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R/EFA.R
In EFA.dimensions: Exploratory Factor Analysis Functions for Assessing Dimensionality
Defines functions
IMAGE_FA
MAXLIKE_FA
PA_FA
Documented in
IMAGE_FA
MAXLIKE_FA
PA_FA
PA_FA <- function( ... ) { .Defunct("EFA", package="EFA.dimensions") }
MAXLIKE_FA <- function( ... ) { .Defunct("EFA", package="EFA.dimensions") }
IMAGE_FA <- function( ... ) { .Defunct("EFA", package="EFA.dimensions") }
# MAXLIKE_FA <- function( ..., top=FALSE, shrink=1.0, textcolor=NULL )
# {
# .Defunct("EFA", package="EFA.dimensions")
# }
#
# IMAGE_FA <- function( ..., top=FALSE, shrink=1.0, textcolor=NULL )
# {
# .Defunct("EFA", package="EFA.dimensions")
# }
EFA <- function (data, extraction = 'paf', corkind='pearson', Nfactors=NULL, Ncases=NULL, iterpaf=100,
rotation='promax', ppower = 3, verbose=TRUE) {
data <- MISSING_DROP(data)
cnoms <- colnames(data) # get colnames
# set up cormat
cordat <- setupcormat(data, corkind=corkind, Ncases=Ncases)
cormat <- cordat$cormat
ctype <- cordat$ctype
Ncases <- cordat$Ncases
Nvars <- dim(cormat)[1]
eigenvalues <- eigen(cormat)$values
varexplNOROT1 <- VarianceExplained(eigenvalues)
# Ratio of the 1st to the 2nd initial eigenvalues
evals12ratio <- eigenvalues[1] / eigenvalues[2]
if (is.null(Nfactors)) {
Nfactors <- EMPKC(cormat, Ncases=Ncases, verbose=FALSE)$NfactorsEMPKC
NfactorsWasNull <- TRUE
} else {NfactorsWasNull <- FALSE}
# get the unrotated loadings for the specified extraction method
if (extraction == 'paf') {
outp <- PA_FA(cormat=cormat, Nfactors=Nfactors, Ncases=Ncases, iterpaf=iterpaf)
loadingsNOROT <- outp$loadingsNOROT
communalities <- outp$communalities
}
if (extraction == 'ml') {
outp <- MAXLIKE_FA(cormat=cormat, Nfactors=Nfactors, Ncases=Ncases)
loadingsNOROT <- outp$loadingsNOROT
communalities <- outp$communalities
}
if (extraction == 'image') {
outp <- IMAGE_FA(cormat=cormat, Nfactors=Nfactors, Ncases=Ncases)
loadingsNOROT <- outp$loadingsNOROT
communalities <- outp$communalities
}
if (extraction == 'minres') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='minres', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'uls') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='uls', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'ols') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='ols', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'wls') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='wls', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'gls') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='gls', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'alpha') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='alpha', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communality # an apparent name error in psych communality rather than communalities
}
if (extraction == 'fullinfo' & cordat$datakind == "notcorrels") {
# run only if data consists of integers
# confirm that the check the fractional parts of each # in data is 0 (better than using is.integer)
if (all(data %%1 == 0)) {
mirt_mod <- mirt::mirt(data=data, item_type=NULL, Nfactors) # , itemtype = "graded"
sum_mirt_mod <- mirt::summary(mirt_mod, rotate = 'varimax')
loadingsNOROT <- sum_mirt_mod$rotF
communalities <- sum_mirt_mod$h2
# # mirt sometimes produces 0 values for factor loadings; changing to a v small #
# loadingsNOROT <- ifelse(loadingsNOROT == 0, .0000001, loadingsNOROT)
} else {
message('\n\n"data" does not consist of integers and so a full-information factor analysis cannot')
