_significance <- list()
place_list = 1
if (k_end < k_running_window){
stop("k_running_window is less than the number of analysed years. Reduce the argument k_running_window")
}
for (w in 0:(k_end - k_running_window)){
dataset_temp <- dataset[(1+w):(k_running_window + w),]
empty_list_datasets[[place_list]] <- dataset_temp
MAKS <- max(as.numeric(row.names(dataset_temp)))
MIN <- min(as.numeric(row.names(dataset_temp)))
empty_list_period[[place_list]] <- paste(MIN, "-", MAKS)
place_list <- place_list + 1
}
for (m in 1:length(empty_list_datasets)){
dataset_temp <- empty_list_datasets[[m]]
if (method == "cor"){
calculation <- cor(dataset_temp[,1], dataset_temp[,2], method = cor_method, use = cor_na_use)
sig <- cor.test(dataset_temp[,1], dataset_temp[,2], method = cor_method, exact=F)$p.value
empty_list[[m]] <- calculation
empty_list_significance[[m]] <- sig
colname = "correlation"
} else if (method == "lm" & metric == "r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
colname = "r.squared"
empty_list[[m]] <- summary(MLR)$r.squared
empty_list_significance[[m]] <- NA
} else if (method == "lm" & metric == "adj.r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
empty_list[[m]] <- summary(MLR)$adj.r.squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else if (method == "brnn" & metric == "r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
empty_list[[m]] <- r_squared
empty_list_significance[[m]] <- NA
colname = "r.squared"
} else {
empty_list[[m]] <- NA
colname = "r.squared"
empty_list_significance[[m]] <- NA
}
} else if (method == "brnn" & metric == "adj.r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
adj_r_squared <- 1 - ((1 - r_squared) * ((nrow(dataset_temp) - 1)) /
(nrow(dataset_temp) - ncol(as.data.frame(response[, 1])) - 1))
empty_list[[m]] <- adj_r_squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else {
empty_list[[m]] <- NA
colname = "adj.r.squared"
empty_list_significance[[m]] <- NA
}
}
}
m1 <- do.call(rbind, empty_list)
m2 <- do.call(rbind, empty_list_period)
m3 <- do.call(rbind, empty_list_significance)
temporal_stability <- data.frame(cbind(m2, format(round(m1, 3), nsmall = 3), format(round(as.numeric(m3), digits = 3), nsmall = 3)))
colnames(temporal_stability) <-c("Period", colname, "p value")
temporal_stability
}
#########################################################################
################## Out of sample estimates ##############################
#########################################################################
dataset = data.frame(optimized_return =dataf[,1], proxy = response)
empty_list = list()
empty_list_period = list()
if (cross_validation_type == "blocked"){
dataset <- dataset
} else if (cross_validation_type == "randomized"){
dataset <- dataset[sample(nrow(dataset)), ]
} else (stop(paste("The cross_validation_type is not selected correctly! It is ", cross_validation_type,
". It should be 'blocked' or 'randomized'!", sep = "")))
foldi <- seq(1:k)
#foldi <- paste("fold_", foldi)
folds <- cut(seq(1, nrow(dataset)), breaks = k, labels = FALSE)
bl = 1
for (m in 1:k){
#Segement your data by fold using the which() function
testIndexes <- which(folds == m, arr.ind = TRUE)
test <- dataset[testIndexes, ]
train <- dataset[-testIndexes, ]
MAKS <- max(as.numeric(row.names(train)))
MIN <- min(as.numeric(row.names(train)))
empty_list_period[[bl]] <- paste(MIN, "-", MAKS)
bl <- bl + 1
MAKS <- max(as.numeric(row.names(test)))
MIN <- min(as.numeric(row.names(test)))
empty_list_period[[bl]] <- paste(MIN, "-", MAKS)
bl <- bl + 1
if (method == "lm" | method == "cor"){
MLR <- lm(optimized_return ~ ., data = train)
train_predicted <- predict(MLR, train)
test_predicted <- predict(MLR, test)
train_observed <- train[, 1]
test_observed <- test[, 1]
calculations <- calculate_metrics(train_predicted, test_predicted,
train_observed, test_observed, test = test,
formula = optimized_return ~ ., digits = 15)
empty_list[[m]] <- calculations
}
if (method == "brnn"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = train, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
train_predicted <- predict(BRNN, train)
test_predicted <- predict(BRNN, test)
train_observed <- train[, 1]
test_observed <- test[, 1]
calculations <- calculate_metrics(train_predicted, test_predicted,
train_observed, test_observed, digits = 15,
test = test,
formula = optimized_return ~ .)
empty_list[[m]] <- calculations
} else {
empty_list[[m]] <- NA
}
}
}
m1 <- do.call(rbind, empty_list)
# m1 <- m1[, -c(3, 4, 7)]
m2 <- do.call(rbind, empty_list_period)
cross_validation <- cbind(Years = m2, m1)
cross_validation$Period <- c("Calibration", "Validation")
cross_validation$CV <- rep(1:k, each = 2)
row.names(cross_validation) <- NULL
if (cross_validation_type == "blocked"){
cross_validation <- dplyr::select(cross_validation, CV, Period, Years, cor, RMSE, RRSE, d, RE, CE, DE)
}
if (cross_validation_type == "randomized"){
cross_validation <- dplyr::select(cross_validation, CV, Period, cor, RMSE, RRSE, d, RE, CE, DE)
}
################################################################
#### Here the final list is being filled with six elements #####
################################################################
# When metohod == "cor", different final_list is created
if (method == "lm" | method == "brnn") {
final_list <- list(calculations = temporal_matrix, method = method,
metric = metric, analysed_period = analysed_period,
optimized_return = dataf_full,
optimized_return_all = dataf_full_original,
transfer_function = p1, temporal_stability = temporal_stability,
cross_validation = cross_validation,
aggregated_climate = do.call(cbind, list_climate))
}
if (method == "cor"){
final_list <- list(calculations = temporal_matrix, method = method,
metric = cor_method, analysed_period = analysed_period,
optimized_return = dataf_full,
optimized_return_all = dataf_full_original,
transfer_function = p1, temporal_stability = temporal_stability,
cross_validation = cross_validation,
aggregated_climate = do.call(cbind, list_climate))
}
plot_heatmapA <- plot_heatmap(final_list, reference_window = reference_window, type = "daily")
plot_extremeA <- plot_extreme(final_list, ylimits = ylimits, reference_window = reference_window, type = "daily")
width_sequence = seq(lower_limit, upper_limit)
if (is.null(plot_specific_window)){
(plot_specificA <- "plot_specific_window is not available. No plot_specific is made!")
} else if (fixed_width != 0){
if (fixed_width != plot_specific_window){
warning(paste0("plot_specific_window and fixed_width differ!",
" fixed_wdith will be used to generate plot_specific!"))
}
plot_specific_window = fixed_width
plot_specificA <- plot_specific(final_list, window_width = plot_specific_window, ylimits = ylimits,
reference_window = reference_window)
} else if (plot_specific_window %in% width_sequence){
plot_specificA <- plot_specific(final_list, window_width = plot_specific_window, ylimits = ylimits,
reference_window = reference_window)
} else (plot_specificA <- "Selected plot_specific_window is not available. No plot_specific is made!")
# Here, for the sake of simplicity, we create final list again
if (method == "lm" | method == "brnn") {
final_list <- list(calculations = temporal_matrix, method = method,
metric = metric, analysed_period = analysed_period,
optimized_return = dataf_full,
optimized_return_all = dataf_full_original,
transfer_function = p1, temporal_stability = temporal_stability,
cross_validation = cross_validation,
plot_heatmap = plot_heatmapA,
plot_extreme = plot_extremeA,
plot_specific = plot_specificA,
PCA_output = PCA_result,
type = "daily",
reference_window = reference_window,
boot_lower = temporal_matrix_lower,
boot_upper = temporal_matrix_upper,
aggregated_climate = do.call(cbind, list_climate))
}
if (method == "cor"){
final_list <- list(calculations = temporal_matrix, method = method,
metric = cor_method, analysed_period = analysed_period,
optimized_return = dataf_full,
optimized_return_all = dataf_full_original,
transfer_function = p1, temporal_stability = temporal_stability,
cross_validation = cross_validation,
plot_heatmap = plot_heatmapA,
plot_extreme = plot_extremeA,
plot_specific = plot_specificA,
PCA_output = PCA_result,
type = "daily",
reference_window = reference_window,
boot_lower = temporal_matrix_lower,
boot_upper = temporal_matrix_upper,
aggregated_climate = do.call(cbind, list_climate))
}
class(final_list) <- 'dmrs'
return(final_list)
}
}
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Defines functions daily_response
Documented in daily_response
#' daily_response
#'
#' Function calculates all possible values of a selected statistical metric
#' between one or more response variables and daily sequences of environmental
#' data. Calculations are based on moving window which is defined with two
#' arguments: window width and a location in a matrix of daily sequences of
#' environmental data. Window width could be fixed (use fixed_width) or
#' variable width (use lower_limit and upper_limit arguments). In this case,
#' all window widths between lower and upper limit will be used. All calculated
#' metrics are stored in a matrix. The location of stored calculated metric
#' in the matrix is indicating a window width (row names) and a location in a
#' matrix of daily sequences of environmental data (column names).
#'
#' @param response a data frame with tree-ring proxy variables as columns and
#' (optional) years as row names. Row.names should be matched with those from a
#' env_data data frame. If not, set row_names_subset = TRUE.
#' @param env_data a data frame of daily sequences of environmental data as
#' columns and years as row names. Each row represents a year and
#' each column represents a day of a year. Row.names should be matched with
#' those from a response data frame. If not, set row_names_subset = TRUE.
#' Alternatively, env_data could be a tidy data with three columns,
#' i.e. Year, DOY and third column representing values of mean temperatures,
#' sum of precipitation etc. If tidy data is passed to the function, set the argument
#' tidy_env_data to TRUE.
#' @param method a character string specifying which method to use. Current
#' possibilities are "cor" (default), "lm" and "brnn".
#' @param cor_method a character string indicating which correlation
#' coefficient is to be computed. One of "pearson" (default), "kendall", or
#' "spearman".
#' @param metric a character string specifying which metric to use. Current
#' possibilities are "r.squared" and "adj.r.squared". If method = "cor",
#' metric is not relevant.
#' @param lower_limit lower limit of window width
#' @param upper_limit upper limit of window width
#' @param fixed_width fixed width used for calculation. If fixed_width is
#' assigned a value, upper_limit and lower_limit will be ignored
#' @param previous_year if set to TRUE, env_data and response variables will be
#' rearranged in a way, that also previous year will be used for calculations of
#' selected statistical metric.
#' @param neurons positive integer that indicates the number of neurons used
#' for brnn method
#' @param brnn_smooth if set to TRUE, a smoothing algorithm is applied that
#' removes unrealistic calculations which are a result of neural net failure.
#' @param remove_insignificant if set to TRUE, removes all correlations bellow
#' the significant threshold level, based on a selected alpha. For "lm" and
#' "brnn" method, squared correlation is used as a threshold
#' @param alpha significance level used to remove insignificant calculations.
#' @param row_names_subset if set to TRUE, row.names are used to subset
#' env_data and response data frames. Only years from both data frames are
#' kept.
