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R/EFA_AVERAGE.R
In EFAtools: Fast and Flexible Implementations of Exploratory Factor Analysis Tools
Defines functions
EFA_AVERAGE
Documented in
EFA_AVERAGE
#' Model averaging across different EFA methods and types
#'
#' Not all EFA procedures always arrive at the same solution. This function allows
#' you perform a number of EFAs from different methods (e.g., Maximum Likelihood
#' and Principal Axis Factoring), with different implementations (e.g., the SPSS
#' and psych implementations of Principal Axis Factoring), and across different
#' rotations of the same type (e.g., multiple oblique rotations, like promax and
#' oblimin). EFA_AVERAGE will then run all these EFAs (using the \code{\link{EFA}}
#' function) and provide a summary across the different solutions.
#'
#' @param x data.frame or matrix. Dataframe or matrix of raw data or matrix with
#' correlations. If raw data is entered, the correlation matrix is found from the
#' data.
#' @param n_factors numeric. Number of factors to extract.
#' @param N numeric. The number of observations. Needs only be specified if a
#' correlation matrix is used. If input is a correlation matrix and \code{N} = NA
#' (default), not all fit indices can be computed.
#' @param method character vector. Any combination of "PAF", "ML", and "ULS",
#' to use principal axis factoring, maximum likelihood, or unweighted least
#' squares (also called minres), respectively, to fit the EFAs. Default is "PAF".
#' @param rotation character vector. Either perform no rotation ("none"),
#' any combination of orthogonal rotations ("varimax", "equamax", "quartimax", "geominT",
#' "bentlerT", and "bifactorT"; using "orthogonal" runs all of these), or of
#' oblique rotations ("promax", "oblimin", "quartimin", "simplimax", "bentlerQ",
#' "geominQ", and "bifactorQ"; using "oblique" runs all of these). Rotation types
#' (no rotation, orthogonal rotations, and oblique rotations) cannot be mixed.
#' Default is "promax".
#' @param type character vector. Any combination of "none" (default), "EFAtools",
#' "psych", and "SPSS" can be entered. "none" allows the specification of various
#' combinations of the arguments controlling both factor extraction methods and
#' the rotations. The others ("EFAtools", "psych", and "SPSS"), control the execution
#' of the respective factor extraction method and rotation to be in line with how
#' it is executed in this package (i.e., the respective default procedure), in the
#' psych package, and in SPSS. A specific psych implementation exists for PAF, ML, varimax,
#' and promax. The SPSS implementation exists for PAF, varimax, and promax. For
#' details, see \code{\link{EFA}}.
#' @param averaging character. One of "mean" (default), and "median". Controls
#' whether the different results should be averaged using the (trimmed) mean,
#' or the median.
#' @param trim numeric. If averaging is set to "mean", this argument controls
#' the trimming of extremes (for details see \code{\link[base:mean]{base::mean}}).
#' By default no trimming is done (i.e., trim = 0).
#' @param salience_threshold numeric. The threshold to use to classify a pattern
#' coefficient or loading as salient (i.e., substantial enough to assign it to
#' a factor). Default is 0.3. Indicator-to-factor correspondences will be inferred
#' based on this threshold. Note that this may not be meaningful if rotation = "none"
#' and n_factors > 1 are used, as no simple structure is present there.
#' @param max_iter numeric. The maximum number of iterations to perform after which
#' the iterative PAF procedure is halted with a warning. Default is 10,000. Note
#' that non-converged procedures are excluded from the averaging procedure.
#' @param init_comm character vector. Any combination of "smc", "mac", and "unity".
#' Controls the methods to estimate the initial communalities in \code{PAF} if
#' "none" is among the specified types. "smc" will use squared multiple
#' correlations, "mac" will use maximum absolute correlations, "unity" will use
#' 1s (for details see \code{\link{EFA}}). Default is \code{c("smc", "mac", "unity")}.
#' @param criterion numeric vector. The convergence criterion used for PAF if
#' "none" is among the specified types.
#' If the change in communalities from one iteration to the next is smaller than
#' this criterion the solution is accepted and the procedure ends.
#' Default is \code{0.001}.
#' @param criterion_type character vector. Any combination of "max_individual" and
#' "sum". Type of convergence criterion used for PAF if "none" is among the
#' specified types. "max_individual" selects the maximum change in any of the
#' communalities from one iteration to the next and tests it against the
#' specified criterion. "sum" takes the difference of
#' the sum of all communalities in one iteration and the sum of all communalities
#' in the next iteration and tests this against the criterion
#' (for details see \code{\link{EFA}}). Default is \code{c("sum", "max_individual")}.
#' @param abs_eigen logical vector. Any combination of TRUE and FALSE.
#' Which algorithm to use in the PAF iterations if "none" is among the specified
#' types. If FALSE, the loadings are computed from the eigenvalues. This is also
#' used by the \code{\link[psych:fa]{psych::fa}} function. If TRUE the
#' loadings are computed with the absolute eigenvalues as done by SPSS
#' (for details see \code{\link{EFA}}). Default is \code{TRUE}.
#' @param varimax_type character vector. Any combination of "svd" and "kaiser".
#' The type of the varimax rotation performed if "none" is among the specified
#' types and "varimax", "promax", "orthogonal", or "oblique" is among the specified
#' rotations. "svd" uses singular value decomposition, as
#' \link[stats:varimax]{stats::varimax} does, and "kaiser" uses the varimax
#' procedure performed in SPSS. This is the original procedure from Kaiser (1958),
#' but with slight alterations in the varimax criterion (for details, see
#' \code{\link{EFA}} and Grieder & Steiner, 2020).
#' Default is \code{c("svd", "kaiser")}.
#' @param normalize logical vector. Any combination of TRUE and FALSE.
#' \code{TRUE} performs a kaiser normalization before the specified rotation(s).
#' Default is \code{TRUE}.
#' @param k_promax numeric vector. The power used for computing the target matrix
#' P in the promax rotation if "none" is among the specified types and "promax"
#' or "oblique" is among the specified rotations. Default is \code{2:4}.
#' @param k_simplimax numeric. The number of 'close to zero loadings' for the
#' simplimax rotation (see \code{\link[GPArotation:GPA]{GPArotation::GPFoblq}})
#' if "simplimax" or "oblique" is among the specified rotations. Default
#' is \code{ncol(x)}, where x is the entered data.
#' @param P_type character vector. Any combination of "norm" and "unnorm".
#' This specifies how the target matrix P is computed in promax rotation if
#' "none" is among the specified types and "promax" or "oblique" is among the
#' specified rotations. "unnorm" will use the unnormalized target matrix as
#' originally done in Hendrickson and White (1964). "norm" will use a
#' normalized target matrix (for details see \code{\link{EFA}}).
#' Default is \code{c("norm", "unnorm")}.
#' @param precision numeric vector. The tolerance for stopping in the rotation
#' procedure(s). Default is 10^-5.
#' @param start_method character vector. Any combination of "psych" and "factanal".
#' How to specify the starting values for the optimization procedure for ML.
#' "psych" takes the starting values specified in \link[psych:fa]{psych::fa}.
#' "factanal" takes the starting values specified in the
#' \link[stats:factanal]{stats::factanal} function. Default is
#' \code{c("psych", "factanal")}.
#' @param use character. Passed to \code{\link[stats:cor]{stats::cor}} if raw data
#' is given as input. Default is "pairwise.complete.obs".
#' @param cor_method character. Passed to \code{\link[stats:cor]{stats::cor}}.
#' Default is "pearson".