message('be conducted. A paf extraction will be used instead.\n')
extraction <- 'paf'
outp <- PA_FA(cormat=cormat, Nfactors=Nfactors, Ncases=Ncases, iterpaf=iterpaf)
loadingsNOROT <- outp$loadingsNOROT
communalities <- outp$communalities
}
}
rownames(loadingsNOROT) <- cnoms
colnames(loadingsNOROT) <- c(paste('Factor ', 1:Nfactors, sep=''))
varexplNOROT2 <- VarianceExplained(eigenvalues, loadings=loadingsNOROT)
cormat_reprod <- loadingsNOROT %*% t(loadingsNOROT); diag(cormat_reprod) <- 1
# communalities
if (!is.matrix(communalities)) communalities <- as.matrix(communalities)
rownames(communalities) <- cnoms
if (ncol(communalities) == 1) colnames(communalities) <- c('Communalities')
if (ncol(communalities) == 2) colnames(communalities) <- c('Initial', 'Extraction')
uniquenesses <- 1 - communalities
# model statistics, based on Revelle
model <- cormat_reprod
#model <- cor.smooth(model) #this replaces the next few lines with a slightly cleaner approach
#r <- cor.smooth(r) #this makes sure that the correlation is positive semi-definite
m.inv.r <- try(solve(model,cormat),silent=TRUE)
dfMODEL <- Nvars * (Nvars - 1) / 2 - Nvars * Nfactors + (Nfactors * (Nfactors - 1) / 2)
objective <- sum(diag((m.inv.r))) - log(det(m.inv.r)) - Nvars
chisqMODEL <- objective * ((Ncases - 1) - (2 * Nvars + 5) / 6 - (2 * Nfactors) / 3) # from Tucker & from factanal
if(!is.nan(chisqMODEL)) if (chisqMODEL < 0) {chisqMODEL <- 0}
if (dfMODEL > 0) {pvalue <- pchisq(chisqMODEL, dfMODEL, lower.tail = FALSE)} else {pvalue <- NA}
# the null model
Fnull <- sum(diag((cormat))) - log(det(cormat)) - Nvars
chisqNULL <- Fnull * ((Ncases - 1) - (2 * Nvars + 5) / 6 )
dfNULL <- Nvars * (Nvars - 1) / 2
fit_coefs <- FIT_COEFS(cormat, cormat_reprod, extraction=extraction, Ncases=Ncases,
chisqMODEL=chisqMODEL, dfMODEL=dfMODEL, verbose=FALSE)
# rotation library(GPArotation)
varexplROT <- loadingsROT <- structure <- pattern <- phi <- NA
if (Nfactors > 1) {
# orthogonal rotations
if (rotation == 'varimax')
loadingsROT <- VARIMAX(loadingsNOROT, verbose=FALSE)$loadingsV
if (rotation == 'quartimax')
loadingsROT <- GPArotation::quartimax(loadingsNOROT)$loadings
if (rotation == 'bentlerT')
loadingsROT <- GPArotation::bentlerT(loadingsNOROT)$loadings
if (rotation == 'equamax')
loadingsROT <- psych::equamax(loadingsNOROT)$loadings
if (rotation == 'geominT')
loadingsROT <- GPArotation::geominT(loadingsNOROT)$loadings
if (rotation == 'bifactorT')
loadingsROT <- GPArotation::bifactorT(loadingsNOROT)$loadings
if (rotation == 'entropy')
loadingsROT <- GPArotation::entropy(loadingsNOROT)$loadings
# GPArotation::parsimax(loadings) not an exported object from 'namespace:GPArotation'
# oblique rotations
if (rotation == 'promax' | rotation == 'PROMAX') {
promaxOutput <- PROMAX(loadingsNOROT, ppower=ppower, verbose=FALSE)
pattern <- promaxOutput$pattern
structure <- promaxOutput$structure
phi <- promaxOutput$phi
}
if (rotation == 'quartimin') {
outp <- GPArotation::quartimin(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'oblimin') {
outp <- GPArotation::oblimin(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'oblimax') {
outp <- GPArotation::oblimax(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'simplimax') {
outp <- GPArotation::simplimax(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'bentlerQ') {
outp <- GPArotation::bentlerQ(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'geominQ') {
outp <- GPArotation::geominQ(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'bifactorQ') {