#' @param PCA_transformation if set to TRUE, all variables in the response
#' data frame will be transformed using PCA transformation.
#' @param log_preprocess if set to TRUE, variables will be transformed with
#' logarithmic transformation before used in PCA
#' @param components_selection character string specifying how to select the Principal
#' Components used as predictors.
#' There are three options: "automatic", "manual" and "plot_selection". If
#' argument is set to automatic, all scores with eigenvalues above 1 will be
#' selected. This threshold could be changed by changing the
#' eigenvalues_threshold argument. If parameter is set to "manual", user should
#' set the number of components with N_components argument. If components
#' selection is set to "plot_selection", Scree plot will be shown and a user must
#' manually enter the number of components to be used as predictors.
#' @param eigenvalues_threshold threshold for automatic selection of Principal Components
#' @param N_components number of Principal Components used as predictors
#' @param aggregate_function character string specifying how the daily data
#' should be aggregated. The default is 'mean', the other options are 'median',
#' 'sum', 'min' and 'max'
#' @param temporal_stability_check character string, specifying, how temporal stability
#' between the optimal selection and response variable(s) will be analysed. Current
#' possibilities are "sequential", "progressive" and "running_window". Sequential check
#' will split data into k splits and calculate selected metric for each split. Progressive
#' check will split data into k splits, calculate metric for the first split and then
#' progressively add 1 split at a time and calculate selected metric. For running window,
#' select the length of running window with the k_running_window argument.
#' @param k_running_window the length of running window for temporal stability check.
#' Applicable only if temporal_stability argument is set to running window.
#' @param k integer, number of breaks (splits) for temporal stability and cross validation
#' analysis.
#' @param cross_validation_type character string, specifying, how to perform cross validation
#' between the optimal selection and response variables. If the argument is set to "blocked",
#' years will not be shuffled. If the argument is set to "randomized", years will be shuffled.
#' @param subset_years a subset of years to be analyzed. Should be given in the form of
#' subset_years = c(1980, 2005)
#' @param plot_specific_window integer representing window width to be displayed
#' for plot_specific
#' @param ylimits limit of the y axes for plot_extreme and plot_specific. It should be
#' given in the form of: ylimits = c(0,1)
#' @param seed optional seed argument for reproducible results
#' @param tidy_env_data if set to TRUE, env_data should be inserted as a data frame with three
#' columns: "Year", "DOY", "Precipitation/Temperature/etc."
#' @param reference_window character string, the reference_window argument describes,
#' how each calculation is referred. There are three different options: 'start'
#' (default), 'end' and 'middle'. If the reference_window argument is set to 'start',
#' then each calculation is related to the starting day of window. If the
#' reference_window argument is set to 'middle', each calculation is related to the
#' middle day of window calculation. If the reference_window argument is set to
#' 'end', then each calculation is related to the ending day of window calculation.
#' For example, if we consider correlations with window from DOY 15 to DOY 35. If
#' reference window is set to 'start', then this calculation will be related to the
#' DOY 15. If the reference window is set to 'end', then this calculation will be
#' related to the DOY 35. If the reference_window is set to 'middle', then this
#' calculation is related to DOY 25.
#' The optimal selection, which describes the optimal consecutive days that returns
#' the highest calculated metric and is obtained by the $plot_extreme output, is the
#' same for all three reference windows.
#' @param boot logical, if TRUE, bootstrap procedure will be used to calculate
#' estimates correlation coefficients, R squared or adjusted R squared metrices
#' @param boot_n The number of bootstrap replicates
#' @param boot_ci_type A character string representing the type of bootstrap intervals
#' required. The value should be any subset of the values c("norm","basic", "stud",
#' "perc", "bca").
#' @param boot_conf_int A scalar or vector containing the confidence level(s) of
#' the required interval(s)
#' @param day_interval a vector of two values: lower and upper time interval of
#' days that will be used to calculate statistical metrics. Negative values indicate
#' previous growing season days. This argument overwrites the calculation
#' limits defined by lower_limit and upper_limit arguments.
#' @param dc_method a character string to determine the method to detrend climate
#' (environmental) data. Possible values are c("Spline", "ModNegExp", "Mean",
#' "Friedman", "ModHugershoff"). Defaults to "none" (see dplR R package).
#' @param dc_nyrs a number giving the rigidity of the smoothing spline, defaults
#' to 0.67 of series length if nyrs is NULL (see dplR R package).
#' @param dc_f a number between 0 and 1 giving the frequency response or wavelength
#' cutoff. Defaults to 0.5 (see dplR R package).
#' @param dc_pos.slope a logical flag. Will allow for a positive slope to be used
#' in method "ModNegExp" and "ModHugershoff". If FALSE the line will be horizontal
#' (see dplR R package).
#' @param dc_constrain.nls a character string which controls the constraints of
#' the "ModNegExp" model and the "ModHugershoff" (see dplR R package).
#' @param dc_span a numeric value controlling method "Friedman", or "cv" (default)
#' for automatic choice by cross-validation (see dplR R package).
#' @param dc_bass a numeric value controlling the smoothness of the fitted curve
#' in method "Friedman" (see dplR R package).
#' @param dc_difference a logical flag. Compute residuals by subtraction if TRUE,
#' otherwise use division (see dplR R package).
#' @param cor_na_use an optional character string giving a method for computing
#' covariances in the presence of missing values for correlation coefficients.
#' This must be (an abbreviation of) one of the strings "everything" (default),
#' "all.obs", "complete.obs", "na.or.complete", or "pairwise.complete.obs". See
#' also the documentation for the base cor() function.
#'
#' @return a list with 17 elements:
#' \enumerate{
#' \item $calculations - a matrix with calculated metrics
#' \item $method - the character string of a method
#' \item $metric - the character string indicating the metric used for calculations
#' \item $analysed_period - the character string specifying the analysed period based on the information from row names. If there are no row names, this argument is given as NA
#' \item $optimized_return - data frame with two columns, response variable and aggregated (averaged) daily data that return the optimal results. This data.frame could be directly used to calibrate a model for climate reconstruction
#' \item $optimized_return_all - a data frame with aggregated daily data, that returned the optimal result for the entire env_data (and not only subset of analysed years)
#' \item $transfer_function - a ggplot object: scatter plot of optimized return and a transfer line of the selected method
#' \item $temporal_stability - a data frame with calculations of selected metric for different temporal subsets
#' \item $cross_validation - a data frame with cross validation results
#' \item $plot_heatmap - ggplot2 object: a heatmap of calculated metrics
#' \item $plot_extreme - ggplot2 object: line plot of a row with the highest value in a matrix of calculated metrics
#' \item $plot_specific - ggplot2 object: line plot of a row with a selected window width in a matrix of calculated metrics
#' \item $PCA_output - princomp object: the result output of the PCA analysis
#' \item $type - the character string describing type of analysis: daily or monthly
#' \item $reference_window - character string, which reference window was used for calculations
#' \item $boot_lower - matrix with lower limit of confidence intervals of bootstrap calculations
#' \item $boot_upper - matrix with upper limit of confidence intervals of bootstrap calculations
#' \item $aggregated_climate - matrix with all aggregated climate series
#'}
#' @export
#'
#' @examples
#' \donttest{
#' # Load the dendroTools R package
#' library(dendroTools)
#'
#' # Load data
#' data(data_MVA)
#' data(data_TRW)
#' data(data_TRW_1)
#' data(example_proxies_individual)
#' data(example_proxies_1)
#' data(LJ_daily_temperatures)
#'
#' # 1 Example with fixed width. Lower and upper limits are ignored.
#' example_daily_response <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures,
#' method = "cor", fixed_width = 40, cor_method = "spearman",
#' row_names_subset = TRUE, previous_year = TRUE,
#' remove_insignificant = TRUE,
#' alpha = 0.0000000000000005, aggregate_function = 'mean',
#' reference_window = "start")
#'
#' summary(example_daily_response)
#' plot(example_daily_response, type = 1)
#' plot(example_daily_response, type = 2)
#'
#' # 2 Example for past and present. Use subset_years argument.
#' example_MVA_early <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures, cor_method = "kendall",
#' method = "cor", lower_limit = 21, upper_limit = 90,
#' row_names_subset = TRUE, previous_year = TRUE,
#' remove_insignificant = TRUE, alpha = 0.05,
#' plot_specific_window = 60, subset_years = c(1940, 1980),
#' aggregate_function = 'sum')
#'
#' example_MVA_late <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures,
#' method = "cor", lower_limit = 21, upper_limit = 60,
#' row_names_subset = TRUE, previous_year = TRUE,
#' remove_insignificant = TRUE, alpha = 0.05,
#' plot_specific_window = 60, subset_years = c(1981, 2010),
#' aggregate_function = 'sum')
#'
#' plot(example_MVA_early, type = 1)
#' plot(example_MVA_late, type = 1)
#' plot(example_MVA_early, type = 2)
#' plot(example_MVA_late, type = 2)
#'
#' # 3 Example PCA
#' example_PCA <- daily_response(response = example_proxies_individual,
#' env_data = LJ_daily_temperatures, method = "lm",
#' lower_limit = 21, upper_limit = 180,
#' row_names_subset = TRUE, remove_insignificant = TRUE,
#' alpha = 0.01, PCA_transformation = TRUE,
#' components_selection = "manual", N_components = 2)
#'
#' summary(example_PCA$PCA_output)
#' summary(example_PCA)
#' plot(example_PCA, type = 2)
#'
#' # 4 Example negative correlations
#' example_neg_cor <- daily_response(response = data_TRW_1,
#' env_data = LJ_daily_temperatures, previous_year = TRUE,
#' method = "cor", lower_limit = 21, upper_limit = 90,
#' row_names_subset = TRUE, remove_insignificant = TRUE,
#' alpha = 0.05)
#'
#' summary(example_neg_cor)
#' plot(example_neg_cor, type = 1)
#' plot(example_neg_cor, type = 2)
#' example_neg_cor$temporal_stability
#'
#' # 5 Example of multiproxy analysis
#' summary(example_proxies_1)
#' cor(example_proxies_1)
#'
#' example_multiproxy <- daily_response(response = example_proxies_1,
#' env_data = LJ_daily_temperatures,
#' method = "lm", metric = "adj.r.squared",
#' lower_limit = 21, upper_limit = 180,
#' row_names_subset = TRUE, previous_year = FALSE,
#' remove_insignificant = TRUE, alpha = 0.05)
#'
#' plot(example_multiproxy, type = 1)
#'
#' # 6 Example to test the temporal stability
#' example_MVA_ts <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures, method = "brnn",
#' lower_limit = 100, metric = "adj.r.squared", upper_limit = 180,
#' row_names_subset = TRUE, remove_insignificant = TRUE, alpha = 0.05,
#' temporal_stability_check = "running_window", k_running_window = 10)
#'
#' example_MVA_ts$temporal_stability
#'
#' # 7 Example with nonlinear brnn estimation
#' example_brnn <- daily_response(response = data_MVA,
#' env_data = LJ_daily_temperatures, method = "brnn", boot = FALSE,
#' lower_limit = 100, metric = "adj.r.squared", upper_limit = 101,
#' row_names_subset = TRUE, remove_insignificant = TRUE, boot_n = 10)
#'
#' summary(example_brnn)
#' }
daily_response <- function(response, env_data, method = "cor",
metric = "r.squared", cor_method = "pearson",
lower_limit = 30, upper_limit = 90, fixed_width = 0,
previous_year = FALSE, neurons = 1,
brnn_smooth = TRUE, remove_insignificant = FALSE,
alpha = .05, row_names_subset = FALSE,
PCA_transformation = FALSE, log_preprocess = TRUE,
components_selection = 'automatic',
eigenvalues_threshold = 1,
N_components = 2, aggregate_function = 'mean',
temporal_stability_check = "sequential", k = 2,
k_running_window = 30, cross_validation_type = "blocked",
subset_years = NULL, plot_specific_window = NULL,
ylimits = NULL, seed = NULL, tidy_env_data = FALSE,
reference_window = 'start', boot = FALSE, boot_n = 1000,
boot_ci_type = "norm", boot_conf_int = 0.95,
day_interval = ifelse(c(previous_year == TRUE,
previous_year == TRUE),
c(-1, 366), c(1, 366)),
dc_method = NULL,
dc_nyrs = NULL,
dc_f = 0.5,
dc_pos.slope = FALSE,
dc_constrain.nls = c("never", "when.fail", "always"),
dc_span = "cv",
dc_bass = 0,
dc_difference = FALSE,
cor_na_use = "everything"
) {
##############################################################################
# 1 day interval is organized
offset_start <- day_interval[1]
offset_end <- day_interval[2]
# if both are positive but previous_year = TRUE
if (offset_start > 0 & offset_end > 0 & previous_year == TRUE){
previous_year <- FALSE
warning(paste0("Previous year is not included in selected day_interval. ",
"The argument previous_year is set to FALSE"))
}
# if both are negative negative
if (offset_start < 0 & offset_end < 0){
offset_start <- abs(offset_start)
offset_end <- abs(offset_end)
# If previous_year is FALSE, we set it to TRUE
if (previous_year == FALSE){
previous_year = TRUE
warning(paste0("Previous year is included in day_interval. ",
"The argument previous_year is set to TRUE"))
}
# if only offset_start is negative
} else if (offset_start < 0 & offset_end > 0){
offset_end <- offset_end + 366
offset_start <- abs(offset_start)
# If previous_year is FALSE, we set it to TRUE
if (previous_year == FALSE){
previous_year = TRUE
warning(paste0("Previous year is included in day_interval. ",
"The argument previous_year is set to TRUE"))
}
}
# Calculate the max_window allowed
max_window <- offset_end - offset_start + 1
# If max_window is greater then upper_limit, it must be reduced
if (upper_limit > max_window){
upper_limit <- max_window
if (fixed_width == 0){
warning(paste0("The upper_limit is outside your day_interval and",
" therefore reduced to the maximum allowed: ",max_window,"."))