#' @param show_progress logical. Whether a progress bar should be shown in the
#' console. Default is TRUE.
#'
#' @details
#'
#' As a first step in this function, a grid is produced containing the setting
#' combinations for the to-be-performed EFAs. These settings are then entered as
#' arguments to the \code{\link{EFA}} function and the EFAs are run in a second
#' step. After all EFAs are run, the factor solutions are averaged and their
#' variability determined in a third step.
#'
#' The grid containing the setting combinations is produced based on the entries
#' to the respective arguments. To this end, all possible combinations resulting
#' in unique EFA models are considered. That is, if, for example, the \code{type}
#' argument was set to \code{c("none", "SPSS")} and one combination of the specific
#' settings entered was identical to the SPSS combination, this combination
#' would be included in the grid and run only once. We include here a list
#' of arguments that are only evaluated under specific conditions:
#'
#' The arguments \code{init_comm}, \code{criterion}, \code{criterion_type},
#' \code{abs_eigen} are only evaluated if "PAF" is included in \code{method}
#' and "none" is included in \code{type}.
#'
#' The argument \code{varimax_type} is only evaluated if "varimax", "promax",
#' "oblique", or "orthogonal" is included in \code{rotation} and "none" is
#' included in \code{type}.
#'
#' The argument \code{normalize} is only evaluated if \code{rotation} is not
#' set to "none" and "none" is included in \code{type}.
#'
#' The argument \code{k_simplimax} is only evaluated if "simplimax" or "oblique"
#' is included in \code{rotation}.
#'
#' The arguments \code{k_promax} and \code{P_type} are only evaluated if
#' "promax" or "oblique" is included in \code{rotation} and "none" is included
#' in \code{type}.
#'
#' The argument \code{start_method} is only evaluated if "ML" is included in
#' \code{method}.
#'
#' To avoid a bias in the averaged factor solutions from problematic solutions,
#' these are excluded prior to averaging. A solution is deemed problematic if
#' at least one of the following is true: an error occurred, the model did not
#' converge, or there is at least one Heywood case (defined as a loading or communality of >= .998).
#' Information on errors, convergence, and Heywood cases are returned in the
#' implementations_grid and a summary of these is given when printing the output.
#' In addition to these, information on the admissibility of the factor solutions
#' is also included. A solution was deemed admissible if (1) no error occurred,
#' (2) the model converged, (3) no Heywood cases are present, and (4) there are
#' at least two salient loadings (i.e., loadings exceeding the specified
#' \code{salience_threshold}) for each factor. So, solutions failing one of the
#' first three of these criteria of admissibility are also deemed problematic and
#' therefore excluded from averaging. However, solutions failing only
#' the fourth criterion of admissibility are still included for averaging.
#' Finally, if all solutions are problematic (e.g., all solutions contain
#' Heywood cases), no averaging is performed and the respective outputs are NA.
#' In this case, the implementations_grid should be inspected to see if there
#' are any error messages, and the separate EFA solutions that are also included
#' in the output can be inspected as well, for example, to see where Heywood
#' cases occurred.
#'
#' A core output of this function includes the average, minimum, and maximum
#' loadings derived from all non-problematic (see above) factor solutions. Please
#' note that these are not entire solutions, but the matrices include the average,
#' minimum, or maximum value for each cell (i.e., each loading separately). This
#' means that, for example, the matrix with the minimum loadings will contain
#' the minimum value in any of the factor solutions for each specific loading,
#' and therefore most likely contains loadings from different factor solutions.
#' The matrices containing the minimum and maximum factor solutions can
#' therefore not be interpreted as whole factor solutions.
#'
#' The output also includes information on the average, minimum, maximum, and
#' variability of the fit indices across the non-problematic factor solutions.
#' It is important to note that not all fit indices are computed for all fit
#' methods: For ML and ULS, all fit indices can be computed, while for PAF, only
#' the common part accounted for (CAF) index (Lorenzo-Seva, Timmerman, & Kiers, 2011)
#' can be computed. As a consequence, if only "PAF" is included in the
#' \code{method} argument, averaging can only be performed for the CAF, and the
#' other fit indices are NA. If a combination of "PAF" and "ML" and/or "ULS" are
#' included in the \code{method} argument, the CAF is averaged across all non-
#' problematic factor solutions, while all other fit indices are only averaged
#' across the ML and ULS solutions. The user should therefore keep in mind that
#' the number of EFAs across which the fit indices are averaged can diverge for
#' the CAF compared to all other fit indices.
#'
#' @return A list of class EFA_AVERAGE containing
#' \item{orig_R}{Original correlation matrix.}
#' \item{h2}{A list with the average, standard deviation, minimum, maximum, and
#' range of the final communality estimates across the factor solutions.}
#' \item{loadings}{A list with the average, standard deviation, minimum, maximum,
#' and range of the final loadings across the factor solutions. If rotation was
#' "none", the unrotated loadings, otherwise the rotated loadings (pattern
#' coefficients).}
#' \item{Phi}{A list with the average, standard deviation, minimum, maximum, and
#' range of the factor intercorrelations across factor solutions obtained with
#' oblique rotations.}
#' \item{ind_fac_corres}{A matrix with each cell containing the proportion of
#' the factor solutions in which the respective indicator-to-factor correspondence
#' occurred, i.e., in which the loading exceeded the specified salience threshold.
#' Note: Rowsums can exceed 1 due to cross-loadings.}
#' \item{vars_accounted}{A list with the average, standard deviation, minimum,
#' maximum, and range of explained variances and sums of squared loadings across
#' the factor solutions. Based on the unrotated loadings.}
#' \item{fit_indices}{A matrix containing the average, standard deviation,
#' minimum, maximum, and range for all applicable fit indices across the respective
#' factor solutions, and the degrees of freedom (df). If the method argument
#' contains ML or ULS: Fit indices derived
#' from the unrotated factor loadings: Chi Square (chisq), including significance
#' level, Comparative Fit Index (CFI), Root Mean Square Error of Approximation
#' (RMSEA), Akaike Information Criterion (AIC), Bayesian Information Criterion
#' (BIC)and the common part accounted for (CAF) index as proposed by
#' Lorenzo-Seva, Timmerman, & Kiers (2011). For PAF, only the CAF can be
#' calculated (see details).}
#' \item{implementations_grid}{A matrix containing, for each performed EFA,
#' the setting combination, if an error occurred (logical), the error message
#' (character), an integer code for convergence as returned by
#' \code{\link[stats:optim]{stats:optim}} (0 indicates successful completion.),
#' if heywood cases occurred (logical, see details for definition), if the
#' solution was admissible (logical, see details for definition), and the fit
#' indices.}
#' \item{efa_list}{A list containing the outputs of all performed EFAs. The names
#' correspond to the rownames from the implementations_grid.}
#' \item{settings}{A list of the settings used.}
#'
#' @source Grieder, S., & Steiner, M.D. (2020). Algorithmic Jingle Jungle:
#' A Comparison of Implementations of Principal Axis Factoring and Promax Rotation
#' in R and SPSS. Manuscript in Preparation.