outp <- GPArotation::bifactorQ(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (!anyNA(loadingsROT)) varexplROT <- VarianceExplained(eigenvalues, loadings=loadingsROT)
if (!anyNA(structure)) {
colnames(structure) <- colnames(phi) <- c(paste('Factor ', 1:Nfactors, sep=''))
rownames(phi) <- c(paste('Factor ', 1:Nfactors, sep=''))
varexplROT <- VarianceExplained(eigenvalues, loadings=structure)
# when factors are correlated, sums of squared loadings cannot be added to obtain a total variance, so remove them from the output
varexplROT <- varexplROT[,1]
}
}
efaOutput <- list(loadingsNOROT = loadingsNOROT,
loadingsROT = loadingsROT,
pattern = pattern,
structure = structure,
phi = phi,
varexplNOROT1 = varexplNOROT1,
varexplNOROT2 = varexplNOROT2,
varexplROT = varexplROT,
evals12ratio = evals12ratio,
cormat_reprod = cormat_reprod,
fit_coefs = fit_coefs,
chisqMODEL = chisqMODEL,
dfMODEL = dfMODEL,
pvalue = pvalue,
chisqNULL = chisqNULL,
dfNULL = dfNULL,
communalities = communalities,
uniquenesses = uniquenesses)
if (verbose == TRUE) {
message('\n\n\nExploratory Factor Analysis')
message('\nThe specified kind of factor extraction method for this analysis: ', extraction)
message('\nThe specified kind of correlations for this analysis: ', ctype)
if (NfactorsWasNull == TRUE) {
message('\nNfactors was not specified and so the EMPKC test was conducted to determine')
message('the number of factors to extract: Nfactors = ', Nfactors,'\n')
} else if (NfactorsWasNull == FALSE) {
message('\nThe specified number of factors to extraction = ', Nfactors,'\n')
}
message('\nCommunalities:\n')
print(round(communalities,2))
message('\n\nTotal Variance Explained (Initial Eigenvalues):\n')
print(round(varexplNOROT1,2), print.gap=4)
message('\nRatio of the 1st to the 2nd initial eigenvalues = ', round(evals12ratio,1))
message('\n\nChi square = ',round(chisqMODEL,2),' df = ',dfMODEL,' p = ',round(pvalue,5))
message('\n\nModel Fit Coefficients:')
message('\nRMSR = ', round(fit_coefs$RMSR,3))
message('\nGFI = ', round(fit_coefs$GFI,3))
message('\nCAF = ', round(fit_coefs$CAF,3))
message('\nRMSEA = ', round(fit_coefs$RMSEA,3))
message('\nTLI = ', round(fit_coefs$TLI,3))
message('\nCFI = ', round(fit_coefs$CFI,3))
message('\nMFI = ', round(fit_coefs$MFI,3))
message('\nBIC = ', round(fit_coefs$BIC,3))
message('\nAIC = ', round(fit_coefs$AIC,3))
message('\nCAIC = ', round(fit_coefs$CAIC,3))
message('\nSABIC = ', round(fit_coefs$SABIC,3))
message('\n\nUnrotated Loadings:\n')
print(round(loadingsNOROT,2), print.gap=3)
message('\n\nTotal Variance Explained (Unrotated Sums of Squared Loadings):\n')
print(round(efaOutput$varexplNOROT2,2), print.gap=4)
if (Nfactors == 1) message('\nNo rotation because there is only one factor\n')
if (Nfactors > 1) {
if (rotation == 'none') message('\nRotation procedure: No rotation')
if (rotation != 'none') {
message('\n\nThe specified rotation procedure: ', rotation)
if (!anyNA(loadingsROT)) {
message('\n\nRotated Loadings:\n')
print(round(efaOutput$loadingsROT,2), print.gap=3)
}
if (!anyNA(pattern)) {
message('\n\nPattern Matrix (standardized factor loadings):\n');
print(round(efaOutput$pattern,2), print.gap=3)
message('\n\nStructure Matrix:\n');
print(round(efaOutput$structure,2), print.gap=3)
message('\n\nFactor Correlations:\n');
print(round(efaOutput$phi,2), print.gap=3)
}
message('\n\nTotal Variance Explained (Rotation Sums of Squared Loadings):\n')
print(round(efaOutput$varexplROT,2), print.gap=4)
}
}
}
return(invisible(efaOutput))
}
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EFA.dimensions documentation built on June 22, 2024, 10:18 a.m.
