##################################################
# Implementation of Beta Binomial Class #
# Kaitlin Cornwell #
# August 3, 2018 #
##################################################
###### Beta Binomial Functions
#' Make Beta Binomial Distribution
#'
#' `make_betabinom()` creates an object that allows for analysis assuming
#' a binomial distribution.
#'
#' The returned tibble can be row bound with other objects from the
#' `make_distribution()` functions. Then multiple models can be worked
#' with at once.
#'
#' This tibble is the input for `set_priors()` and `fit_model()` functions.
#'
#' @param ... A comma separated list of predictors that will be used in the
#' model, given as unquoted expressions. 1 if fitting an intercept
#' only model
#'
#' @return A tibble with one row. The tibble will contain information stating
#' that it is a beta binomial model and will contain the right hand side of
#' a model formula by creating a linear combination of predictors
#'
#' @examples
#' make_betabinom(1)
#' make_betabinom(x)
#' make_betabinom(x, y)
#'
#' @export
make_betabinom <- function(...) {
# the binomial distribution is fit using VGAM::vglm
# it takes in a formula and would set family = betabinom
# make the list of predictors into expressions
predictors = enexprs(...)
# output the tibble
tibble(model_type = "BetaBinomial", model_eq = write_equation(predictors))
}
### Beta Binomial Base/default Class
#' Constructor for Beta Binomial distribution
#'
#' @param model_object an object coming from the `fit_model()` function
#' @param outcome the variable to be used as the dependent variable provided
#' as an expression
#' @param group the variable to be used as the grouping variable provided
#' as an expression
#' @param opt the model options provided as a function call to `model_options()`
#'
#' @return An object of class BetaBinomial
BetaBinomial <- function(model_object, outcome, group = NA, opt = NA) {
# make arguments into expressions
outcome = enexpr(outcome)
group = enexpr(group)
values <- tibble(outcome = c(expr(!!outcome)),
group = c(expr(!!group)),
equation = c(expr(!!model_object$model_eq)))
# if there are model options put them in the object
if (!is.an(opt))
values <- bind_cols(values, as_tibble(opt))
# set the class
attr(values, "class") <- "BetaBinomial"
values
}
# Beta Binomial fit_object
# should not run
#' @export
fit_object.BetaBinomial <- function(model_object, model_data) {
stop("You have not defined the type of model fit properly")
}
#' @export
simulate_distribution.BetaBinomial <- function(object, model_results, values, nsim, seed) {
stop("You have not defined the type of model fit properly")
}
# Beta Binomial model_prediction()
# should not run
#' @export
model_prediction.BetaBinomial <- function(model_object, model_results, id, new_values = NA) {
stop("You have not defined the type of model fit properly")
}
# Beta Binomial inv_transformation()
# should not run
#' @export
inv_transformation.BetaBinomial <- function(model_object, model_results, id, predictions) {
stop("You have not defined the type of model fit properly")
}
#' @export
model_distribution.BetaBinomial <- function(model_object, model_results, id, hist = FALSE) {
stop("You have not defined the type of model fit properly")
}
### Beta Binomial Frequentist class
#' Constructor for BetaBinomial Frequentist distribution
#'
#' @param model_object an object coming from the `fit_model()` function
#' @param outcome the variable to be used as the dependent variable provided
#' as an expression
#' @param group the variable to be used as the grouping variable provided
#' as an expression
#' @param opt the model options provided as a function call to `model_options()`
#'
#' @return An object of class BetaBinomial.Frequentist
BetaBinomial.Frequentist <- function(model_object, outcome, group = NA, opt = NA) {
# make arguments into expressions
outcome = enexpr(outcome)
group = enexpr(group)
values <- tibble(outcome = c(expr(!!outcome)),
group = c(expr(!!group)),
equation = c(expr(!!model_object$model_eq)))
# add max option to be used if given a vector of successes
if ("max" %in% names(opt)) {
max <- expr(!!opt$max)
values <- bind_cols(values, max = opt$max)
}
# set the class
attr(values, "class") <- c("BetaBinomial.Frequentist", "BetaBinomial")
values
}
# Fits the Beta Binomial model with a Frequentist framework
# arguments: model_object - an object of class BetaBinomial.Frequentist
# model_data - the dataset to be used to fit the model
# returns: the S4 object from vglm along with relevant model information including type of fit and equation
#' @export
fit_object.BetaBinomial.Frequentist <- function(model_object, model_data) {
# if fitting a model with success/failure outcome instead of 0/1
if ("max" %in% names(model_object))
outcome <- expr(cbind(!!model_object$outcome[[1]], !!model_object$max - !!model_object$outcome[[1]]))
else
outcome <- expr(!!model_object$outcome[[1]])
# if fitting an intercept only model
if (quo_name(model_object$equation[[1]]) == "1")
mod_formula <- expr(!!outcome ~ 1)
else
# if not intercept only use the given predictor
mod_formula <- expr(!!outcome ~ !!model_object$equation[[1]])
# if there is a grouping variable given then group the data
if (!is.na(model_object$group)) {
groups <- model_data %>% select(!!model_object$group[[1]]) %>% distinct()