#' @source Hendrickson, A. E., & White, P. O. (1964). Promax: A quick method for
#' rotation to oblique simple structure. British Journal of Statistical Psychology,
#' 17 , 65–70. doi: 10.1111/j.2044-8317.1964.tb00244.x
#' @source Lorenzo-Seva, U., Timmerman, M. E., & Kiers, H. A. L. (2011). The
#' Hull Method for Selecting the Number of Common Factors, Multivariate Behavioral
#' Research, 46, 340-364, doi: 10.1080/00273171.2011.564527
#' @source Kaiser, H. F. (1958). The varimax criterion for analytic rotation in
#' factor analysis. Psychometrika, 23, 187–200. doi: 10.1007/BF02289233
#'
#' @export
#'
#' @examples
#' \dontrun{
#' # Averaging across different implementations of PAF and promax rotation (72 EFAs)
#' Aver_PAF <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500)
#'
#' # Use median instead of mean for averaging (72 EFAs)
#' Aver_PAF_md <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500,
#' averaging = "median")
#'
#' # Averaging across different implementations of PAF and promax rotation,
#' # and across ULS and different versions of ML (108 EFAs)
#' Aver_meth_ext <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500,
#' method = c("PAF", "ULS", "ML"))
#'
#' # Averaging across one implementation each of PAF (EFAtools type), ULS, and
#' # ML with one implementation of promax (EFAtools type) (3 EFAs)
#' Aver_meth <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500,
#' method = c("PAF", "ULS", "ML"), type = "EFAtools",
#' start_method = "psych")
#'
#' # Averaging across different oblique rotation methods, using one implementation
#' # of ML and one implementation of promax (EFAtools type) (7 EFAs)
#' Aver_rot <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500,
#' method = "ML", rotation = "oblique", type = "EFAtools",
#' start_method = "psych")
#'}
#'
EFA_AVERAGE <- function(x, n_factors, N = NA, method = "PAF", rotation = "promax",
type = "none", averaging = c("mean", "median"), trim = 0,
salience_threshold = .3,
max_iter = 1e4,
init_comm = c("smc", "mac", "unity"),
criterion = c(1e-3),
criterion_type = c("sum", "max_individual"),
abs_eigen = c(TRUE),
varimax_type = c("svd", "kaiser"),
normalize = TRUE,
k_promax = 2:4, k_simplimax = ncol(x),
P_type = c("norm", "unnorm"), precision = 1e-5,
start_method = c("psych", "factanal"),
use = c("pairwise.complete.obs", "all.obs",
"complete.obs", "everything", "na.or.complete"),
cor_method = c("pearson", "spearman", "kendall"),
show_progress = TRUE) {
# Perform argument checks
if(!inherits(x, c("matrix", "data.frame"))){
stop(crayon::red$bold(cli::symbol$circle_cross), crayon::red(" 'x' is neither a matrix nor a dataframe. Either provide a correlation matrix or a dataframe or matrix with raw data.\n"))
}
checkmate::assert_count(n_factors)
checkmate::assert_count(N, na.ok = TRUE)
checkmate::assert_subset(method, c("PAF", "ML", "ULS"),
empty.ok = FALSE)
checkmate::assert_subset(rotation, c("none", "orthogonal", "oblique", "varimax",
"equamax", "quartimax", "geominT", "bentlerT",
"bifactorT", "promax", "oblimin", "quartimin",
"simplimax", "bentlerQ", "geominQ", "bifactorQ"),
empty.ok = FALSE)
checkmate::assert_subset(type, c("none", "EFAtools", "psych", "SPSS"),
empty.ok = FALSE)
averaging <- match.arg(averaging)
checkmate::assert_number(trim, lower = 0, upper = 0.5)
checkmate::assert_number(salience_threshold, lower = 0, upper = 1)
checkmate::assert_count(max_iter)
checkmate::assert_subset(init_comm, c("smc", "mac", "unity"),
empty.ok = FALSE)
checkmate::assert_vector(criterion, strict = TRUE, any.missing = FALSE,
min.len = 1)
checkmate::assert_true(all(criterion > 0 & criterion < 1))
checkmate::assert_subset(criterion_type, c("max_individual", "sum"),
empty.ok = FALSE)
checkmate::assert_subset(abs_eigen, c(TRUE, FALSE),
empty.ok = FALSE)
checkmate::assert_subset(varimax_type, c("svd", "kaiser"),
empty.ok = FALSE)
checkmate::assert_subset(normalize, c(TRUE, FALSE),
empty.ok = FALSE)
checkmate::assert_vector(k_promax, strict = TRUE, any.missing = FALSE,
min.len = 1)
checkmate::assert_vector(k_simplimax, strict = TRUE, any.missing = FALSE,
min.len = 1)
checkmate::assert_subset(P_type, c("unnorm", "norm"),
empty.ok = FALSE)
checkmate::assert_vector(precision, strict = TRUE, any.missing = FALSE,
min.len = 1)
checkmate::assert_true(all(precision > 0 & precision < 1))
checkmate::assert_subset(start_method, c("psych", "factanal"),
empty.ok = FALSE)
use <- match.arg(use)
cor_method <- match.arg(cor_method)
checkmate::assert_flag(show_progress)
# Check if it is a correlation matrix
if(.is_cormat(x)){
R <- x
} else {
message(cli::col_cyan(cli::symbol$info, " 'x' was not a correlation matrix. Correlations are found from entered raw data.\n"))
if (!is.na(N)) {
warning(crayon::yellow$bold("!"), crayon::yellow(" 'N' was set and data entered. Taking N from data.\n"))
}
R <- stats::cor(x, use = use, method = cor_method)
colnames(R) <- colnames(x)
N <- nrow(x)
}
# Check if correlation matrix is invertable, if it is not, stop with message
R_i <- try(solve(R), silent = TRUE)
if (inherits(R_i, "try-error")) {
stop(crayon::red$bold(cli::symbol$circle_cross), crayon::red(" Correlation matrix is singular, no further analyses are performed\n"))
}
# Check if correlation matrix is positive definite, if it is not,
# smooth the matrix (cor.smooth throws a warning)
if (any(eigen(R, symmetric = TRUE, only.values = TRUE)$values <= .Machine$double.eps^.6)) {
R <- psych::cor.smooth(R)
}
# Check if model is identified
# calculate degrees of freedom
m <- ncol(R)
df <- ((m - n_factors)**2 - (m + n_factors)) / 2
if(df < 0){
stop(crayon::red$bold(cli::symbol$circle_cross), crayon::red(" The model is underidentified. Please enter a lower number of factors or use a larger number of indicators and try again.\n"))
} else if (df == 0){
warning(crayon::yellow$bold("!"), crayon::yellow(" The model is just identified (df = 0). We suggest to try again with a lower number of factors or a larger number of indicators.\n"))
}
if (n_factors == 1 && !all(rotation == "none")) {
message(cli::col_cyan(cli::symbol$info, " 'n_factors' is 1, but rotation != 'none'. Setting rotation to 'none' to avoid many warnings, as 1-factor solutions cannot be rotated.\n"))
rotation <- "none"
}
### create the grid with all combinations of the input arguments
grid_list <- list()
if ("PAF" %in% method) {
if ("EFAtools" %in% type) {
grid_list[["ftls_pf"]] <- .type_grid(method = "PAF", init_comm = "smc",
criterion = 1e-3, criterion_type = "sum",
abs_eigen = TRUE, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("psych" %in% type) {
grid_list[["psch_pf"]] <- .type_grid(method = "PAF", init_comm = "smc",
criterion = 1e-3, criterion_type = "sum",
abs_eigen = FALSE, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "unnorm",
precision = 1e-5,
varimax_type = "svd",
k_simplimax = k_simplimax)
}
if ("SPSS" %in% type) {
grid_list[["spss_pf"]] <- .type_grid(method = "PAF", init_comm = "smc",
criterion = 1e-3, criterion_type = "max_individual",
abs_eigen = TRUE, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("none" %in% type) {
grid_list[["nn_pf"]] <- .type_grid(method = "PAF", init_comm = init_comm,
criterion = criterion, criterion_type = criterion_type,