}
}
# Now, if upper_limit > max_window, we make them the same
if (lower_limit > max_window){
lower_limit <- max_window
if (fixed_width == 0){
warning(paste0("The lower_limit is outside your day_interval and",
" therefore reduced to the minimum allowed: ",max_window,"."))
}
}
# Also correction for fixed_window approach
if (fixed_width > max_window){
stop(paste0("The selected fixed_width is outside your day_interval.",
" Decrease the fixed_width argument to at least: ",max_window,"."))
}
if (previous_year == FALSE){
offset_end <- 366 - offset_end
} else {
offset_end <- 732 - offset_end
}
##############################################################################
if (fixed_width != 0){
lower_limit = 30
upper_limit = 200
}
if (!is.null(seed)) {
set.seed(seed)
}
# Defining global variables
median <- NULL
proxy <- NULL
optimized_return <- NULL
transfer_f <- NULL
journal_theme <- NULL
CV <- NULL
Period <- NULL
Years <- NULL
yearABC <- NULL
RMSE <- NULL
RE <- NULL
CE <- NULL
DE <- NULL
d <- NULL
temporal_matrix_lower <- NULL
temporal_matrix_upper <- NULL
# If there is a column name samp.depth in response data frame, warning is given
if ("samp.depth" %in% colnames(response)){
samp.depth_index <- grep("samp.depth", colnames(response))
response <- response[, -samp.depth_index,F]
warning("Removed the samp.depth from response data frame")
}
# If there is more than 2 columns in response data frame, give a warning
if (ncol(response) > 1){
warning(paste0("Your response data frame has more than 1 column! Are you doing a multiproxy research?",
" If so, OK. If not, check your response data frame!"))
}
# If env_data is given in tidy version, transformation is needed
if (tidy_env_data == TRUE){
n_col_tidy_DF <- ncol(env_data)
colnames_tidy_DF <- colnames(env_data)
if (ncol(env_data) != 3){
stop(paste("env_data was inserted in tidy version (tidy_env_data is set to TRUE).",
"env_data should have 3 columns, but it has", n_col_tidy_DF, "instead!"))
}
if (colnames_tidy_DF[1] != "Year"){
stop(paste("env_data was inserted in tidy version (tidy_env_data is set to TRUE).",
"The first column name of the env_data should be 'Year', but it is",
colnames_tidy_DF[1], "instead!"))
}
if (colnames_tidy_DF[2] != "DOY"){
stop(paste("env_data was inserted in tidy version (tidy_env_data is set to TRUE).",
"The second column name of the env_data should be 'DOY', but it is",
colnames_tidy_DF[2], "instead!"))
}
value_variable = colnames(env_data)[3]
env_data <- dcast(env_data, Year~DOY, value.var = value_variable)
env_data <- years_to_rownames(env_data, "Year")
}
# PART 1 - general data arrangements, warnings and stops
# Both bojects (response and env_data) are converted to data frames
response <- data.frame(response)
env_data <- data.frame(env_data)
# Here we save the original env and response data that will be used later
response_original <- response
env_data_original <- env_data
# For metric calculations, both objects need to have the same length,
# with the exception, when row_names_subset is set to TRUE
# Stop message in case both data frames do not have the same length
if (nrow(response) != nrow(env_data) & row_names_subset == FALSE)
stop("Length of env_data and response records differ")
# Stop in case of method == "cor" and ncol(proxies) > 1
# Correlations could be calculated only for one variable
if (method == "cor" & ncol(response) > 1)
stop(paste("More than 1 variable in response data frame not suitable ",
"for 'cor' method. Use 'lm' or 'brnn'"))
#######################################################
# Rules for previous_year = FALSE
if (previous_year == FALSE){
# Stop message if fixed_width is not between 0 and 366
if (fixed_width < 0 | fixed_width > 366)
stop("fixed_width should be between 1 and 366")
if (lower_limit > upper_limit)
stop("lower_limit can not be higher than upper_limit!")
if (lower_limit > 366 | lower_limit < 1)
stop("lower_limit out of bounds! It should be between 1 and 366")
if (upper_limit > 366 | upper_limit < 1)
stop("upper_limit out of bounds! It should be between 1 and 366")
# Rules for previous_year = TRUE
} else if (previous_year == TRUE){
# Stop message if fixed_width is not between 0 and 366
if (fixed_width < 0 | fixed_width > 732)
stop("fixed_width should be between 1 and 732")
if (lower_limit > upper_limit)
stop("lower_limit can not be higher than upper_limit!")
if (lower_limit > 732 | lower_limit < 1)
stop("lower_limit out of bounds! It should be between 1 and 366")
if (upper_limit > 732 | upper_limit < 1)
stop("upper_limit out of bounds! It should be between 1 and 366")
}
# Make sure the selected method is appropriate
if (!is.null(dc_method)){
if (!(dc_method %in% c("Spline", "ModNegExp", "Mean", "Friedman", "ModHugershoff"))){
stop(paste0('dc_method should be one of "Spline", "ModNegExp", "Mean", "Friedman", "ModHugershoff",
but instead it is:',dc_method))
}
}
# Warn users in case of missing values (selected threshold is 270 days)
env_temp <- env_data[row.names(env_data) %in% row.names(response),]
# Subset of years
if (!is.null(subset_years)){
lower_subset <- subset_years[1]
upper_subset <- subset_years[2]
subset_seq <- seq(lower_subset, upper_subset)
env_temp <- subset(env_temp, row.names(env_temp) %in% subset_seq)
}
na_problem <- data.frame(na_sum = rowSums(is.na(env_temp)))
na_problem <- na_problem[na_problem$na_sum > 270, , F]
problematic_years <- paste0(row.names(na_problem), sep = "", collapse=", ")
if (nrow(na_problem) > 0){
warning(paste0("Problematic years with missing values are present: ", problematic_years))
}
# Data manipulation
# If use.previous == TRUE, env_data data has to be rearranged accordingly
if (previous_year == TRUE) {
# FIRST, both data frames need to be arranged, the most recent year is the first one
env_data$yearABC <- row.names(env_data)
env_data <- dplyr::arrange(env_data, desc(yearABC))
env_data <- years_to_rownames(env_data, "yearABC")
env_data_previous <- env_data[-1, , F]
env_data_current <- env_data[-nrow(env_data), ,F]
row_names_current <- row.names(env_data_current)
env_data <- cbind(env_data_previous, env_data_current)
env_data <- data.frame(env_data)
row.names(env_data) <- row_names_current
env_data_original <- env_data
# response$yearABC <- row.names(response)
# response <- dplyr::arrange(response, desc(yearABC))
# response <- years_to_rownames(response, "yearABC")
# response <- data.frame(response[-nrow(response),,F ])
# response <- data.frame(response)
# response_original <- response
}
# If row_names_subset == TRUE, data is subseted and ordered based on matching
# row.names. Additionally, number of characters in row.names is checked.
# There should be at least three characters (assuming years before 100 will
# never be analysed, there is no such environmental data available)
if (row_names_subset == TRUE & nchar(row.names(env_data)[1]) >= 3){
ncol_response <- ncol(response)
colnames_response <- colnames(response)
env_data$yearABC <- row.names(env_data)
response$yearABC <- row.names(response)
temporal_data <- merge(response, env_data, by = "yearABC")
response <- data.frame(temporal_data[, c(2:(1 + ncol_response))],
row.names = temporal_data$yearABC)
colnames(response) <- colnames_response
env_data <- data.frame(temporal_data[, c((1 + ncol_response + 1):
ncol(temporal_data))],
row.names = temporal_data$yearABC)
}
# if row.names of env_data and the response data frames are not equal,
# warning is given.
if (sum(row.names(env_data) == row.names(response)) != nrow(env_data)) {
warning("row.names between env_data and response do not match!")
}
# If row_names_subset == TRUE, but row.names does not appear to be years,
# error is given.
if (row_names_subset == TRUE & nchar(row.names(env_data)[1]) < 3){
stop(paste("row.names does not appear to be years!",
"At least three characters needed!"))