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Defines functions IMAGE_FA MAXLIKE_FA PA_FA
Documented in IMAGE_FA MAXLIKE_FA PA_FA
PA_FA <- function( ... ) { .Defunct("EFA", package="EFA.dimensions") }
MAXLIKE_FA <- function( ... ) { .Defunct("EFA", package="EFA.dimensions") }
IMAGE_FA <- function( ... ) { .Defunct("EFA", package="EFA.dimensions") }
# MAXLIKE_FA <- function( ..., top=FALSE, shrink=1.0, textcolor=NULL )
# {
# .Defunct("EFA", package="EFA.dimensions")
# }
#
# IMAGE_FA <- function( ..., top=FALSE, shrink=1.0, textcolor=NULL )
# {
# .Defunct("EFA", package="EFA.dimensions")
# }
EFA <- function (data, extraction = 'paf', corkind='pearson', Nfactors=NULL, Ncases=NULL, iterpaf=100,
rotation='promax', ppower = 3, verbose=TRUE) {
data <- MISSING_DROP(data)
cnoms <- colnames(data) # get colnames
# set up cormat
cordat <- setupcormat(data, corkind=corkind, Ncases=Ncases)
cormat <- cordat$cormat
ctype <- cordat$ctype
Ncases <- cordat$Ncases
Nvars <- dim(cormat)[1]
eigenvalues <- eigen(cormat)$values
varexplNOROT1 <- VarianceExplained(eigenvalues)
# Ratio of the 1st to the 2nd initial eigenvalues
evals12ratio <- eigenvalues[1] / eigenvalues[2]
if (is.null(Nfactors)) {
Nfactors <- EMPKC(cormat, Ncases=Ncases, verbose=FALSE)$NfactorsEMPKC
NfactorsWasNull <- TRUE
} else {NfactorsWasNull <- FALSE}
# get the unrotated loadings for the specified extraction method
if (extraction == 'paf') {
outp <- PA_FA(cormat=cormat, Nfactors=Nfactors, Ncases=Ncases, iterpaf=iterpaf)
loadingsNOROT <- outp$loadingsNOROT
communalities <- outp$communalities
}
if (extraction == 'ml') {
outp <- MAXLIKE_FA(cormat=cormat, Nfactors=Nfactors, Ncases=Ncases)
loadingsNOROT <- outp$loadingsNOROT
communalities <- outp$communalities
}
if (extraction == 'image') {
outp <- IMAGE_FA(cormat=cormat, Nfactors=Nfactors, Ncases=Ncases)
loadingsNOROT <- outp$loadingsNOROT
communalities <- outp$communalities
}
if (extraction == 'minres') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='minres', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'uls') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='uls', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'ols') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='ols', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'wls') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='wls', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'gls') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='gls', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communalities
}
if (extraction == 'alpha') {
outp <- psych::fa(r=cormat, nfactors=Nfactors, n.obs=Ncases, fm='alpha', rotate='none')
loadingsNOROT <- outp$loadings[1:dim(outp$loadings)[1], 1:dim(outp$loadings)[2], drop=FALSE]
communalities <- outp$communality # an apparent name error in psych communality rather than communalities
}
if (extraction == 'fullinfo' & cordat$datakind == "notcorrels") {
# run only if data consists of integers
# confirm that the check the fractional parts of each # in data is 0 (better than using is.integer)
if (all(data %%1 == 0)) {
mirt_mod <- mirt::mirt(data=data, item_type=NULL, Nfactors) # , itemtype = "graded"
sum_mirt_mod <- mirt::summary(mirt_mod, rotate = 'varimax')
loadingsNOROT <- sum_mirt_mod$rotF
communalities <- sum_mirt_mod$h2
# # mirt sometimes produces 0 values for factor loadings; changing to a v small #
# loadingsNOROT <- ifelse(loadingsNOROT == 0, .0000001, loadingsNOROT)
} else {
message('\n\n"data" does not consist of integers and so a full-information factor analysis cannot')
