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#' ctmaEmpCov
#'
#' @description changes a full covariance matrix by selecting target variables, recoding them, combining them (compute the
#' mean of two or more variables), and by adding rows/columns with NA if focal variables are not available.
#'
#' @param targetVariables (col-/row-) number or names of the target variables
#' @param recodeVariables (col-/row-) number or names of the target variables require inverse coding
#' @param combineVariables list of vectors, which put together the targeted variables that should be used for composite variables
#' @param combineVariablesNames new names for combined variables - not really important
#' @param missingVariables missing variables
#' @param nlatents number of (latent) variables - actually it is the number of all variables
#' @param Tpoints number of time points.
#' @param sampleSize sample size
#' @param pairwiseN matrix of same dimensions as empcov containing possible pairwiseN.
#' @param empcov empirical correlation matrix
#'
#' @importFrom psych corr.test
#' @importFrom MASS mvrnorm
#' @importFrom crayon red blue
#'
#' @export ctmaEmpCov
#'
#' @examples
#' source17 <- c()
#' delta_t17 <- c(12)
#' sampleSize17 <- 440
#' empcov17 <- matrix(
#' c( 1.00, -0.60, -0.36, 0.20, 0.62, -0.47, -0.18, 0.20,
#' -0.60, 1.00, 0.55, -0.38, -0.43, 0.52, 0.27, -0.21,
#' -0.36, 0.55, 1.00, -0.47, -0.26, 0.37, 0.51, -0.28,
#' 0.20, -0.38, -0.47, 1.00, 0.15, -0.28, -0.35, 0.56,
#' 0.62, -0.43, -0.26, 0.15, 1.00, -0.63, -0.30, 0.27,
#' -0.47, 0.52, 0.37, -0.28, -0.63, 1.00, 0.55, -0.37,
#' -0.18, 0.27, 0.51, -0.35, -0.30, 0.55, 1.00, -0.51,
#' 0.20, -0.21, -0.28, 0.56, 0.27, -0.37, -0.51, 1.00),
#' nrow=8, ncol=8)
#' moderator17 <- c(3, 2)
#' rownames(empcov17) <- colnames(empcov17) <-
#' c("Workload_1", "Exhaustion_1", "Cynicism_1", "Values_1",
#' "Workload_2", "Exhaustion_2", "Cynicism_2", "Values_2")
#' targetVariables17 <-
#' c("Workload_1", "Exhaustion_1", "Cynicism_1",
#' "Workload_2", "Exhaustion_2", "Cynicism_2")
#' recodeVariables17 <- c("Workload_1", "Workload_2")
#' combineVariables17 <- list("Workload_1", c("Exhaustion_1", "Cynicism_1"),
#' "Workload_2", c("Exhaustion_2", "Cynicism_2"))
#' combineVariablesNames17 <- c("Demands_1", "Burnout_1",
#' "Demands_2", "Burnout_2")
#' missingVariables17 <- c();
#' results17 <- ctmaEmpCov(targetVariables = targetVariables17,
#' recodeVariables = recodeVariables17,
#' combineVariables = combineVariables17,
#' combineVariablesNames = combineVariablesNames17,
#' missingVariables = missingVariables17,
#' nlatents = 2, sampleSize = sampleSize17,
#' Tpoints = 2, empcov = empcov17)
#' empcov17 <- results17$r
#'
#' @return returns a list with two elements. The first element (results$r) contains the adapted correlation matrix, and
#' the second element (results$pairwiseNNew) an adapted version of a matrix of pairwise N if pariwiseN was provided for
#' the original correlation matrix supplied.
#'
ctmaEmpCov <- function(targetVariables=NULL, recodeVariables=c(), combineVariables=c(),
combineVariablesNames=c(), missingVariables=c(),
nlatents=NULL, Tpoints=NULL, sampleSize=NULL, pairwiseN=NULL, empcov=NULL) {
# check
if (is.null(sampleSize) & is.null(pairwiseN) ) {
ErrorMsg <- "\nSample size (sampleSize) or pairwise N (pairwiseN) has to be provided! \nGood luck for the next try!"
stop(ErrorMsg)
}
if (is.null(empcov)) {
ErrorMsg <- "\nEmpirical correlation matrix has to be provided! \nGood luck for the next try!"