}
# If PCA_transformation = TRUE, PCA is performed
if (PCA_transformation == TRUE) {
# Logarithmic transformation before PCA
if (log_preprocess == TRUE) {
if (sum(response <= 0) > 1){
stop("your response data contains negative observations. Please set the argument log_preprocess to FALSE")
}
response <- data.frame(log(response))
}
PCA_result <- princomp(response, cor = TRUE)
if (components_selection == 'automatic'){
subset_vector <- PCA_result$sdev > eigenvalues_threshold
response <- as.data.frame(PCA_result$scores[, subset_vector])
}
if (components_selection == 'manual'){
response <- as.data.frame(PCA_result$scores[, 1:N_components])
}
if (components_selection == 'plot_selection'){
plot(PCA_result, type = 'l')
fun <- function(){
N_PC <- readline("What number of PC scores should be used as predictors? ")
return(N_PC)
}
N_PC <- fun()
response <- as.data.frame(PCA_result$scores[, 1:as.numeric(N_PC)])
}
number_PC <- ncol(response)
df_names <- paste( "PC_", seq(1:number_PC), sep = "")
colnames(response) <- df_names
} else (PCA_result <- "No PCA result avalialbe !")
# Subset of years
if (!is.null(subset_years)){
lower_subset <- subset_years[1]
upper_subset <- subset_years[2]
if (lower_subset > upper_subset){
stop("Change the order of elements in the subset_years argument! First element should be lower than the second!")
}
subset_seq <- seq(lower_subset, upper_subset)
if (any(!(subset_seq %in% row.names(response)))){
stop(paste0("Undefined columns selected. Subset years don't exist",
" in the response data frame. Change the subset_years argument"))
}
if (any(!(subset_seq %in% row.names(env_data)))){
stop(paste0("Undefined columns selected. Subset years don't exist",
" in the env_data data frame. Change the subset_years argument"))
}
response <- subset(response, row.names(response) %in% subset_seq)
env_data <- subset(env_data, row.names(env_data) %in% subset_seq)
}
# NA values are not allowed and must be removed from response data.frame
if (sum(is.na(response)) > 0){
prob_year <- row.names(response[is.na(response), , drop = F])
stop(paste0("NA is not allowed in response data frame. ",
"Problematic year is ", prob_year))
}
# PART 2 - Based on the selected function arguments, different chunks of code
# will be used. For demonstration:
# A) Chunks are used if fixed.withd != 0
# A.1 method == "cor"
# A.2 method == "lm"
# A.3 method == "brnn"
# B) Chunks are used if fixed.withd == 0
# B.1 method == "cor"
# B.2 method == "lm"
# B.3 method == "brnn"
# this is a list for climate and and holder for saving mm
list_climate <- list()
mm <- 1
# A.1 method = "cor"
if (fixed_width != 0 & method == "cor") {
# This is an empty matrix, currently filled with NA's
# Latter, calculations will be stored in this matrix
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = 1,
ncol = (ncol(env_data) - fixed_width) + 1)
} else if (reference_window == 'end') {
temporal_matrix <- matrix(NA, nrow = 1, ncol = (ncol(env_data)))
} else if (reference_window == 'middle') {
temporal_matrix <- matrix(NA, nrow = 1,
ncol = round2((ncol(env_data) - fixed_width +
1 + fixed_width/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (fixed_width != max_window){
pb <- txtProgressBar(min = 0, max = (ncol(env_data) - fixed_width - offset_end - offset_start + 1),
style = 3)
}
b = 0
# An iterating loop. In each itteration x is calculated and represents
# response (dependent) variable. X is a moving average. Window width of
# a moving window is fixed_width. Next, statistical metric is calculated
# based on a selected method (cor, lm or brnn). Calculation is stored in
# temporal matrix.
for (j in (0 + offset_start -1): (ncol(env_data) - max((fixed_width + offset_end), offset_end))) {
b = b + 1
if (aggregate_function == 'median'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , median, na.rm = TRUE)
}
} else if (aggregate_function == 'sum'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , sum, na.rm = TRUE)
}
} else if (aggregate_function == 'mean'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- rowMeans(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]), na.rm = TRUE)
}
} else if (aggregate_function == 'min'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , min, na.rm = TRUE) }
} else if (aggregate_function == 'max'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , max, na.rm = TRUE)
}
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + fixed_width)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_correlation <- cor(response[, 1], x[, 1], method = cor_method)
temporal_lower <- NA
temporal_upper <- NA
} else if (boot == TRUE){
temp_df_boot <- cbind(response[, 1], x[, 1])
calc <- boot(temp_df_boot, boot_f_cor, cor.type = cor_method, R = boot_n)
temporal_correlation <- colMeans(calc$t)[1]
ci_int <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type), silent = TRUE)
if (class(ci_int)[[1]] == "try-error"){
temporal_lower <- NA
temporal_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_lower <- ci_int$norm[2]
temporal_upper <- ci_int$norm[3]
} else if (boot_ci_type == "perc"){
temporal_lower <- ci_int$perc[4]
temporal_upper <- ci_int$perc[5]
} else if (boot_ci_type == "stud") {
temporal_lower <- ci_int$student[4]
temporal_upper <- ci_int$student[5]
} else if (boot_ci_type == "basic") {
temporal_lower <- ci_int$basic[4]
temporal_upper <- ci_int$basic[5]
} else if (boot_ci_type == "bca") {
temporal_lower <- ci_int$bca[4]
temporal_upper <- ci_int$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
print(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
# Each calculation is printed. Reason: usually it takes several minutes
# to go through all loops and therefore, users might think that R is
# not responding. But if each calculation is printed, user could be
# confident, that R is responding.
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_correlation
temporal_matrix_lower[1, j + 1] <- temporal_lower
temporal_matrix_upper[1, j + 1] <- temporal_upper
} else if (reference_window == 'end'){
temporal_matrix[1, j + fixed_width] <- temporal_correlation
temporal_matrix_lower[1, j + fixed_width] <- temporal_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_correlation
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_upper
}
if (fixed_width != max_window){setTxtProgressBar(pb, b)}
}
if (fixed_width != max_window){close(pb)}
# temporal_matrix is given rownames and colnames. Rownames represent a
# window width used fot calculations. Colnames represent the position of
# moving window in a original env_data data frame.
row.names(temporal_matrix) <- fixed_width
row.names(temporal_matrix_lower) <- fixed_width
row.names(temporal_matrix_upper) <- fixed_width
temporal_colnames <- as.vector(seq(from = 1,
to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# A.2 method == "lm"
# For a description see A.1
if (fixed_width != 0 & method == "lm") {
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = 1,
ncol = (ncol(env_data) - fixed_width) + 1)
} else if (reference_window == 'end') {
temporal_matrix <- matrix(NA, nrow = 1, ncol = (ncol(env_data)))
} else if (reference_window == 'middle') {
temporal_matrix <- matrix(NA, nrow = 1,
ncol = round2((ncol(env_data) - fixed_width +
1 + fixed_width/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (fixed_width != max_window){
pb <- txtProgressBar(min = 0, max = (ncol(env_data) - fixed_width - offset_end - offset_start + 1),
style = 3)}
b = 0
for (j in (0 + offset_start -1): (ncol(env_data) - max((fixed_width + offset_end), offset_end))) {
b = b + 1
if (aggregate_function == 'median'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(env_data[1:nrow(env_data),
(1 + j) : (j + fixed_width)],1 , median, na.rm = TRUE)
}
} else if (aggregate_function == 'sum'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j) : (j + fixed_width)]
} else {
x <- apply(env_data[1:nrow(env_data),
(1 + j) : (j + fixed_width)],1 , median, na.rm = TRUE)
}
} else if (aggregate_function == 'mean'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- rowMeans(env_data[1:nrow(env_data),
(1 + j) : (j + fixed_width)], na.rm = TRUE)
}
} else if (aggregate_function == 'min'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j) : (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j) : (j + fixed_width)]),1 , min, na.rm = TRUE) }
} else if (aggregate_function == 'max'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , max, na.rm = TRUE)
}
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + fixed_width)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_df <- data.frame(cbind(x, response))
temporal_model <- lm(x ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
temporal_r_squared <- temporal_summary$r.squared
temporal_adj_r_squared <- temporal_summary$adj.r.squared
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else if (boot == TRUE){
temporal_df <- data.frame(cbind(x, response))
calc <- boot(data = temporal_df, statistic = boot_f_lm, R = boot_n, lm.formula = "x ~ .")