message('be conducted. A paf extraction will be used instead.\n')
extraction <- 'paf'
outp <- PA_FA(cormat=cormat, Nfactors=Nfactors, Ncases=Ncases, iterpaf=iterpaf)
loadingsNOROT <- outp$loadingsNOROT
communalities <- outp$communalities
}
}
rownames(loadingsNOROT) <- cnoms
colnames(loadingsNOROT) <- c(paste('Factor ', 1:Nfactors, sep=''))
varexplNOROT2 <- VarianceExplained(eigenvalues, loadings=loadingsNOROT)
cormat_reprod <- loadingsNOROT %*% t(loadingsNOROT); diag(cormat_reprod) <- 1
# communalities
if (!is.matrix(communalities)) communalities <- as.matrix(communalities)
rownames(communalities) <- cnoms
if (ncol(communalities) == 1) colnames(communalities) <- c('Communalities')
if (ncol(communalities) == 2) colnames(communalities) <- c('Initial', 'Extraction')
uniquenesses <- 1 - communalities
# model statistics, based on Revelle
model <- cormat_reprod
#model <- cor.smooth(model) #this replaces the next few lines with a slightly cleaner approach
#r <- cor.smooth(r) #this makes sure that the correlation is positive semi-definite
m.inv.r <- try(solve(model,cormat),silent=TRUE)
dfMODEL <- Nvars * (Nvars - 1) / 2 - Nvars * Nfactors + (Nfactors * (Nfactors - 1) / 2)
objective <- sum(diag((m.inv.r))) - log(det(m.inv.r)) - Nvars
chisqMODEL <- objective * ((Ncases - 1) - (2 * Nvars + 5) / 6 - (2 * Nfactors) / 3) # from Tucker & from factanal
if(!is.nan(chisqMODEL)) if (chisqMODEL < 0) {chisqMODEL <- 0}
if (dfMODEL > 0) {pvalue <- pchisq(chisqMODEL, dfMODEL, lower.tail = FALSE)} else {pvalue <- NA}
# the null model
Fnull <- sum(diag((cormat))) - log(det(cormat)) - Nvars
chisqNULL <- Fnull * ((Ncases - 1) - (2 * Nvars + 5) / 6 )
dfNULL <- Nvars * (Nvars - 1) / 2
fit_coefs <- FIT_COEFS(cormat, cormat_reprod, extraction=extraction, Ncases=Ncases,
chisqMODEL=chisqMODEL, dfMODEL=dfMODEL, verbose=FALSE)
# rotation library(GPArotation)
varexplROT <- loadingsROT <- structure <- pattern <- phi <- NA
if (Nfactors > 1) {
# orthogonal rotations
if (rotation == 'varimax')
loadingsROT <- VARIMAX(loadingsNOROT, verbose=FALSE)$loadingsV
if (rotation == 'quartimax')
loadingsROT <- GPArotation::quartimax(loadingsNOROT)$loadings
if (rotation == 'bentlerT')
loadingsROT <- GPArotation::bentlerT(loadingsNOROT)$loadings
if (rotation == 'equamax')
loadingsROT <- psych::equamax(loadingsNOROT)$loadings
if (rotation == 'geominT')
loadingsROT <- GPArotation::geominT(loadingsNOROT)$loadings
if (rotation == 'bifactorT')
loadingsROT <- GPArotation::bifactorT(loadingsNOROT)$loadings
if (rotation == 'entropy')
loadingsROT <- GPArotation::entropy(loadingsNOROT)$loadings
# GPArotation::parsimax(loadings) not an exported object from 'namespace:GPArotation'
# oblique rotations
if (rotation == 'promax' | rotation == 'PROMAX') {
promaxOutput <- PROMAX(loadingsNOROT, ppower=ppower, verbose=FALSE)
pattern <- promaxOutput$pattern
structure <- promaxOutput$structure
phi <- promaxOutput$phi
}
if (rotation == 'quartimin') {
outp <- GPArotation::quartimin(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'oblimin') {
outp <- GPArotation::oblimin(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'oblimax') {
outp <- GPArotation::oblimax(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'simplimax') {
outp <- GPArotation::simplimax(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'bentlerQ') {
outp <- GPArotation::bentlerQ(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'geominQ') {
outp <- GPArotation::geominQ(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (rotation == 'bifactorQ') {
outp <- GPArotation::bifactorQ(loadingsNOROT)