abs_eigen = abs_eigen, start_method = NA,
rotation = rotation, k_promax = k_promax,
normalize = normalize, P_type = P_type,
precision = precision,
varimax_type = varimax_type,
k_simplimax = k_simplimax)
}
}
if ("ML" %in% method) {
if ("EFAtools" %in% type) {
grid_list[["ftls_ml"]] <- .type_grid(method = "ML", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = "psych",
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("psych" %in% type) {
grid_list[["psch_ml"]] <- .type_grid(method = "ML", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = "psych",
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "unnorm",
precision = 1e-5,
varimax_type = "svd",
k_simplimax = k_simplimax)
}
if ("SPSS" %in% type) {
grid_list[["spss_ml"]] <- .type_grid(method = "ML", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = "psych",
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("none" %in% type) {
grid_list[["nn_ml"]] <- .type_grid(method = "ML", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = start_method,
rotation = rotation, k_promax = k_promax,
normalize = normalize, P_type = P_type,
precision = precision,
varimax_type = varimax_type,
k_simplimax = k_simplimax)
}
}
if ("ULS" %in% method) {
if ("EFAtools" %in% type) {
grid_list[["ftls_ls"]] <- .type_grid(method = "ULS", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("psych" %in% type) {
grid_list[["psch_ls"]] <- .type_grid(method = "ULS", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "unnorm",
precision = 1e-5,
varimax_type = "svd",
k_simplimax = k_simplimax)
}
if ("SPSS" %in% type) {
grid_list[["spss_ls"]] <- .type_grid(method = "ULS", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("none" %in% type) {
grid_list[["nn_ls"]] <- .type_grid(method = "ULS", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = NA,
rotation = rotation, k_promax = k_promax,
normalize = normalize, P_type = P_type,
precision = precision,
varimax_type = varimax_type,
k_simplimax = k_simplimax)
}
}
arg_grid <- unique(do.call(rbind, grid_list))
### Run all efas
if (nrow(arg_grid) == 1) {
warning(crayon::yellow$bold("!"), crayon::yellow(" There was only one combination of arguments, returning normal EFA output.\n"))
return(EFA(R, n_factors, N = N, method = arg_grid$method, rotation = arg_grid$rotation,
type = "none", max_iter = max_iter, init_comm = arg_grid$init_comm,
criterion = arg_grid$criterion, criterion_type = arg_grid$criterion_type,
abs_eigen = arg_grid$abs_eigen, varimax_type = arg_grid$varimax_type,
k = ifelse(arg_grid$rotation == "promax", arg_grid$k_promax, arg_grid$k_simplimax),
normalize = arg_grid$normalize, P_type = arg_grid$P_type, precision = precision,
order_type = "eigen", start_method = arg_grid$start_method))
}
if (isTRUE(show_progress)) {
progressr::handlers("progress")
} else {
progressr::handlers("void")
}
progressr::with_progress({
n_efa <- nrow(arg_grid)
if (n_efa <= 10) {
stepsize <- 1
} else {
stepsize <- round(n_efa / 100 * 10)
}
efa_progress_bar <- progressr::progressor(steps = n_efa / stepsize)
efa_progress_bar("Running EFAs:", class = "sticky", amount = 0)
efa_list <- future.apply::future_lapply(1:n_efa,
function(i, methods, rotations,
init_comms, criteria,
criterion_types, abs_eigens,
varimax_types, k_ps, k_ss,
normalizes, P_types, start_methods) {
if (i %% stepsize == 0){
efa_progress_bar(message = sprintf("Running EFA %g of %g", i, n_efa))
}
try(EFA(R, n_factors, N = N, method = methods[i], rotation = rotations[i],
type = "none", max_iter = max_iter, init_comm = init_comms[i],
criterion = criteria[i], criterion_type = criterion_types[i],
abs_eigen = abs_eigens[i], varimax_type = varimax_types[i],
k = ifelse(rotations[i] == "promax",k_ps[i], k_ss[i]),
normalize = normalizes[i], P_type = P_types[i], precision = precision,
order_type = "eigen", start_method = start_methods[i], maxit = 5e4),
silent = TRUE)
}, methods = arg_grid$method, rotations = arg_grid$rotation,
init_comms = arg_grid$init_comm, criteria = arg_grid$criterion,
criterion_types = arg_grid$criterion_type, abs_eigens = arg_grid$abs_eigen,
varimax_types = arg_grid$varimax_type, k_ps = arg_grid$k_promax,
k_ss = arg_grid$k_simplimax, normalizes = arg_grid$normalize,
P_types = arg_grid$P_type, start_methods = arg_grid$start_method,
future.seed = TRUE)
if (n_efa %% 10 != 0){
efa_progress_bar(message = "Done Running EFAs ")
}
})
names(efa_list) <- rownames(arg_grid)
### Extract relevant information from EFA outputs
if (isTRUE(show_progress)) {
.show_av_progress("\U0001f3c3", "Extracting data...")
}
ext_list <- .extract_data(efa_list, R, n_factors, n_efa, rotation, salience_threshold)
if (all(isTRUE(ext_list$for_grid$errors) | ext_list$for_grid$converged != 0 |
isTRUE(ext_list$for_grid$heywood))) {
av_list <- list(
h2 = NA,
loadings = NA,
phi = NA,
ind_fac_corres = NA,
vars_accounted = NA,
fit_indices = NA)
} else {
if (n_factors > 1) {
if (isTRUE(show_progress)) {
.show_av_progress("\U0001f6b6", "Reordering factors...")
}
re_list <- .array_reorder(ext_list$vars_accounted, ext_list$L, ext_list$L_corres,
ext_list$phi, ext_list$extract_phi, n_factors)
} else {
re_list <- ext_list
}
if (isTRUE(show_progress)) {
.show_av_progress("\U0001f3c3", "Averaging data...")
}
av_list <- suppressWarnings(
.average_values(re_list$vars_accounted, re_list$L, re_list$L_corres,
ext_list$h2, re_list$phi, ext_list$extract_phi, averaging,
trim, ext_list$for_grid[, c("chisq", "p_chi", "caf", "cfi",
"rmsea", "aic", "bic")], df,
colnames(R)))
}
arg_grid <- cbind(arg_grid, ext_list$for_grid)
settings <- list(
method = method,
rotation = rotation,
type = type,
n_factors = n_factors,
N = N,
init_comm = init_comm,
criterion = criterion,
criterion_type = criterion_type,
abs_eigen = abs_eigen,
varimax_type = varimax_type,
normalize = normalize,
k_promax = k_promax,
k_simplimax = k_simplimax,
P_type = P_type,
precision = precision,
start_method = start_method,
use = use,
cor_method = cor_method,
max_iter = max_iter,
averaging = averaging,
trim = trim,
salience_threshold = salience_threshold
)
# Create output
output <- list(
orig_R = R,
h2 = av_list$h2,
loadings = av_list$loadings,
Phi = av_list$phi,
ind_fac_corres = av_list$ind_fac_corres,
vars_accounted = av_list$vars_accounted,
fit_indices = av_list$fit_indices,
implementations_grid = arg_grid,
efa_list = efa_list,
settings = settings
)
class(output) <- "EFA_AVERAGE"
if (isTRUE(show_progress)) {
.show_av_progress("", "", done = TRUE)
}
return(output)
}
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Defines functions EFA_AVERAGE
Documented in EFA_AVERAGE
#' Model averaging across different EFA methods and types
#'
#' Not all EFA procedures always arrive at the same solution. This function allows
#' you perform a number of EFAs from different methods (e.g., Maximum Likelihood
#' and Principal Axis Factoring), with different implementations (e.g., the SPSS
#' and psych implementations of Principal Axis Factoring), and across different
#' rotations of the same type (e.g., multiple oblique rotations, like promax and
#' oblimin). EFA_AVERAGE will then run all these EFAs (using the \code{\link{EFA}}
#' function) and provide a summary across the different solutions.