temporal_r_squared <- colMeans(calc$t)[1]
temporal_adj_r_squared <- colMeans(calc$t)[2]
ci_int_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 1), silent = TRUE)
ci_int_adj_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 2), silent = TRUE)
if (class(ci_int_r_squared)[[1]] == "try-error"){
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_r_squared_lower <- ci_int_r_squared$norm[2]
temporal_r_squared_upper <- ci_int_r_squared$norm[3]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$norm[2]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$norm[3]
} else if (boot_ci_type == "perc"){
temporal_r_squared_lower <- ci_int_r_squared$perc[4]
temporal_r_squared_upper <- ci_int_r_squared$perc[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$perc[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$perc[5]
} else if (boot_ci_type == "stud") {
temporal_r_squared_lower <- ci_int_r_squared$studen[4]
temporal_r_squared_upper <- ci_int_r_squared$studen[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$studen[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$studen[5]
} else if (boot_ci_type == "basic") {
temporal_r_squared_lower <- ci_int_r_squared$basic[4]
temporal_r_squared_upper <- ci_int_r_squared$basic[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$basic[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$basic[5]
} else if (boot_ci_type == "bca") {
temporal_r_squared_lower <- ci_int_r_squared$bca[4]
temporal_r_squared_upper <- ci_int_r_squared$bca[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$bca[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
stop(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (metric == "r.squared"){
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_r_squared
temporal_matrix_lower[1, j + 1] <- temporal_r_squared_lower
temporal_matrix_upper[1, j + 1] <- temporal_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[1, j + fixed_width] <- temporal_r_squared
temporal_matrix_lower[1, j + fixed_width] <- temporal_r_squared_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared_upper
}
}
if (metric == "adj.r.squared"){
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_adj_r_squared
temporal_matrix_lower[1, j + 1] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, j + 1] <- temporal_adj_r_squared_upper
} else if (reference_window == 'end'){
temporal_matrix[1, j + fixed_width] <- temporal_adj_r_squared
temporal_matrix_lower[1, j + fixed_width] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_adj_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared_upper
}
}
if (fixed_width != max_window){setTxtProgressBar(pb, b)}
}
if (fixed_width != max_window){close(pb)}
row.names(temporal_matrix) <- fixed_width
row.names(temporal_matrix_lower) <- fixed_width
row.names(temporal_matrix_upper) <- fixed_width
temporal_colnames <- as.vector(seq(from = 1,
to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# A.3 method == "brnn"
# For a description see A.1
if (fixed_width != 0 & method == "brnn") {
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = 1,
ncol = (ncol(env_data) - fixed_width) + 1)
} else if (reference_window == 'end') {
temporal_matrix <- matrix(NA, nrow = 1, ncol = (ncol(env_data)))
} else if (reference_window == 'middle') {
temporal_matrix <- matrix(NA, nrow = 1,
ncol = round2((ncol(env_data) - fixed_width +
1 + fixed_width/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (fixed_width != max_window){
pb <- txtProgressBar(min = 0, max = (ncol(env_data) - fixed_width - offset_end - offset_start + 1),
style = 3)}
b = 0
for (j in (0 + offset_start -1): (ncol(env_data) - max((fixed_width + offset_end), offset_end))) {
b = b + 1
if (aggregate_function == 'median'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)],1 , median, na.rm = TRUE)
}
} else if (aggregate_function == 'sum'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)],1 , sum, na.rm = TRUE)
}
} else if (aggregate_function == 'mean') {
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- rowMeans(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)], na.rm = TRUE)
}
} else if (aggregate_function == 'min'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , min, na.rm = TRUE) }
} else if (aggregate_function == 'max'){
if (fixed_width == 1){
x <- env_data[1:nrow(env_data), (1 + j): (j + fixed_width)]
} else {
x <- apply(data.frame(env_data[1:nrow(env_data),
(1 + j): (j + fixed_width)]),1 , max, na.rm = TRUE)}
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + fixed_width)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_df <- data.frame(cbind(x, response))
capture.output(temporal_model <- try(brnn(x ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6),
silent = TRUE))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
if (class(temporal_model)[[1]] != "try-error"){
temporal_r_squared <- 1 - (sum((x[, 1] - temporal_predictions) ^ 2) /
sum((x[, 1] - mean(x[, 1])) ^ 2))
temporal_adj_r_squared <- 1 - ((1 - temporal_r_squared) *
((nrow(x) - 1)) /
(nrow(x) -
ncol(as.data.frame(temporal_df))
- 1 + 1))
}
temporal_r_squared_lower <- NA
temporal_r_squared_upper <- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else if (boot == TRUE){
temporal_df <- data.frame(cbind(x, response))
calc <- boot(data = temporal_df, statistic = boot_f_brnn, R = boot_n, brnn.formula = "x ~ .", neurons = neurons)
temporal_r_squared <- colMeans(calc$t)[1]
temporal_adj_r_squared <- colMeans(calc$t)[2]
ci_int_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 1), silent = TRUE)
ci_int_adj_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 2), silent = TRUE)
if (class(ci_int_r_squared)[[1]] == "try-error"){
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_r_squared_lower <- ci_int_r_squared$norm[2]
temporal_r_squared_upper <- ci_int_r_squared$norm[3]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$norm[2]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$norm[3]
} else if (boot_ci_type == "perc"){
temporal_r_squared_lower <- ci_int_r_squared$perc[4]
temporal_r_squared_upper <- ci_int_r_squared$perc[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$perc[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$perc[5]
} else if (boot_ci_type == "stud") {
temporal_r_squared_lower <- ci_int_r_squared$studen[4]
temporal_r_squared_upper <- ci_int_r_squared$studen[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$studen[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$studen[5]
} else if (boot_ci_type == "basic") {
temporal_r_squared_lower <- ci_int_r_squared$basic[4]
temporal_r_squared_upper <- ci_int_r_squared$basic[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$basic[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$basic[5]
} else if (boot_ci_type == "bca") {
temporal_r_squared_lower <- ci_int_r_squared$bca[4]
temporal_r_squared_upper <- ci_int_r_squared$bca[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$bca[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
stop(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (metric == "r.squared"){
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_r_squared
temporal_matrix_lower[1, j + 1] <- temporal_r_squared_lower
temporal_matrix_upper[1, j + 1] <- temporal_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[1, j + fixed_width] <- temporal_r_squared
temporal_matrix_lower[1, j + fixed_width] <- temporal_r_squared_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_r_squared_upper
}
}
if (metric == "adj.r.squared"){
if (reference_window == 'start'){
temporal_matrix[1, j + 1] <- temporal_adj_r_squared
temporal_matrix_lower[1, j + 1] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, j + 1] <- temporal_adj_r_squared_upper
} else if (reference_window == 'end'){
temporal_matrix[1, j + fixed_width] <- temporal_adj_r_squared
temporal_matrix_lower[1, j + fixed_width] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, j + fixed_width] <- temporal_adj_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared
temporal_matrix_lower[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared_lower
temporal_matrix_upper[1, round2(j + 1 + fixed_width/2, 0)] <- temporal_adj_r_squared_upper
}
}
if (fixed_width != max_window){setTxtProgressBar(pb, b)}
}
if (fixed_width != max_window){close(pb)}
row.names(temporal_matrix) <- fixed_width
row.names(temporal_matrix_lower) <- fixed_width
row.names(temporal_matrix_upper) <- fixed_width
temporal_colnames <- as.vector(seq(from = 1,
to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# B fixed_width == 0, in this case, lower_limit and upper_limit arguments
# will be used to define window width of a moving window.
# B.1 method == "cor"
if (fixed_width == 0 & method == "cor") {
# This is an empty matrix, currently filled with NA's
# Latter, calculations will be stored in this matrix
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data) - lower_limit) + 1)
} else if (reference_window == 'end'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data)))
} else if (reference_window == 'middle'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = round2((ncol(env_data) - lower_limit +
1 + lower_limit/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
# An iterating double loop: 1 outer loop) iterating from lower_limit :
# upper_limit defines windo.width used for a moving window. 2) inner loop
# defines the starting position of a moving window.
# In each itteration, x is calculated and represents a response (dependent)
# variable. x is a moving average, based on rowMeans/apply function.
# Next, statistical metric is calculated based on a selected method (cor,
# lm or brnn). Calculation is stored in temporal matrix in a proper place.
# The position of stored calculation is informative later used for
# indiciating optimal values.
if (upper_limit != lower_limit){
pb <- txtProgressBar(min = 0, max = (upper_limit - lower_limit), style = 3)
}
b = 0
for (K in lower_limit:upper_limit) {
b = b + 1
for (j in (0 + offset_start -1): (ncol(env_data) - max((K + offset_end), offset_end))) {
if (aggregate_function == 'median'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , median, na.rm = TRUE)
} else if (aggregate_function == 'sum'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , sum, na.rm = TRUE)
} else if (aggregate_function == 'mean'){
x <- rowMeans(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]), na.rm = TRUE)
} else if(aggregate_function == 'min'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , min, na.rm = TRUE)
} else if (aggregate_function == 'max'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , max, na.rm = TRUE)
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + K)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_correlation <- cor(response[, 1], x[, 1], method = cor_method, use = cor_na_use)
temporal_lower <- NA
temporal_upper <- NA
} else if (boot == TRUE){
temp_df_boot <- cbind(response[, 1], x[, 1])
calc <- boot(temp_df_boot, boot_f_cor, cor.type = cor_method, R = boot_n)
temporal_correlation <- colMeans(calc$t)[1]
ci_int <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type), silent = TRUE)
if (class(ci_int)[[1]] == "try-error"){
temporal_lower <- NA
temporal_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_lower <- ci_int$norm[2]
temporal_upper <- ci_int$norm[3]
} else if (boot_ci_type == "perc"){
temporal_lower <- ci_int$perc[4]
temporal_upper <- ci_int$perc[5]
} else if (boot_ci_type == "stud") {
temporal_lower <- ci_int$student[4]
temporal_upper <- ci_int$student[5]
} else if (boot_ci_type == "basic") {
temporal_lower <- ci_int$basic[4]
temporal_upper <- ci_int$basic[5]
} else if (boot_ci_type == "bca") {
temporal_lower <- ci_int$bca[4]
temporal_upper <- ci_int$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
print(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_correlation
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_upper
} else if (reference_window == 'end'){
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_correlation
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_correlation
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_upper
}
}
if (upper_limit != lower_limit){setTxtProgressBar(pb, b)}
}
if (upper_limit != lower_limit){close(pb)}
# temporal_matrix is given rownames and colnames. Rownames represent a
# window width used fot calculations. Colnames represent the position of
# moving window in a original env_data data frame.
temporal_rownames <- as.vector(seq(from = lower_limit, to = upper_limit,
by = 1))
row.names(temporal_matrix) <- temporal_rownames
row.names(temporal_matrix_lower) <- temporal_rownames
row.names(temporal_matrix_upper) <- temporal_rownames
temporal_colnames <- as.vector(seq(from = 1,
to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# B.2 method == "lm"
# For a description see B.1
if (fixed_width == 0 & method == "lm") {
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data) - lower_limit) + 1)
} else if (reference_window == 'end'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data)))
} else if (reference_window == 'middle'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = round2((ncol(env_data) - lower_limit +
1 + lower_limit/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (upper_limit != lower_limit){
pb <- txtProgressBar(min = 0, max = (upper_limit - lower_limit), style = 3)
}
b = 0
for (K in lower_limit:upper_limit) {
b = b + 1
for (j in (0 + offset_start -1): (ncol(env_data) - max((K + offset_end), offset_end))) {
if (aggregate_function == 'median'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , median, na.rm = TRUE)
} else if (aggregate_function == 'sum'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , sum, na.rm = TRUE)
} else if (aggregate_function == 'mean'){
x <- rowMeans(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]), na.rm = TRUE)
} else if(aggregate_function == 'min'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , min, na.rm = TRUE)
} else if (aggregate_function == 'max'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , max, na.rm = TRUE)
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + K)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_df <- data.frame(cbind(x, response))
temporal_model <- lm(x ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
temporal_r_squared <- temporal_summary$r.squared
temporal_adj_r_squared <- temporal_summary$adj.r.squared
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else if (boot == TRUE){
temporal_df <- data.frame(cbind(x, response))
calc <- boot(data = temporal_df, statistic = boot_f_lm, R = boot_n, lm.formula = "x ~ .")