pattern <- outp$loadings
phi <- outp$Phi
structure <- pattern %*% phi
}
if (!anyNA(loadingsROT)) varexplROT <- VarianceExplained(eigenvalues, loadings=loadingsROT)
if (!anyNA(structure)) {
colnames(structure) <- colnames(phi) <- c(paste('Factor ', 1:Nfactors, sep=''))
rownames(phi) <- c(paste('Factor ', 1:Nfactors, sep=''))
varexplROT <- VarianceExplained(eigenvalues, loadings=structure)
# when factors are correlated, sums of squared loadings cannot be added to obtain a total variance, so remove them from the output
varexplROT <- varexplROT[,1]
}
}
efaOutput <- list(loadingsNOROT = loadingsNOROT,
loadingsROT = loadingsROT,
pattern = pattern,
structure = structure,
phi = phi,
varexplNOROT1 = varexplNOROT1,
varexplNOROT2 = varexplNOROT2,
varexplROT = varexplROT,
evals12ratio = evals12ratio,
cormat_reprod = cormat_reprod,
fit_coefs = fit_coefs,
chisqMODEL = chisqMODEL,
dfMODEL = dfMODEL,
pvalue = pvalue,
chisqNULL = chisqNULL,
dfNULL = dfNULL,
communalities = communalities,
uniquenesses = uniquenesses)
if (verbose == TRUE) {
message('\n\n\nExploratory Factor Analysis')
message('\nThe specified kind of factor extraction method for this analysis: ', extraction)
message('\nThe specified kind of correlations for this analysis: ', ctype)
if (NfactorsWasNull == TRUE) {
message('\nNfactors was not specified and so the EMPKC test was conducted to determine')
message('the number of factors to extract: Nfactors = ', Nfactors,'\n')
} else if (NfactorsWasNull == FALSE) {
message('\nThe specified number of factors to extraction = ', Nfactors,'\n')
}
message('\nCommunalities:\n')
print(round(communalities,2))
message('\n\nTotal Variance Explained (Initial Eigenvalues):\n')
print(round(varexplNOROT1,2), print.gap=4)
message('\nRatio of the 1st to the 2nd initial eigenvalues = ', round(evals12ratio,1))
message('\n\nChi square = ',round(chisqMODEL,2),' df = ',dfMODEL,' p = ',round(pvalue,5))
message('\n\nModel Fit Coefficients:')
message('\nRMSR = ', round(fit_coefs$RMSR,3))
message('\nGFI = ', round(fit_coefs$GFI,3))
message('\nCAF = ', round(fit_coefs$CAF,3))
message('\nRMSEA = ', round(fit_coefs$RMSEA,3))
message('\nTLI = ', round(fit_coefs$TLI,3))
message('\nCFI = ', round(fit_coefs$CFI,3))
message('\nMFI = ', round(fit_coefs$MFI,3))
message('\nBIC = ', round(fit_coefs$BIC,3))
message('\nAIC = ', round(fit_coefs$AIC,3))
message('\nCAIC = ', round(fit_coefs$CAIC,3))
message('\nSABIC = ', round(fit_coefs$SABIC,3))
message('\n\nUnrotated Loadings:\n')
print(round(loadingsNOROT,2), print.gap=3)
message('\n\nTotal Variance Explained (Unrotated Sums of Squared Loadings):\n')
print(round(efaOutput$varexplNOROT2,2), print.gap=4)
if (Nfactors == 1) message('\nNo rotation because there is only one factor\n')
if (Nfactors > 1) {
if (rotation == 'none') message('\nRotation procedure: No rotation')
if (rotation != 'none') {
message('\n\nThe specified rotation procedure: ', rotation)
if (!anyNA(loadingsROT)) {
message('\n\nRotated Loadings:\n')
print(round(efaOutput$loadingsROT,2), print.gap=3)
}
if (!anyNA(pattern)) {
message('\n\nPattern Matrix (standardized factor loadings):\n');
print(round(efaOutput$pattern,2), print.gap=3)
message('\n\nStructure Matrix:\n');
print(round(efaOutput$structure,2), print.gap=3)
message('\n\nFactor Correlations:\n');
print(round(efaOutput$phi,2), print.gap=3)
}
message('\n\nTotal Variance Explained (Rotation Sums of Squared Loadings):\n')
print(round(efaOutput$varexplROT,2), print.gap=4)
}
}
}
return(invisible(efaOutput))
}
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