#'
#' @param x data.frame or matrix. Dataframe or matrix of raw data or matrix with
#' correlations. If raw data is entered, the correlation matrix is found from the
#' data.
#' @param n_factors numeric. Number of factors to extract.
#' @param N numeric. The number of observations. Needs only be specified if a
#' correlation matrix is used. If input is a correlation matrix and \code{N} = NA
#' (default), not all fit indices can be computed.
#' @param method character vector. Any combination of "PAF", "ML", and "ULS",
#' to use principal axis factoring, maximum likelihood, or unweighted least
#' squares (also called minres), respectively, to fit the EFAs. Default is "PAF".
#' @param rotation character vector. Either perform no rotation ("none"),
#' any combination of orthogonal rotations ("varimax", "equamax", "quartimax", "geominT",
#' "bentlerT", and "bifactorT"; using "orthogonal" runs all of these), or of
#' oblique rotations ("promax", "oblimin", "quartimin", "simplimax", "bentlerQ",
#' "geominQ", and "bifactorQ"; using "oblique" runs all of these). Rotation types
#' (no rotation, orthogonal rotations, and oblique rotations) cannot be mixed.
#' Default is "promax".
#' @param type character vector. Any combination of "none" (default), "EFAtools",
#' "psych", and "SPSS" can be entered. "none" allows the specification of various
#' combinations of the arguments controlling both factor extraction methods and
#' the rotations. The others ("EFAtools", "psych", and "SPSS"), control the execution
#' of the respective factor extraction method and rotation to be in line with how
#' it is executed in this package (i.e., the respective default procedure), in the
#' psych package, and in SPSS. A specific psych implementation exists for PAF, ML, varimax,
#' and promax. The SPSS implementation exists for PAF, varimax, and promax. For
#' details, see \code{\link{EFA}}.
#' @param averaging character. One of "mean" (default), and "median". Controls
#' whether the different results should be averaged using the (trimmed) mean,
#' or the median.
#' @param trim numeric. If averaging is set to "mean", this argument controls
#' the trimming of extremes (for details see \code{\link[base:mean]{base::mean}}).
#' By default no trimming is done (i.e., trim = 0).
#' @param salience_threshold numeric. The threshold to use to classify a pattern
#' coefficient or loading as salient (i.e., substantial enough to assign it to
#' a factor). Default is 0.3. Indicator-to-factor correspondences will be inferred
#' based on this threshold. Note that this may not be meaningful if rotation = "none"
#' and n_factors > 1 are used, as no simple structure is present there.
#' @param max_iter numeric. The maximum number of iterations to perform after which
#' the iterative PAF procedure is halted with a warning. Default is 10,000. Note
#' that non-converged procedures are excluded from the averaging procedure.
#' @param init_comm character vector. Any combination of "smc", "mac", and "unity".
#' Controls the methods to estimate the initial communalities in \code{PAF} if
#' "none" is among the specified types. "smc" will use squared multiple
#' correlations, "mac" will use maximum absolute correlations, "unity" will use
#' 1s (for details see \code{\link{EFA}}). Default is \code{c("smc", "mac", "unity")}.
#' @param criterion numeric vector. The convergence criterion used for PAF if
#' "none" is among the specified types.
#' If the change in communalities from one iteration to the next is smaller than
#' this criterion the solution is accepted and the procedure ends.
#' Default is \code{0.001}.
#' @param criterion_type character vector. Any combination of "max_individual" and
#' "sum". Type of convergence criterion used for PAF if "none" is among the
#' specified types. "max_individual" selects the maximum change in any of the
#' communalities from one iteration to the next and tests it against the
#' specified criterion. "sum" takes the difference of
#' the sum of all communalities in one iteration and the sum of all communalities
#' in the next iteration and tests this against the criterion
#' (for details see \code{\link{EFA}}). Default is \code{c("sum", "max_individual")}.
#' @param abs_eigen logical vector. Any combination of TRUE and FALSE.
#' Which algorithm to use in the PAF iterations if "none" is among the specified
#' types. If FALSE, the loadings are computed from the eigenvalues. This is also
#' used by the \code{\link[psych:fa]{psych::fa}} function. If TRUE the
#' loadings are computed with the absolute eigenvalues as done by SPSS
#' (for details see \code{\link{EFA}}). Default is \code{TRUE}.
#' @param varimax_type character vector. Any combination of "svd" and "kaiser".
#' The type of the varimax rotation performed if "none" is among the specified
#' types and "varimax", "promax", "orthogonal", or "oblique" is among the specified
#' rotations. "svd" uses singular value decomposition, as
#' \link[stats:varimax]{stats::varimax} does, and "kaiser" uses the varimax
#' procedure performed in SPSS. This is the original procedure from Kaiser (1958),
#' but with slight alterations in the varimax criterion (for details, see
#' \code{\link{EFA}} and Grieder & Steiner, 2020).
#' Default is \code{c("svd", "kaiser")}.
#' @param normalize logical vector. Any combination of TRUE and FALSE.
#' \code{TRUE} performs a kaiser normalization before the specified rotation(s).
#' Default is \code{TRUE}.
#' @param k_promax numeric vector. The power used for computing the target matrix
#' P in the promax rotation if "none" is among the specified types and "promax"
#' or "oblique" is among the specified rotations. Default is \code{2:4}.
#' @param k_simplimax numeric. The number of 'close to zero loadings' for the
#' simplimax rotation (see \code{\link[GPArotation:GPA]{GPArotation::GPFoblq}})
#' if "simplimax" or "oblique" is among the specified rotations. Default
#' is \code{ncol(x)}, where x is the entered data.
#' @param P_type character vector. Any combination of "norm" and "unnorm".
#' This specifies how the target matrix P is computed in promax rotation if
#' "none" is among the specified types and "promax" or "oblique" is among the
#' specified rotations. "unnorm" will use the unnormalized target matrix as
#' originally done in Hendrickson and White (1964). "norm" will use a
#' normalized target matrix (for details see \code{\link{EFA}}).
#' Default is \code{c("norm", "unnorm")}.
#' @param precision numeric vector. The tolerance for stopping in the rotation
#' procedure(s). Default is 10^-5.
#' @param start_method character vector. Any combination of "psych" and "factanal".
#' How to specify the starting values for the optimization procedure for ML.
#' "psych" takes the starting values specified in \link[psych:fa]{psych::fa}.
#' "factanal" takes the starting values specified in the
#' \link[stats:factanal]{stats::factanal} function. Default is
#' \code{c("psych", "factanal")}.
#' @param use character. Passed to \code{\link[stats:cor]{stats::cor}} if raw data
#' is given as input. Default is "pairwise.complete.obs".
#' @param cor_method character. Passed to \code{\link[stats:cor]{stats::cor}}.
#' Default is "pearson".
#' @param show_progress logical. Whether a progress bar should be shown in the
#' console. Default is TRUE.
#'
#' @details
#'
#' As a first step in this function, a grid is produced containing the setting
#' combinations for the to-be-performed EFAs. These settings are then entered as
#' arguments to the \code{\link{EFA}} function and the EFAs are run in a second
#' step. After all EFAs are run, the factor solutions are averaged and their
#' variability determined in a third step.