temporal_r_squared <- colMeans(calc$t)[1]
temporal_adj_r_squared <- colMeans(calc$t)[2]
ci_int_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 1), silent = TRUE)
ci_int_adj_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 2), silent = TRUE)
if (class(ci_int_r_squared)[[1]] == "try-error"){
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_r_squared_lower <- ci_int_r_squared$norm[2]
temporal_r_squared_upper <- ci_int_r_squared$norm[3]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$norm[2]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$norm[3]
} else if (boot_ci_type == "perc"){
temporal_r_squared_lower <- ci_int_r_squared$perc[4]
temporal_r_squared_upper <- ci_int_r_squared$perc[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$perc[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$perc[5]
} else if (boot_ci_type == "stud") {
temporal_r_squared_lower <- ci_int_r_squared$studen[4]
temporal_r_squared_upper <- ci_int_r_squared$studen[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$studen[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$studen[5]
} else if (boot_ci_type == "basic") {
temporal_r_squared_lower <- ci_int_r_squared$basic[4]
temporal_r_squared_upper <- ci_int_r_squared$basic[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$basic[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$basic[5]
} else if (boot_ci_type == "bca") {
temporal_r_squared_lower <- ci_int_r_squared$bca[4]
temporal_r_squared_upper <- ci_int_r_squared$bca[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$bca[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
stop(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (metric == "r.squared"){
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared_upper
}
}
if (metric == "adj.r.squared"){
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared_upper
}
}
}
if (upper_limit != lower_limit){setTxtProgressBar(pb, b)}
}
if (upper_limit != lower_limit){close(pb)}
temporal_rownames <- as.vector(seq(from = lower_limit, to = upper_limit, by = 1))
row.names(temporal_matrix) <- temporal_rownames
row.names(temporal_matrix_lower) <- temporal_rownames
row.names(temporal_matrix_upper) <- temporal_rownames
temporal_colnames <- as.vector(seq(from = 1, to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# B.3 method == "brnn"
# For a description see B.1
if (fixed_width == 0 & method == "brnn") {
if (reference_window == 'start'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data) - lower_limit) + 1)
} else if (reference_window == 'end'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = (ncol(env_data)))
} else if (reference_window == 'middle'){
temporal_matrix <- matrix(NA, nrow = (upper_limit - lower_limit + 1),
ncol = round2((ncol(env_data) - lower_limit +
1 + lower_limit/2 ),0))
}
# Here I create two additional temporal matrices, which will be used to store
# lower and upper limits of bootstrap estimates
temporal_matrix_lower <- temporal_matrix
temporal_matrix_upper <- temporal_matrix
if (upper_limit != lower_limit){
pb <- txtProgressBar(min = 0, max = (upper_limit - lower_limit), style = 3)
}
b = 0
for (K in lower_limit:upper_limit) {
b = b + 1
for (j in (0 + offset_start -1): (ncol(env_data) - max((K + offset_end), offset_end))) {
if (aggregate_function == 'median'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , median, na.rm = TRUE)
} else if (aggregate_function == 'sum'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , sum, na.rm = TRUE)
} else if (aggregate_function == 'mean'){
x <- rowMeans(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]), na.rm = TRUE)
} else if(aggregate_function == 'min'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , min, na.rm = TRUE)
} else if (aggregate_function == 'max'){
x <- apply(data.frame(env_data[1:nrow(env_data), (1 + j) : (j + K)]),1 , max, na.rm = TRUE)
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
if (!is.null(dc_method)){
x <- dplR::detrend(data.frame(x), method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
} else {
x <- matrix(x, nrow = nrow(env_data), ncol = 1)
}
x_list <- x
colnames(x_list) <- paste0(j + 1, "_" ,j + K)
row.names(x_list) <- row.names(env_data)
list_climate[[mm]] <- x_list
mm = mm + 1
if (boot == FALSE){
temporal_df <- data.frame(cbind(x, response))
capture.output(temporal_model <- try(brnn(x ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6),
silent = TRUE))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
if (class(temporal_model)[[1]] != "try-error"){
temporal_r_squared <- 1 - (sum((x[, 1] - temporal_predictions) ^ 2) /
sum((x[, 1] - mean(x[, 1])) ^ 2))
temporal_adj_r_squared <- 1 - ((1 - temporal_r_squared) *
((nrow(x) - 1)) /
(nrow(x) -
ncol(as.data.frame(temporal_df))
- 1 + 1))
} else {
temporal_r_squared <- NA
temporal_adj_r_squared <- NA
}
temporal_r_squared_lower <- NA
temporal_r_squared_upper <- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else if (boot == TRUE){
temporal_df <- data.frame(cbind(x, response))
calc <- boot(data = temporal_df, statistic = boot_f_brnn, R = boot_n, brnn.formula = "x ~ .", neurons = neurons)
temporal_r_squared <- colMeans(calc$t)[1]
temporal_adj_r_squared <- colMeans(calc$t)[2]
ci_int_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 1), silent = TRUE)
ci_int_adj_r_squared <- try(boot.ci(calc, conf = boot_conf_int, type = boot_ci_type, index = 2), silent = TRUE)
if (class(ci_int_r_squared)[[1]] == "try-error"){
temporal_r_squared_lower<- NA
temporal_r_squared_upper<- NA
temporal_adj_r_squared_lower <- NA
temporal_adj_r_squared_upper <- NA
} else {
if (boot_ci_type == "norm"){
temporal_r_squared_lower <- ci_int_r_squared$norm[2]
temporal_r_squared_upper <- ci_int_r_squared$norm[3]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$norm[2]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$norm[3]
} else if (boot_ci_type == "perc"){
temporal_r_squared_lower <- ci_int_r_squared$perc[4]
temporal_r_squared_upper <- ci_int_r_squared$perc[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$perc[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$perc[5]
} else if (boot_ci_type == "stud") {
temporal_r_squared_lower <- ci_int_r_squared$studen[4]
temporal_r_squared_upper <- ci_int_r_squared$studen[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$studen[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$studen[5]
} else if (boot_ci_type == "basic") {
temporal_r_squared_lower <- ci_int_r_squared$basic[4]
temporal_r_squared_upper <- ci_int_r_squared$basic[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$basic[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$basic[5]
} else if (boot_ci_type == "bca") {
temporal_r_squared_lower <- ci_int_r_squared$bca[4]
temporal_r_squared_upper <- ci_int_r_squared$bca[5]
temporal_adj_r_squared_lower <- ci_int_adj_r_squared$bca[4]
temporal_adj_r_squared_upper <- ci_int_adj_r_squared$bca[5]
} else {
stop("boot_ci_type should be 'norm', 'perc', 'stud', 'basic' or 'bca'")
}
}
} else {
stop(paste0("boot should be TRUE or FALSE, instead it is ", boot))
}
if (metric == "r.squared"){
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_r_squared_upper
}
}
if (metric == "adj.r.squared"){
if (reference_window == 'start'){
temporal_matrix[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + 1] <- temporal_adj_r_squared_upper
} else if (reference_window == 'end') {
temporal_matrix[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, j + K] <- temporal_adj_r_squared_upper
} else if (reference_window == 'middle'){
temporal_matrix[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared
temporal_matrix_lower[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared_lower
temporal_matrix_upper[(K - lower_limit) + 1, round2(j + 1 + K/2, 0)] <- temporal_adj_r_squared_upper
}
}
}
if (upper_limit != lower_limit){setTxtProgressBar(pb, b)}
}
if (upper_limit != lower_limit){close(pb)}
temporal_rownames <- as.vector(seq(from = lower_limit, to = upper_limit, by = 1))
row.names(temporal_matrix) <- temporal_rownames
row.names(temporal_matrix_lower) <- temporal_rownames
row.names(temporal_matrix_upper) <- temporal_rownames
temporal_colnames <- as.vector(seq(from = 1, to = ncol(temporal_matrix), by = 1))
colnames(temporal_matrix) <- temporal_colnames
colnames(temporal_matrix_lower) <- temporal_colnames
colnames(temporal_matrix_upper) <- temporal_colnames
}
# PART 3: smoothing function, if brnn method is used. It turnes out, that
# brnn sometimes (1 - 3 % of calculations) fails to construct a realistic
# result. In those cases, much lower r.squared (or adj.r.squared) are
# calculated. smooth_matrix function removes unrealistic calculations and
# replace them with mean of values in a window 3 x 3. Maximum value
# is not affected by any means.
# [i - 1, j - 1], [i - 1, j], [i - 1, j + 1]
# [ i, j - 1], [ i, j], [ i, j + 1]
# [i + 1, j - 1], [i + 1, j], [i + 1, j + 1]
if (method == "brnn" & brnn_smooth == TRUE){
temporal_matrix <- smooth_matrix(temporal_matrix, factor_drop = 0.7,
repeats = 2)
}
# To enhance the visualisation, insignificant values
# are removed if remove_insignificant == TRUE
if (remove_insignificant == TRUE){
critical_threshold_cor <- critical_r(nrow(response), alpha = alpha)
critical_threshold_cor2 <- critical_threshold_cor ^ 2
# 1 Method is correlation
if (method == "cor") {
temporal_matrix[abs(temporal_matrix) < abs(critical_threshold_cor)] <- NA
# 2 lm and brnn method
} else if (method == "lm" | method == "brnn") {
temporal_matrix[abs(temporal_matrix) < abs(critical_threshold_cor2)] <- NA
}
}
if(is.finite(mean(temporal_matrix, na.rm = TRUE)) == FALSE){
warning("All calculations are insignificant! Please change the alpha argument.")
final_list <- list(calculations = temporal_matrix,
method = method,
metric = cor_method,
analysed_period = NA,
optimized_return = NA,
optimized_return_all = NA,
transfer_function = NA, temporal_stability = NA,
cross_validation = NA,
plot_heatmap = NA,
plot_extreme = NA,
plot_specific = NA,
PCA_output = NA,
type = "daily",
reference_window = reference_window,
boot_lower = temporal_matrix_lower,
boot_upper = temporal_matrix_upper,
aggregated_climate = NA )
class(final_list) <- 'dmrs'
return(final_list)
} else {
########################################################################
# PART 4: Final list is being created and returned as a function output#
########################################################################
# The first three elements of the final list are already created: calculated
# values, method and metric used.
# Here we create the fourth element: the optimal sequence of days that
# returns the best selected statistical metric. We name it optimal_return.
# In case of negative correlations, different strategy is applied.
# For more detailed description see plot_extreme()
if(is.finite(mean(temporal_matrix, na.rm = TRUE)) == FALSE){
stop("All calculations are insignificant! Change the alpha argument!")
}
overall_max <- max(temporal_matrix, na.rm = TRUE)
overall_min <- min(temporal_matrix, na.rm = TRUE)
# absolute vales of overall_maximum and overall_minimum are compared and
# one of the following two if functions is used
# There are unimportant warnings produced:
# no non-missing arguments to max; returning -Inf
if ((abs(overall_max) >= abs(overall_min)) == TRUE) {
# maximum value is located. Row indeces are needed to query information
# about the window width used to calculate the maximum. Column name is
# needed to query the starting day.
max_result <- suppressWarnings(which.max(apply(temporal_matrix,
MARGIN = 2, max,
na.rm = TRUE)))
plot_column <- max_result
max_index <- which.max(temporal_matrix[, names(max_result)])
row_index <- row.names(temporal_matrix)[max_index]
}
if ((abs(overall_max) < abs(overall_min)) == TRUE) {
min_result <- suppressWarnings(which.min(apply(temporal_matrix,
MARGIN = 2, min,
na.rm = TRUE)))
plot_column <- min_result
min_index <- which.min(temporal_matrix[, names(min_result)])
row_index <- row.names(temporal_matrix)[min_index]
}
# The fourth return element is being created: rowMeans/ apply of optimal sequence:
# So, here we consider more options, based on the reference_winow
# option 1: reference window = "start"
if (reference_window == 'start'){
if (aggregate_function == 'median'){
dataf <- data.frame(apply(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf <- data.frame(apply(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf <- data.frame(rowMeans(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),
na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf <- data.frame(apply(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf <- data.frame(apply(data.frame(env_data[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1)]),1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
# if detrending was applied, should also be applied here
if (!is.null(dc_method)){
dataf <- dplR::detrend(dataf, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
dataf_full <- cbind(response, dataf)
colnames(dataf_full)[ncol(dataf_full)] <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
## Once again, the same procedure, to get the optimal sequence, but this time for whole data, not only
# for the analysed period.
if (aggregate_function == 'median'){
dataf_original <- data.frame(apply(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf_original <- data.frame(apply(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf_original <- data.frame(rowMeans(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),
na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf_original <- data.frame(apply(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf_original <- data.frame(apply(data.frame(env_data_original[, as.numeric(plot_column):
(as.numeric(plot_column) +
as.numeric(row_index) - 1), drop = FALSE]),1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
dataf_full_original <- dataf_original
if (!is.null(dc_method)){
dataf_full_original <- dplR::detrend(dataf_full_original, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
colnames(dataf_full_original) <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
# Additional check: (we should get the same metric as before in the loop)
if (method == "lm" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$r.squared
}
if (method == "lm" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$adj.r.squared
}
if (method == "brnn" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model,
temporal_df), silent = TRUE)
optimized_result <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
}
if (method == "brnn" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ .,
data = temporal_df, neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
temporal_r_squared <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
optimized_result <- 1 - ((1 - temporal_r_squared) *
((nrow(temporal_df) - 1)) /
(nrow(temporal_df) -
ncol(as.data.frame(response[, 1])) - 1))
}
if (method == "cor"){
optimized_result <- cor(dataf, response, method = cor_method, use = cor_na_use)
}
# Just give a nicer colmname
colnames(dataf) <- "Optimized return"
}
# Option 2: reference window = "end"
if (reference_window == 'end'){
if (aggregate_function == 'median'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , mean, na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf <- data.frame(apply(env_data[, (as.numeric(plot_column) - as.numeric(row_index) + 1):
(as.numeric(plot_column)), drop = FALSE],1 , max, na.rm = TRUE))
} else {
stop(paste0("gate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
# if detrending was applied, should also be applied here
if (!is.null(dc_method)){
dataf <- dplR::detrend(dataf, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
dataf_full <- cbind(response, dataf)
colnames(dataf_full)[ncol(dataf_full)] <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
## Once again, the same procedure, to get the optimal sequence, but this time for whole data, not only
# for the analysed period.
if (aggregate_function == 'median'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , mean, na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf_original <- data.frame(apply(env_data_original[, (as.numeric(plot_column) - (as.numeric(row_index) + 1):
as.numeric(plot_column)), drop = FALSE],1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median or sum."))