model_data <- model_data %>% group_by(!!model_object$group[[1]]) %>% nest()
}
else {
model_data <- model_data %>% nest()
}
# get the glm per group and add variables for identification
results <- model_data %>%
rowwise() %>%
do(model_results = as_result(vglm(formula = !!mod_formula, family = betabinomial, data = .$data),
model_data = .$data)) %>%
mutate(model_type = "BetaBinomial", fit_type = "Frequentist", model_eq = model_object$equation)
if (!is.na(model_object$group))
results <- bind_cols(groups, results)
results
}
# Predicts values for the model
# arguments: model_object - an object of type BetaBinomial.Frequentist
# model_results - an S4 object of class vglm contianing the fit model information
# id - an id value to be appended to final dataset
# pred_values - the values at which to carry out prediction at
# returns: a tibble with each row a predicted value of the dataset
#' @export
model_prediction.BetaBinomial.Frequentist <- function(model_object, model_results, id, new_values = NA) {
if (is.na(new_values) %>% all()) {
# get the predictors of the model
preds <- get_predictors(model_object$equation)[-c(1,2)]
# if intercept only model
if ((preds == "1") %>% all())
new_values <- tibble(intercept = rep(model_results$result@coefficients[1], times = nrow(model_results$result@x)))
else
# subset data to be appended to prediction results
new_values <- model_results$result@x %>% as_tibble() %>% select(-`(Intercept)`)
# get predictions for original dataset
predictions <- predictvglm(model_results$result)
}
else {
# get predictions for new dataset
predictions <- predictvglm(model_results$result, new_values)
}
# format the results
predictions %>%
as_tibble() %>%
select(`logit(mu)`) %>%
bind_cols(new_values) %>%
# add id column
mutate(id = id) %>%
rename(!!model_object$outcome[[1]] := `logit(mu)`)
}
# Perform the inverse transformation of the link function
# arguments: model_object - an object of type BetaBinomial.Frequentist
# model_results - an S4 object of class vglm contianing the fit model information
# id - an id value to be appended to final dataset
# predictions - the values at which to carry out prediction at
# returns: a tibble with each row the value of the mean at the given predictors
#' @export
inv_transformation.BetaBinomial.Frequentist <- function(model_object, model_results, id, predictions) {
# get max number of trails for use to get mean
# if the model was fit with success/failure parameterization
if (grepl("cbind", model_results@call$formula) %>% any()) {
n <- str_extract(deparse(model_results@call$formula), "(?<=, )[:digit:]+(?= )")
n <- as.numeric(n)
}
# if the model was fit with 0/1 parameterization
else
n <- 1
# carry out the inverse transformation
predictions %>% mutate(!!model_object$outcome[[1]] := inv.logit(!!model_object$outcome[[1]]) * n)
}
# Simuate values from the given model
# arguments: model_objects - an object of type BetaBinomial.Frequentist
# model_results - an S4 object of class vglm contianing the fit model information
# values - the values at which to carry out simulation at
# nsim - number of datasets to simulate
# seed - value to set for random number generation
# returns: a tibble with each row a simulated value at the given predictors
#' @export
simulate_distribution.BetaBinomial.Frequentist <- function(model_objects, model_results, values, nsim = 1, seed = NULL) {
# if the model was fit with # of successes/failures
if (grepl("cbind", model_results@call$formula) %>% any()) {
# get n from the model statement
n <- str_extract(deparse(model_results@call$formula), "(?<=, )[:digit:]+(?= )")
n <- as.numeric(n)
}
# if the model was fit with 0/1
else
n <- 1
# get the probability of success
values <- values %>%
mutate(prob = inv.logit(!!model_objects$outcome[[1]]))
# carry out the simulation
set.seed(seed)
values$prob %>%
map(~ rbetabinom(nsim, n, .x)) %>%
unlist() %>%
as_tibble() %>%
bind_cols(.,
values %>% slice(rep(1:n(), each = nsim))) %>%
select(-!!model_objects$outcome[[1]], -prob) %>%
rename(!!model_objects$outcome[[1]] := value)
}
#' @export
model_distribution.BetaBinomial.Frequentist <- function(model_object, model_results, id, hist = FALSE) {
# if the model was fit with # of successes/failures
if (grepl("cbind", model_results$result@call$formula) %>% any()) {
# get n from the model statement
n <- str_extract(deparse(model_results$result@call$formula), "(?<=, )[:digit:]+(?= )")
n <- as.numeric(n)
}
# if the model was fit with 0/1
else
n <- 1
bounds <- model_results$result@y %>%
as_tibble() %>%
summarise(min = min(.), max = max(.))
graphing_tbl <- tibble(x = 0:n,
y = dbetabinom(x,size=n,inv.logit(coef(model_results$result)[[1]]),
inv.logit(coef(model_results$result)[[2]])),
id = id)
if (hist) {
hist_data <- model_results$data %>%
select(!!model_object$outcome[[1]]) %>%
group_by(!!model_object$outcome[[1]]) %>%
summarise(n = n()) %>%
rename(x = y)
graphing_tbl <- inner_join(graphing_tbl, hist_data, by = "x")
}
model_plot <- ggplot(graphing_tbl, aes(x = x))
if (hist)
model_plot <- model_plot + geom_bar(aes(y = n/sum(n)), stat = "identity")
model_plot +
geom_line(aes(y = y), col = id) +
ggtitle(glue("{id} - Beta Binomial")) +
theme(legend.position = "none") +
labs(y = "Density")
}
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