#'
#' The grid containing the setting combinations is produced based on the entries
#' to the respective arguments. To this end, all possible combinations resulting
#' in unique EFA models are considered. That is, if, for example, the \code{type}
#' argument was set to \code{c("none", "SPSS")} and one combination of the specific
#' settings entered was identical to the SPSS combination, this combination
#' would be included in the grid and run only once. We include here a list
#' of arguments that are only evaluated under specific conditions:
#'
#' The arguments \code{init_comm}, \code{criterion}, \code{criterion_type},
#' \code{abs_eigen} are only evaluated if "PAF" is included in \code{method}
#' and "none" is included in \code{type}.
#'
#' The argument \code{varimax_type} is only evaluated if "varimax", "promax",
#' "oblique", or "orthogonal" is included in \code{rotation} and "none" is
#' included in \code{type}.
#'
#' The argument \code{normalize} is only evaluated if \code{rotation} is not
#' set to "none" and "none" is included in \code{type}.
#'
#' The argument \code{k_simplimax} is only evaluated if "simplimax" or "oblique"
#' is included in \code{rotation}.
#'
#' The arguments \code{k_promax} and \code{P_type} are only evaluated if
#' "promax" or "oblique" is included in \code{rotation} and "none" is included
#' in \code{type}.
#'
#' The argument \code{start_method} is only evaluated if "ML" is included in
#' \code{method}.
#'
#' To avoid a bias in the averaged factor solutions from problematic solutions,
#' these are excluded prior to averaging. A solution is deemed problematic if
#' at least one of the following is true: an error occurred, the model did not
#' converge, or there is at least one Heywood case (defined as a loading or communality of >= .998).
#' Information on errors, convergence, and Heywood cases are returned in the
#' implementations_grid and a summary of these is given when printing the output.
#' In addition to these, information on the admissibility of the factor solutions
#' is also included. A solution was deemed admissible if (1) no error occurred,
#' (2) the model converged, (3) no Heywood cases are present, and (4) there are
#' at least two salient loadings (i.e., loadings exceeding the specified
#' \code{salience_threshold}) for each factor. So, solutions failing one of the
#' first three of these criteria of admissibility are also deemed problematic and
#' therefore excluded from averaging. However, solutions failing only
#' the fourth criterion of admissibility are still included for averaging.
#' Finally, if all solutions are problematic (e.g., all solutions contain
#' Heywood cases), no averaging is performed and the respective outputs are NA.
#' In this case, the implementations_grid should be inspected to see if there
#' are any error messages, and the separate EFA solutions that are also included
#' in the output can be inspected as well, for example, to see where Heywood
#' cases occurred.
#'
#' A core output of this function includes the average, minimum, and maximum
#' loadings derived from all non-problematic (see above) factor solutions. Please
#' note that these are not entire solutions, but the matrices include the average,
#' minimum, or maximum value for each cell (i.e., each loading separately). This
#' means that, for example, the matrix with the minimum loadings will contain
#' the minimum value in any of the factor solutions for each specific loading,
#' and therefore most likely contains loadings from different factor solutions.
#' The matrices containing the minimum and maximum factor solutions can
#' therefore not be interpreted as whole factor solutions.
#'
#' The output also includes information on the average, minimum, maximum, and
#' variability of the fit indices across the non-problematic factor solutions.
#' It is important to note that not all fit indices are computed for all fit
#' methods: For ML and ULS, all fit indices can be computed, while for PAF, only
#' the common part accounted for (CAF) index (Lorenzo-Seva, Timmerman, & Kiers, 2011)
#' can be computed. As a consequence, if only "PAF" is included in the
#' \code{method} argument, averaging can only be performed for the CAF, and the
#' other fit indices are NA. If a combination of "PAF" and "ML" and/or "ULS" are
#' included in the \code{method} argument, the CAF is averaged across all non-
#' problematic factor solutions, while all other fit indices are only averaged
#' across the ML and ULS solutions. The user should therefore keep in mind that
#' the number of EFAs across which the fit indices are averaged can diverge for
#' the CAF compared to all other fit indices.
#'
#' @return A list of class EFA_AVERAGE containing
#' \item{orig_R}{Original correlation matrix.}
#' \item{h2}{A list with the average, standard deviation, minimum, maximum, and
#' range of the final communality estimates across the factor solutions.}
#' \item{loadings}{A list with the average, standard deviation, minimum, maximum,
#' and range of the final loadings across the factor solutions. If rotation was
#' "none", the unrotated loadings, otherwise the rotated loadings (pattern
#' coefficients).}
#' \item{Phi}{A list with the average, standard deviation, minimum, maximum, and
#' range of the factor intercorrelations across factor solutions obtained with
#' oblique rotations.}
#' \item{ind_fac_corres}{A matrix with each cell containing the proportion of
#' the factor solutions in which the respective indicator-to-factor correspondence
#' occurred, i.e., in which the loading exceeded the specified salience threshold.
#' Note: Rowsums can exceed 1 due to cross-loadings.}
#' \item{vars_accounted}{A list with the average, standard deviation, minimum,
#' maximum, and range of explained variances and sums of squared loadings across
#' the factor solutions. Based on the unrotated loadings.}
#' \item{fit_indices}{A matrix containing the average, standard deviation,
#' minimum, maximum, and range for all applicable fit indices across the respective
#' factor solutions, and the degrees of freedom (df). If the method argument
#' contains ML or ULS: Fit indices derived
#' from the unrotated factor loadings: Chi Square (chisq), including significance
#' level, Comparative Fit Index (CFI), Root Mean Square Error of Approximation
#' (RMSEA), Akaike Information Criterion (AIC), Bayesian Information Criterion
#' (BIC)and the common part accounted for (CAF) index as proposed by
#' Lorenzo-Seva, Timmerman, & Kiers (2011). For PAF, only the CAF can be
#' calculated (see details).}
#' \item{implementations_grid}{A matrix containing, for each performed EFA,
#' the setting combination, if an error occurred (logical), the error message
#' (character), an integer code for convergence as returned by
#' \code{\link[stats:optim]{stats:optim}} (0 indicates successful completion.),
#' if heywood cases occurred (logical, see details for definition), if the
#' solution was admissible (logical, see details for definition), and the fit
#' indices.}
#' \item{efa_list}{A list containing the outputs of all performed EFAs. The names
#' correspond to the rownames from the implementations_grid.}
#' \item{settings}{A list of the settings used.}
#'
#' @source Grieder, S., & Steiner, M.D. (2020). Algorithmic Jingle Jungle:
#' A Comparison of Implementations of Principal Axis Factoring and Promax Rotation
#' in R and SPSS. Manuscript in Preparation.