}
dataf_full_original <- dataf_original
if (!is.null(dc_method)){
dataf_full_original <- dplR::detrend(dataf_full_original, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
colnames(dataf_full_original) <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
# Additional check: (we should get the same metric as before in the loop)
if (method == "lm" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$r.squared
}
if (method == "lm" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$adj.r.squared
}
if (method == "brnn" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model,
temporal_df), silent = TRUE)
optimized_result <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
}
if (method == "brnn" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ .,
data = temporal_df, neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
temporal_r_squared <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
optimized_result <- 1 - ((1 - temporal_r_squared) *
((nrow(temporal_df) - 1)) /
(nrow(temporal_df) -
ncol(as.data.frame(response[, 1])) - 1))
}
if (method == "cor"){
optimized_result <- cor(dataf, response, method = cor_method, use = cor_na_use)
}
# Just give a nicer colname
colnames(dataf) <- "Optimized return"
}
# option 3: reference window = "middle"
if (reference_window == 'middle'){
if (as.numeric(row_index)%%2 == 0){
adjustment_1 = 0
adjustment_2 = 1
} else {
adjustment_1 = 1
adjustment_2 = 2
}
if (aggregate_function == 'median'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , mean, na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf <- data.frame(apply(env_data[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min or max."))
}
# if detrending was applied, should also be applied here
if (!is.null(dc_method)){
dataf <- dplR::detrend(dataf, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
dataf_full <- cbind(response, dataf)
colnames(dataf_full)[ncol(dataf_full)] <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
## Once again, the same procedure, to get the optimal sequence, but this time for whole data, not only
# for the analysed period.
if (aggregate_function == 'median'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , median, na.rm = TRUE))
} else if (aggregate_function == 'sum'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , sum, na.rm = TRUE))
} else if (aggregate_function == 'mean'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , mean, na.rm = TRUE))
} else if (aggregate_function == 'min'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , min, na.rm = TRUE))
} else if (aggregate_function == 'max'){
dataf_original <- data.frame(apply(env_data_original[, (round2((as.numeric(plot_column) - (as.numeric(row_index))/2)) - adjustment_1):
(round2((as.numeric(plot_column) + as.numeric(row_index)/2)) - adjustment_2), drop = FALSE],
1 , max, na.rm = TRUE))
} else {
stop(paste0("aggregate function is ", aggregate_function, ". Instead it should be mean, median, sum, min, max."))
}
dataf_full_original <- dataf_original
if (!is.null(dc_method)){
dataf_full_original <- dplR::detrend(dataf_full_original, method = dc_method, nyrs = dc_nyrs, f = dc_f,
pos.slope = dc_pos.slope, constrain.nls = dc_constrain.nls,
span = dc_span, bass = dc_bass, difference = dc_difference)
}
colnames(dataf_full_original) <- "Optimized_return"
colnames(dataf) <- "Optimized.rowNames"
# Additional check: (we should get the same metric as before in the loop)
if (method == "lm" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$r.squared
}
if (method == "lm" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
temporal_model <- lm(Optimized.rowNames ~ ., data = temporal_df)
temporal_summary <- summary(temporal_model)
optimized_result <- temporal_summary$adj.r.squared
}
if (method == "brnn" & metric == "r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ ., data = temporal_df,
neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model,
temporal_df), silent = TRUE)
optimized_result <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
}
if (method == "brnn" & metric == "adj.r.squared"){
temporal_df <- data.frame(cbind(dataf, response))
capture.output(temporal_model <- brnn(Optimized.rowNames ~ .,
data = temporal_df, neurons = neurons, tol = 1e-6))
temporal_predictions <- try(predict.brnn(temporal_model, temporal_df),
silent = TRUE)
temporal_r_squared <- 1 - (sum((temporal_df[, 1] -
temporal_predictions) ^ 2) /
sum((temporal_df[, 1] -
mean(temporal_df[, 1])) ^ 2))
optimized_result <- 1 - ((1 - temporal_r_squared) *
((nrow(temporal_df) - 1)) /
(nrow(temporal_df) -
ncol(as.data.frame(response[, 1])) - 1))
}
if (method == "cor"){
optimized_result <- cor(dataf, response, method = cor_method, use = cor_na_use)
}
# Just give a nicer colname
colnames(dataf) <- "Optimized return"
}
##############################################################################
# If detrending was used, it also needs to be applied on optimized return
# Element 5
# Here we create the fifth element of the final list: Analysed period in the
# form of min(year) - max(year), e.g. 1950 - 2015
min_env_data <- min(as.numeric(row.names(env_data)))
min_response <- min(as.numeric(row.names(response)))
max_env_data <- max(as.numeric(row.names(env_data)))
max_response <- max(as.numeric(row.names(response)))
min_together <- min(min_env_data, min_response)
max_together <- min(max_env_data, max_response)
analysed_period <- paste(as.character(min_together),
as.character(max_together),
sep = " - ")
if (nchar(analysed_period) < 9) {
analysed_period <- NA
}
# Here, the transfer function is being created
transfer_data = data.frame(proxy = response[,1], optimized_return =dataf[,1])
lm_model = lm(optimized_return ~ proxy, data = transfer_data)
capture.output(brnn_model <- try(brnn(optimized_return ~ proxy, data = transfer_data, neurons = neurons), silent = TRUE))
full_range = data.frame(proxy = seq(from = min(response[,1]), to = max(response[,1]), length.out = 100))
if (method == "lm" | method == "cor"){
full_range$transfer_f = predict(lm_model, full_range)
}
if (method == "brnn"){
full_range$transfer_f = predict.brnn(brnn_model, full_range)
}
# String for titles
if (method == "cor"){
title_string <- "Correlation Coefficients"
} else if (method == "lm"){
title_string <- "Linear Regression"
} else if (method == "brnn"){
title_string <- "ANN With Bayesian Regularization"
} else (print("The selection of method is not correct"))
# The definition of theme
journal_theme <- theme_bw() +
theme(axis.text = element_text(size = 16, face = "bold"),
axis.title = element_text(size = 18), text = element_text(size = 18),
plot.title = element_text(size = 16, face = "bold"))
p1 <- ggplot(transfer_data, aes(proxy, optimized_return)) +
geom_point() +
geom_line(aes(proxy, transfer_f), full_range) +
journal_theme +
ggtitle(paste("Analysed Period:", analysed_period, "\nMethod:", title_string))
analysed_period
# If there is more than one independent variable in the model,
# transfer function is not given, since we should return a 3d model
if (ncol(response) > 1){
p1 <- "No transfer function is created for two or more response variables"
}
#######################################################################
############## The temporal stability of optimized_return #############
#######################################################################
dataset = data.frame(optimized_return = dataf[,1], proxy = response)
empty_list = list()
empty_list_period = list()
empty_list_significance = list()
temporal_stability <- data.frame()
# 1. Progressive stability check
if (temporal_stability_check == "progressive"){
foldi <- seq(1:k)
#foldi <- paste("fold_", foldi)
folds <- cut(seq(1, nrow(dataset)), breaks = k, labels = FALSE)
for (m in 1:k){
#Segement your data by fold using the which() function
trainIndexes <- which(folds <= m, arr.ind = TRUE)
dataset_temp <- dataset[trainIndexes, ]
MAKS <- max(as.numeric(row.names(dataset_temp)))
MIN <- min(as.numeric(row.names(dataset_temp)))
empty_list_period[[m]] <- paste(MIN, "-", MAKS)
if (method == "cor"){
calculation <- cor(dataset_temp[,1], dataset_temp[,2], method = cor_method, use = cor_na_use)
sig <- cor.test(dataset_temp[,1], dataset_temp[,2], method = cor_method, exact=F)$p.value
empty_list_significance[[m]] <- sig
empty_list[[m]] <- calculation
colname = "correlation"
} else if (method == "lm" & metric == "r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
colname = "r.squared"
empty_list[[m]] <- summary(MLR)$r.squared
empty_list_significance[[m]] <- NA
} else if (method == "lm" & metric == "adj.r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
empty_list[[m]] <- summary(MLR)$adj.r.squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else if (method == "brnn" & metric == "r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
empty_list[[m]] <- r_squared
empty_list_significance[[m]] <- NA
colname = "r.squared"
} else {
empty_list[[m]] <- NA
colname = "r.squared"
empty_list_significance[[m]] <- NA
}
} else if (method == "brnn" & metric == "adj.r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
adj_r_squared <- 1 - ((1 - r_squared) * ((nrow(dataset_temp) - 1)) /
(nrow(dataset_temp) - ncol(as.data.frame(response[, 1])) - 1))
empty_list[[m]] <- adj_r_squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else {
empty_list[[m]] <- NA
colname = "adj.r.squared"
}
}
}
m1 <- do.call(rbind, empty_list)
m2 <- do.call(rbind, empty_list_period)
m3 <- do.call(rbind, empty_list_significance)
temporal_stability <- data.frame(cbind(m2, format(round(m1, 3), nsmall = 3), format(round(m3, 4), nsmall = 3)))
colnames(temporal_stability) <-c("Period", colname, "p value")
temporal_stability
}
# 2. Sequential stability check
if (temporal_stability_check == "sequential"){
foldi <- seq(1:k)
#foldi <- paste("fold_", foldi)
folds <- cut(seq(1, nrow(dataset)), breaks = k, labels = FALSE)
for (m in 1:k){
#Segement your data by fold using the which() function
trainIndexes <- which(folds == m, arr.ind = TRUE)
dataset_temp <- dataset[trainIndexes, ]
MAKS <- max(as.numeric(row.names(dataset_temp)))
MIN <- min(as.numeric(row.names(dataset_temp)))
empty_list_period[[m]] <- paste(MIN, "-", MAKS)
if (method == "cor"){
calculation <- cor(dataset_temp[,1], dataset_temp[,2], method = cor_method, use = cor_na_use)
sig <- cor.test(dataset_temp[,1], dataset_temp[,2], method = cor_method, exact=F)$p.value
empty_list[[m]] <- calculation
empty_list_significance[[m]] <- sig