stop(ErrorMsg)
}
# correct and then replace pairwise N (not required for data generation; only to provide corrected pairwise N after variables are combined)
if (!(is.null(pairwiseN))) {
tmp1 <- which(colnames(empcov) %in% targetVariables)
pairwiseN <- pairwiseN[tmp1, tmp1]
pairwiseNbackup <- pairwiseN
if (is.null(sampleSize)) sampleSize <- max(pairwiseN) # max to avoid 0
pairwiseN <- NULL
} else {
pairwiseNbackup <- matrix(sampleSize, dim(empcov)[1], dim(empcov)[2])
}
# select subset of variables
if (!(is.null(targetVariables))) {
tmp1 <- which(colnames(empcov) %in% targetVariables)
empcov <- empcov[targetVariables, targetVariables]; empcov
} else {
tmp1 <- 1:dim(empcov)[1]
}
# recode variables (correlations)
for (i in recodeVariables) {
empcov[i, ] <- -1 * empcov[i, ]
empcov[ ,i] <- -1 * empcov[ ,i]
}
# combine variables
tmpData <- as.data.frame(MASS::mvrnorm(n=sampleSize, mu=rep(0, dim(empcov)[1]), Sigma=empcov, empirical = TRUE))
newPairwiseN <- c()
if(length(combineVariables) > 0) {
for (i in 1:length(combineVariables)) {
tmp1 <- which(targetVariables %in% combineVariables[[i]]); tmp1
if (length(tmp1) > 1) {
newPairwiseN[i] <- min(pairwiseNbackup[tmp1, tmp1]); newPairwiseN[i]
tmp2 <- pairwiseNbackup; tmp2
diag(tmp2) <- 99999999
lowerPart <- 1:(min(tmp1)-1); lowerPart
upperPart <- (max(tmp1)+1):(dim(pairwiseNbackup)[1]); upperPart
if (min(lowerPart) >= 1) {
tmp3lower <- min(tmp2[tmp1, lowerPart]); tmp3lower
pairwiseNbackup[lowerPart, tmp1] <- tmp3lower
pairwiseNbackup[tmp1, lowerPart] <- tmp3lower
}
if (max(upperPart) <= (dim(empcov)[1])) {
tmp3upper <- min(tmp2[tmp1, upperPart]); tmp3upper
pairwiseNbackup[upperPart, tmp1] <- tmp3upper
pairwiseNbackup[tmp1, upperPart] <- tmp3upper
}
pairwiseNbackup[tmp1, tmp1] <- newPairwiseN[i]
}
tmpData$tmpName <- apply(tmpData[combineVariables[[i]]], 1, mean, na.rm=TRUE)
tmp <- names(tmpData); tmp
tmp[length(tmp)] <- combineVariablesNames[i]; tmp
names(tmpData) <- tmp; names(tmpData)
}
data <- tmpData[, -c(1:(dim(empcov)[1]))]
tmp1 <- unlist(lapply(combineVariables,function(extract) length(extract))); tmp1
targetCols <- c()
for (j in 1:(length(tmp1))) targetCols[j] <- sum(tmp1[1:j])
pairwiseN <- pairwiseNbackup[targetCols , targetCols]
} else {
data <- tmpData
}
tmp <- psych::corr.test(data, ci=FALSE)
empcovNew <- tmp$r
pairwiseNNew <- tmp$n
if (exists("pairwiseNbackup")) pairwiseNNew <- pairwiseNbackup
# the var of combined variables != 0 => cov to cor
dc <- diag(empcovNew)
So <- sqrt(dc)
ds <- diag(1/So)
Mo <- ds %*% empcovNew %*% ds
Mo <- Mo - 0.5*(Mo-t(Mo)) # Correct any round-off error
empcovNew <- tmpMat <- Mo
# impute missingness pattern
numberOfMissingVars <- length(missingVariables); numberOfMissingVars
if (numberOfMissingVars > 0) {
presentVariables <- which(!((1:(Tpoints*nlatents)) %in% missingVariables)); presentVariables
tmpMat <- tmpMatN <- matrix(NA, Tpoints*nlatents, Tpoints*nlatents)
counter <- 1
for (i in 1:(Tpoints*nlatents)) {
if (i %in% missingVariables) {
tmpMat[i, ] <- NA
tmpMat[ ,i] <- NA
if (exists("pairwiseN")) {
tmpMatN[i, ] <- 0
tmpMatN[, i] <- 0
}
} else {
tmpMat[presentVariables[counter], presentVariables] <- empcovNew[counter, ]
tmpMat[presentVariables ,presentVariables[counter]] <- empcovNew[ ,counter]
if (exists("pairwiseN")) {
tmpMatN[presentVariables[counter], presentVariables] <- pairwiseN[counter, ]
tmpMatN[presentVariables ,presentVariables[counter]] <- pairwiseN[ ,counter]
}
counter <- counter + 1
}
}
pairwiseNNew <- tmpMatN
}
results <- list()
results$r <- tmpMat
results$pairwiseNNew <- pairwiseNNew
return(results)
}
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