#' @source Hendrickson, A. E., & White, P. O. (1964). Promax: A quick method for
#' rotation to oblique simple structure. British Journal of Statistical Psychology,
#' 17 , 65–70. doi: 10.1111/j.2044-8317.1964.tb00244.x
#' @source Lorenzo-Seva, U., Timmerman, M. E., & Kiers, H. A. L. (2011). The
#' Hull Method for Selecting the Number of Common Factors, Multivariate Behavioral
#' Research, 46, 340-364, doi: 10.1080/00273171.2011.564527
#' @source Kaiser, H. F. (1958). The varimax criterion for analytic rotation in
#' factor analysis. Psychometrika, 23, 187–200. doi: 10.1007/BF02289233
#'
#' @export
#'
#' @examples
#' \dontrun{
#' # Averaging across different implementations of PAF and promax rotation (72 EFAs)
#' Aver_PAF <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500)
#'
#' # Use median instead of mean for averaging (72 EFAs)
#' Aver_PAF_md <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500,
#' averaging = "median")
#'
#' # Averaging across different implementations of PAF and promax rotation,
#' # and across ULS and different versions of ML (108 EFAs)
#' Aver_meth_ext <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500,
#' method = c("PAF", "ULS", "ML"))
#'
#' # Averaging across one implementation each of PAF (EFAtools type), ULS, and
#' # ML with one implementation of promax (EFAtools type) (3 EFAs)
#' Aver_meth <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500,
#' method = c("PAF", "ULS", "ML"), type = "EFAtools",
#' start_method = "psych")
#'
#' # Averaging across different oblique rotation methods, using one implementation
#' # of ML and one implementation of promax (EFAtools type) (7 EFAs)
#' Aver_rot <- EFA_AVERAGE(test_models$baseline$cormat, n_factors = 3, N = 500,
#' method = "ML", rotation = "oblique", type = "EFAtools",
#' start_method = "psych")
#'}
#'
EFA_AVERAGE <- function(x, n_factors, N = NA, method = "PAF", rotation = "promax",
type = "none", averaging = c("mean", "median"), trim = 0,
salience_threshold = .3,
max_iter = 1e4,
init_comm = c("smc", "mac", "unity"),
criterion = c(1e-3),
criterion_type = c("sum", "max_individual"),
abs_eigen = c(TRUE),
varimax_type = c("svd", "kaiser"),
normalize = TRUE,
k_promax = 2:4, k_simplimax = ncol(x),
P_type = c("norm", "unnorm"), precision = 1e-5,
start_method = c("psych", "factanal"),
use = c("pairwise.complete.obs", "all.obs",
"complete.obs", "everything", "na.or.complete"),
cor_method = c("pearson", "spearman", "kendall"),
show_progress = TRUE) {
# Perform argument checks
if(!inherits(x, c("matrix", "data.frame"))){
stop(crayon::red$bold(cli::symbol$circle_cross), crayon::red(" 'x' is neither a matrix nor a dataframe. Either provide a correlation matrix or a dataframe or matrix with raw data.\n"))
}
checkmate::assert_count(n_factors)
checkmate::assert_count(N, na.ok = TRUE)
checkmate::assert_subset(method, c("PAF", "ML", "ULS"),
empty.ok = FALSE)
checkmate::assert_subset(rotation, c("none", "orthogonal", "oblique", "varimax",
"equamax", "quartimax", "geominT", "bentlerT",
"bifactorT", "promax", "oblimin", "quartimin",
"simplimax", "bentlerQ", "geominQ", "bifactorQ"),
empty.ok = FALSE)
checkmate::assert_subset(type, c("none", "EFAtools", "psych", "SPSS"),
empty.ok = FALSE)
averaging <- match.arg(averaging)
checkmate::assert_number(trim, lower = 0, upper = 0.5)
checkmate::assert_number(salience_threshold, lower = 0, upper = 1)
checkmate::assert_count(max_iter)
checkmate::assert_subset(init_comm, c("smc", "mac", "unity"),
empty.ok = FALSE)
checkmate::assert_vector(criterion, strict = TRUE, any.missing = FALSE,
min.len = 1)
checkmate::assert_true(all(criterion > 0 & criterion < 1))
checkmate::assert_subset(criterion_type, c("max_individual", "sum"),
empty.ok = FALSE)
checkmate::assert_subset(abs_eigen, c(TRUE, FALSE),
empty.ok = FALSE)
checkmate::assert_subset(varimax_type, c("svd", "kaiser"),
empty.ok = FALSE)
checkmate::assert_subset(normalize, c(TRUE, FALSE),
empty.ok = FALSE)
checkmate::assert_vector(k_promax, strict = TRUE, any.missing = FALSE,
min.len = 1)
checkmate::assert_vector(k_simplimax, strict = TRUE, any.missing = FALSE,
min.len = 1)
checkmate::assert_subset(P_type, c("unnorm", "norm"),
empty.ok = FALSE)
checkmate::assert_vector(precision, strict = TRUE, any.missing = FALSE,
min.len = 1)
checkmate::assert_true(all(precision > 0 & precision < 1))
checkmate::assert_subset(start_method, c("psych", "factanal"),
empty.ok = FALSE)
use <- match.arg(use)
cor_method <- match.arg(cor_method)
checkmate::assert_flag(show_progress)
# Check if it is a correlation matrix
if(.is_cormat(x)){
R <- x
} else {
message(cli::col_cyan(cli::symbol$info, " 'x' was not a correlation matrix. Correlations are found from entered raw data.\n"))
if (!is.na(N)) {
warning(crayon::yellow$bold("!"), crayon::yellow(" 'N' was set and data entered. Taking N from data.\n"))
}
R <- stats::cor(x, use = use, method = cor_method)
colnames(R) <- colnames(x)
N <- nrow(x)
}
# Check if correlation matrix is invertable, if it is not, stop with message
R_i <- try(solve(R), silent = TRUE)
if (inherits(R_i, "try-error")) {
stop(crayon::red$bold(cli::symbol$circle_cross), crayon::red(" Correlation matrix is singular, no further analyses are performed\n"))
}
# Check if correlation matrix is positive definite, if it is not,
# smooth the matrix (cor.smooth throws a warning)
if (any(eigen(R, symmetric = TRUE, only.values = TRUE)$values <= .Machine$double.eps^.6)) {
R <- psych::cor.smooth(R)
}
# Check if model is identified
# calculate degrees of freedom
m <- ncol(R)
df <- ((m - n_factors)**2 - (m + n_factors)) / 2
if(df < 0){
stop(crayon::red$bold(cli::symbol$circle_cross), crayon::red(" The model is underidentified. Please enter a lower number of factors or use a larger number of indicators and try again.\n"))
} else if (df == 0){
warning(crayon::yellow$bold("!"), crayon::yellow(" The model is just identified (df = 0). We suggest to try again with a lower number of factors or a larger number of indicators.\n"))
}
if (n_factors == 1 && !all(rotation == "none")) {
message(cli::col_cyan(cli::symbol$info, " 'n_factors' is 1, but rotation != 'none'. Setting rotation to 'none' to avoid many warnings, as 1-factor solutions cannot be rotated.\n"))
rotation <- "none"
}
### create the grid with all combinations of the input arguments
grid_list <- list()
if ("PAF" %in% method) {
if ("EFAtools" %in% type) {
grid_list[["ftls_pf"]] <- .type_grid(method = "PAF", init_comm = "smc",
criterion = 1e-3, criterion_type = "sum",
abs_eigen = TRUE, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("psych" %in% type) {
grid_list[["psch_pf"]] <- .type_grid(method = "PAF", init_comm = "smc",
criterion = 1e-3, criterion_type = "sum",
abs_eigen = FALSE, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "unnorm",
precision = 1e-5,
varimax_type = "svd",
k_simplimax = k_simplimax)
}
if ("SPSS" %in% type) {
grid_list[["spss_pf"]] <- .type_grid(method = "PAF", init_comm = "smc",