colname = "correlation"
} else if (method == "lm" & metric == "r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
colname = "r.squared"
empty_list[[m]] <- summary(MLR)$r.squared
empty_list_significance[[m]] <- NA
} else if (method == "lm" & metric == "adj.r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
empty_list[[m]] <- summary(MLR)$adj.r.squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else if (method == "brnn" & metric == "r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
empty_list[[m]] <- r_squared
empty_list_significance[[m]] <- NA
colname = "r.squared"
} else {
empty_list[[m]] <- NA
colname = "r.squared"
empty_list_significance[[m]] <- NA
}
} else if (method == "brnn" & metric == "adj.r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
adj_r_squared <- 1 - ((1 - r_squared) * ((nrow(dataset_temp) - 1)) /
(nrow(dataset_temp) - ncol(as.data.frame(response[, 1])) - 1))
empty_list[[m]] <- adj_r_squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else {
empty_list[[m]] <- NA
colname = "adj.r.squared"
empty_list_significance[[m]] <- NA
}
}
}
m1 <- do.call(rbind, empty_list)
m2 <- do.call(rbind, empty_list_period)
m3 <- do.call(rbind, empty_list_significance)
temporal_stability <- data.frame(cbind(m2, format(round(m1, 3), nsmall = 3), format(round(m3, 4), nsmall = 3)))
colnames(temporal_stability) <-c("Period", colname, "p value")
temporal_stability
}
# 3. running_window
if (temporal_stability_check == "running_window"){
k_end <- nrow(dataset)
place_list <- 1
empty_list_datasets <- list()
empty_list_period <- list()
empty_list <- list()
empty_list_significance <- list()
place_list = 1
if (k_end < k_running_window){
stop("k_running_window is less than the number of analysed years. Reduce the argument k_running_window")
}
for (w in 0:(k_end - k_running_window)){
dataset_temp <- dataset[(1+w):(k_running_window + w),]
empty_list_datasets[[place_list]] <- dataset_temp
MAKS <- max(as.numeric(row.names(dataset_temp)))
MIN <- min(as.numeric(row.names(dataset_temp)))
empty_list_period[[place_list]] <- paste(MIN, "-", MAKS)
place_list <- place_list + 1
}
for (m in 1:length(empty_list_datasets)){
dataset_temp <- empty_list_datasets[[m]]
if (method == "cor"){
calculation <- cor(dataset_temp[,1], dataset_temp[,2], method = cor_method, use = cor_na_use)
sig <- cor.test(dataset_temp[,1], dataset_temp[,2], method = cor_method, exact=F)$p.value
empty_list[[m]] <- calculation
empty_list_significance[[m]] <- sig
colname = "correlation"
} else if (method == "lm" & metric == "r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
colname = "r.squared"
empty_list[[m]] <- summary(MLR)$r.squared
empty_list_significance[[m]] <- NA
} else if (method == "lm" & metric == "adj.r.squared"){
MLR <- lm(optimized_return ~ ., data = dataset_temp)
empty_list[[m]] <- summary(MLR)$adj.r.squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else if (method == "brnn" & metric == "r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
empty_list[[m]] <- r_squared
empty_list_significance[[m]] <- NA
colname = "r.squared"
} else {
empty_list[[m]] <- NA
colname = "r.squared"
empty_list_significance[[m]] <- NA
}
} else if (method == "brnn" & metric == "adj.r.squared"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = dataset_temp, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
predictions <- predict(BRNN, dataset_temp, neurons = neurons)
r_squared <- 1 - (sum((dataset_temp[, 1] - predictions) ^ 2) /
sum((dataset_temp[, 1] - mean(dataset_temp[, 1])) ^ 2))
adj_r_squared <- 1 - ((1 - r_squared) * ((nrow(dataset_temp) - 1)) /
(nrow(dataset_temp) - ncol(as.data.frame(response[, 1])) - 1))
empty_list[[m]] <- adj_r_squared
empty_list_significance[[m]] <- NA
colname = "adj.r.squared"
} else {
empty_list[[m]] <- NA
colname = "adj.r.squared"
empty_list_significance[[m]] <- NA
}
}
}
m1 <- do.call(rbind, empty_list)
m2 <- do.call(rbind, empty_list_period)
m3 <- do.call(rbind, empty_list_significance)
temporal_stability <- data.frame(cbind(m2, format(round(m1, 3), nsmall = 3), format(round(as.numeric(m3), digits = 3), nsmall = 3)))
colnames(temporal_stability) <-c("Period", colname, "p value")
temporal_stability
}
#########################################################################
################## Out of sample estimates ##############################
#########################################################################
dataset = data.frame(optimized_return =dataf[,1], proxy = response)
empty_list = list()
empty_list_period = list()
if (cross_validation_type == "blocked"){
dataset <- dataset
} else if (cross_validation_type == "randomized"){
dataset <- dataset[sample(nrow(dataset)), ]
} else (stop(paste("The cross_validation_type is not selected correctly! It is ", cross_validation_type,
". It should be 'blocked' or 'randomized'!", sep = "")))
foldi <- seq(1:k)
#foldi <- paste("fold_", foldi)
folds <- cut(seq(1, nrow(dataset)), breaks = k, labels = FALSE)
bl = 1
for (m in 1:k){
#Segement your data by fold using the which() function
testIndexes <- which(folds == m, arr.ind = TRUE)
test <- dataset[testIndexes, ]
train <- dataset[-testIndexes, ]
MAKS <- max(as.numeric(row.names(train)))
MIN <- min(as.numeric(row.names(train)))
empty_list_period[[bl]] <- paste(MIN, "-", MAKS)
bl <- bl + 1
MAKS <- max(as.numeric(row.names(test)))
MIN <- min(as.numeric(row.names(test)))
empty_list_period[[bl]] <- paste(MIN, "-", MAKS)
bl <- bl + 1
if (method == "lm" | method == "cor"){
MLR <- lm(optimized_return ~ ., data = train)
train_predicted <- predict(MLR, train)
test_predicted <- predict(MLR, test)
train_observed <- train[, 1]
test_observed <- test[, 1]
calculations <- calculate_metrics(train_predicted, test_predicted,
train_observed, test_observed, test = test,
formula = optimized_return ~ ., digits = 15)
empty_list[[m]] <- calculations
}
if (method == "brnn"){
capture.output(BRNN <- try(brnn(optimized_return ~ ., data = train, neurons = neurons), silent = TRUE))
if (class(BRNN)[[1]] != "try-error"){
train_predicted <- predict(BRNN, train)
test_predicted <- predict(BRNN, test)
train_observed <- train[, 1]
test_observed <- test[, 1]
calculations <- calculate_metrics(train_predicted, test_predicted,
train_observed, test_observed, digits = 15,
test = test,
formula = optimized_return ~ .)
empty_list[[m]] <- calculations
} else {
empty_list[[m]] <- NA
}
}
}
m1 <- do.call(rbind, empty_list)
# m1 <- m1[, -c(3, 4, 7)]
m2 <- do.call(rbind, empty_list_period)
cross_validation <- cbind(Years = m2, m1)
cross_validation$Period <- c("Calibration", "Validation")
cross_validation$CV <- rep(1:k, each = 2)
row.names(cross_validation) <- NULL
if (cross_validation_type == "blocked"){
cross_validation <- dplyr::select(cross_validation, CV, Period, Years, cor, RMSE, RRSE, d, RE, CE, DE)
}
if (cross_validation_type == "randomized"){
cross_validation <- dplyr::select(cross_validation, CV, Period, cor, RMSE, RRSE, d, RE, CE, DE)
}
################################################################
#### Here the final list is being filled with six elements #####
################################################################
# When metohod == "cor", different final_list is created
if (method == "lm" | method == "brnn") {
final_list <- list(calculations = temporal_matrix, method = method,
metric = metric, analysed_period = analysed_period,
optimized_return = dataf_full,
optimized_return_all = dataf_full_original,
transfer_function = p1, temporal_stability = temporal_stability,
cross_validation = cross_validation,
aggregated_climate = do.call(cbind, list_climate))
}
if (method == "cor"){
final_list <- list(calculations = temporal_matrix, method = method,
metric = cor_method, analysed_period = analysed_period,
optimized_return = dataf_full,
optimized_return_all = dataf_full_original,
transfer_function = p1, temporal_stability = temporal_stability,
cross_validation = cross_validation,
aggregated_climate = do.call(cbind, list_climate))
}
plot_heatmapA <- plot_heatmap(final_list, reference_window = reference_window, type = "daily")
plot_extremeA <- plot_extreme(final_list, ylimits = ylimits, reference_window = reference_window, type = "daily")
width_sequence = seq(lower_limit, upper_limit)
if (is.null(plot_specific_window)){
(plot_specificA <- "plot_specific_window is not available. No plot_specific is made!")
} else if (fixed_width != 0){
if (fixed_width != plot_specific_window){
warning(paste0("plot_specific_window and fixed_width differ!",
" fixed_wdith will be used to generate plot_specific!"))
}
plot_specific_window = fixed_width
plot_specificA <- plot_specific(final_list, window_width = plot_specific_window, ylimits = ylimits,
reference_window = reference_window)
} else if (plot_specific_window %in% width_sequence){
plot_specificA <- plot_specific(final_list, window_width = plot_specific_window, ylimits = ylimits,
reference_window = reference_window)
} else (plot_specificA <- "Selected plot_specific_window is not available. No plot_specific is made!")
# Here, for the sake of simplicity, we create final list again
if (method == "lm" | method == "brnn") {
final_list <- list(calculations = temporal_matrix, method = method,
metric = metric, analysed_period = analysed_period,
optimized_return = dataf_full,
optimized_return_all = dataf_full_original,
transfer_function = p1, temporal_stability = temporal_stability,
cross_validation = cross_validation,
plot_heatmap = plot_heatmapA,
plot_extreme = plot_extremeA,
plot_specific = plot_specificA,
PCA_output = PCA_result,
type = "daily",
reference_window = reference_window,
boot_lower = temporal_matrix_lower,
boot_upper = temporal_matrix_upper,
aggregated_climate = do.call(cbind, list_climate))
}
if (method == "cor"){
final_list <- list(calculations = temporal_matrix, method = method,
metric = cor_method, analysed_period = analysed_period,
optimized_return = dataf_full,
optimized_return_all = dataf_full_original,
transfer_function = p1, temporal_stability = temporal_stability,
cross_validation = cross_validation,
plot_heatmap = plot_heatmapA,
plot_extreme = plot_extremeA,
plot_specific = plot_specificA,
PCA_output = PCA_result,
type = "daily",
reference_window = reference_window,
boot_lower = temporal_matrix_lower,
boot_upper = temporal_matrix_upper,
aggregated_climate = do.call(cbind, list_climate))
}
class(final_list) <- 'dmrs'
return(final_list)
}
}
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