criterion = 1e-3, criterion_type = "max_individual",
abs_eigen = TRUE, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("none" %in% type) {
grid_list[["nn_pf"]] <- .type_grid(method = "PAF", init_comm = init_comm,
criterion = criterion, criterion_type = criterion_type,
abs_eigen = abs_eigen, start_method = NA,
rotation = rotation, k_promax = k_promax,
normalize = normalize, P_type = P_type,
precision = precision,
varimax_type = varimax_type,
k_simplimax = k_simplimax)
}
}
if ("ML" %in% method) {
if ("EFAtools" %in% type) {
grid_list[["ftls_ml"]] <- .type_grid(method = "ML", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = "psych",
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("psych" %in% type) {
grid_list[["psch_ml"]] <- .type_grid(method = "ML", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = "psych",
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "unnorm",
precision = 1e-5,
varimax_type = "svd",
k_simplimax = k_simplimax)
}
if ("SPSS" %in% type) {
grid_list[["spss_ml"]] <- .type_grid(method = "ML", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = "psych",
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("none" %in% type) {
grid_list[["nn_ml"]] <- .type_grid(method = "ML", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = start_method,
rotation = rotation, k_promax = k_promax,
normalize = normalize, P_type = P_type,
precision = precision,
varimax_type = varimax_type,
k_simplimax = k_simplimax)
}
}
if ("ULS" %in% method) {
if ("EFAtools" %in% type) {
grid_list[["ftls_ls"]] <- .type_grid(method = "ULS", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("psych" %in% type) {
grid_list[["psch_ls"]] <- .type_grid(method = "ULS", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "unnorm",
precision = 1e-5,
varimax_type = "svd",
k_simplimax = k_simplimax)
}
if ("SPSS" %in% type) {
grid_list[["spss_ls"]] <- .type_grid(method = "ULS", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = NA,
rotation = rotation, k_promax = 4,
normalize = TRUE, P_type = "norm",
precision = 1e-5,
varimax_type = "kaiser",
k_simplimax = k_simplimax)
}
if ("none" %in% type) {
grid_list[["nn_ls"]] <- .type_grid(method = "ULS", init_comm = NA,
criterion = NA, criterion_type = NA,
abs_eigen = NA, start_method = NA,
rotation = rotation, k_promax = k_promax,
normalize = normalize, P_type = P_type,
precision = precision,
varimax_type = varimax_type,
k_simplimax = k_simplimax)
}
}
arg_grid <- unique(do.call(rbind, grid_list))
### Run all efas
if (nrow(arg_grid) == 1) {
warning(crayon::yellow$bold("!"), crayon::yellow(" There was only one combination of arguments, returning normal EFA output.\n"))
return(EFA(R, n_factors, N = N, method = arg_grid$method, rotation = arg_grid$rotation,
type = "none", max_iter = max_iter, init_comm = arg_grid$init_comm,
criterion = arg_grid$criterion, criterion_type = arg_grid$criterion_type,
abs_eigen = arg_grid$abs_eigen, varimax_type = arg_grid$varimax_type,
k = ifelse(arg_grid$rotation == "promax", arg_grid$k_promax, arg_grid$k_simplimax),
normalize = arg_grid$normalize, P_type = arg_grid$P_type, precision = precision,
order_type = "eigen", start_method = arg_grid$start_method))
}
if (isTRUE(show_progress)) {
progressr::handlers("progress")
} else {
progressr::handlers("void")
}
progressr::with_progress({
n_efa <- nrow(arg_grid)
if (n_efa <= 10) {
stepsize <- 1
} else {
stepsize <- round(n_efa / 100 * 10)
}
efa_progress_bar <- progressr::progressor(steps = n_efa / stepsize)
efa_progress_bar("Running EFAs:", class = "sticky", amount = 0)
efa_list <- future.apply::future_lapply(1:n_efa,
function(i, methods, rotations,
init_comms, criteria,
criterion_types, abs_eigens,
varimax_types, k_ps, k_ss,
normalizes, P_types, start_methods) {
if (i %% stepsize == 0){
efa_progress_bar(message = sprintf("Running EFA %g of %g", i, n_efa))
}
try(EFA(R, n_factors, N = N, method = methods[i], rotation = rotations[i],
type = "none", max_iter = max_iter, init_comm = init_comms[i],
criterion = criteria[i], criterion_type = criterion_types[i],
abs_eigen = abs_eigens[i], varimax_type = varimax_types[i],
k = ifelse(rotations[i] == "promax",k_ps[i], k_ss[i]),
normalize = normalizes[i], P_type = P_types[i], precision = precision,
order_type = "eigen", start_method = start_methods[i], maxit = 5e4),
silent = TRUE)
}, methods = arg_grid$method, rotations = arg_grid$rotation,
init_comms = arg_grid$init_comm, criteria = arg_grid$criterion,
criterion_types = arg_grid$criterion_type, abs_eigens = arg_grid$abs_eigen,
varimax_types = arg_grid$varimax_type, k_ps = arg_grid$k_promax,
k_ss = arg_grid$k_simplimax, normalizes = arg_grid$normalize,
P_types = arg_grid$P_type, start_methods = arg_grid$start_method,
future.seed = TRUE)
if (n_efa %% 10 != 0){
efa_progress_bar(message = "Done Running EFAs ")
}
})
names(efa_list) <- rownames(arg_grid)
### Extract relevant information from EFA outputs
if (isTRUE(show_progress)) {
.show_av_progress("\U0001f3c3", "Extracting data...")
}
ext_list <- .extract_data(efa_list, R, n_factors, n_efa, rotation, salience_threshold)
if (all(isTRUE(ext_list$for_grid$errors) | ext_list$for_grid$converged != 0 |
isTRUE(ext_list$for_grid$heywood))) {
av_list <- list(
h2 = NA,
loadings = NA,
phi = NA,
ind_fac_corres = NA,
vars_accounted = NA,
fit_indices = NA)
} else {
if (n_factors > 1) {
if (isTRUE(show_progress)) {
.show_av_progress("\U0001f6b6", "Reordering factors...")
}
re_list <- .array_reorder(ext_list$vars_accounted, ext_list$L, ext_list$L_corres,
ext_list$phi, ext_list$extract_phi, n_factors)
} else {
re_list <- ext_list
}
if (isTRUE(show_progress)) {
.show_av_progress("\U0001f3c3", "Averaging data...")
}
av_list <- suppressWarnings(
.average_values(re_list$vars_accounted, re_list$L, re_list$L_corres,
ext_list$h2, re_list$phi, ext_list$extract_phi, averaging,
trim, ext_list$for_grid[, c("chisq", "p_chi", "caf", "cfi",
"rmsea", "aic", "bic")], df,
colnames(R)))
}
arg_grid <- cbind(arg_grid, ext_list$for_grid)
settings <- list(
method = method,
rotation = rotation,
type = type,
n_factors = n_factors,
N = N,
init_comm = init_comm,
criterion = criterion,
criterion_type = criterion_type,
abs_eigen = abs_eigen,
varimax_type = varimax_type,
normalize = normalize,
k_promax = k_promax,
k_simplimax = k_simplimax,
P_type = P_type,
precision = precision,
start_method = start_method,
use = use,
cor_method = cor_method,
max_iter = max_iter,
averaging = averaging,
trim = trim,
salience_threshold = salience_threshold
)
# Create output
output <- list(
orig_R = R,
h2 = av_list$h2,
loadings = av_list$loadings,
Phi = av_list$phi,
ind_fac_corres = av_list$ind_fac_corres,
vars_accounted = av_list$vars_accounted,
fit_indices = av_list$fit_indices,
implementations_grid = arg_grid,
efa_list = efa_list,
settings = settings
)
class(output) <- "EFA_AVERAGE"
if (isTRUE(show_progress)) {
.show_av_progress("", "", done = TRUE)
}
return(output)
}
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