Nothing
R/factor.stats.R
In psych: Procedures for Psychological, Psychometric, and Personality Research
#added the coarse option (defaulting to TRUE) 8/25/23
"factor.stats" <-
function(r=NULL,f,phi=NULL,n.obs=NA,np.obs=NULL,alpha=.1,fm=NULL,smooth=TRUE, coarse=TRUE) {
fa.stats(r=r,f=f,phi=phi,n.obs=n.obs,np.obs=np.obs,alpha=alpha,fm=fm,smooth=smooth,coarse=coarse)}
"fa.stats" <-
function(r=NULL,f,phi=NULL,n.obs=NA,np.obs=NULL,alpha=.05,fm=NULL,smooth=TRUE,coarse=TRUE) {
#revised June 21, 2010 to add RMSEA etc.
#revised August 25, 2011 to add cor.smooth for smoothing
#revised November 10, 2012 to add stats for the minchi option of factoring
#revised February 28, 2014 to emphasize empirical chi 2 and report empirical BIC
#revised March 9, 2015 to report NA if RMSEA values are not in the confidence intervals
cl <- match.call()
conf.level <- alpha
if((!is.matrix(f)) && (!is.data.frame(f))) {#do a number of things that use f as list
if(is.null(r) && (!is.null(f$r)) ) r <- f$r #we found the correlation while factoring
#if(is.na(n.obs) && (!is.null(f$np.obs))) {np.obs <- f$np.obs}
f <- as.matrix(f$loadings)} else {f <- as.matrix(f)}
n <- dim(r)[2] #number of variables
if(dim(r)[1] !=n ) {n.obs = dim(r)[1]
r <- cor(r,use="pairwise")
}
if(is.data.frame(r)) r <- as.matrix(r)
nfactors <- dim(f)[2] # number of factors
if(is.null(phi)) {model <- f %*% t(f)} else {model <- f %*% phi %*% t(f)}
residual<- r - model
r2 <- sum(r*r)
rstar2 <- sum(residual*residual)
result <- list(residual = residual)
result$dof <- dof <- n * (n-1)/2 - n * nfactors + (nfactors *(nfactors-1)/2)
#r2.off <- r
#diag(r2.off) <- 0
# r2.off <- sum(r2.off^2)
r2.off <- r2 - tr(r)
diag(residual) <- 0
if(is.null(np.obs)) {rstar.off <- sum(residual^2)
result$ENull <- r2.off * n.obs #the empirical null model
result$chi <- rstar.off * n.obs #this is the empirical chi square
result$rms <- sqrt(rstar.off/(n*(n-1))) #this is the empirical rmsea
result$nh <- n.obs
if (result$dof > 0) {result$EPVAL <- pchisq(result$chi, result$dof, lower.tail = FALSE)
result$crms <- sqrt(rstar.off/(2*result$dof) )
result$EBIC <- result$chi - result$dof * log(n.obs)
result$ESABIC <- result$chi - result$dof * log((n.obs+2)/24) } else {result$EPVAL <- NA
result$crms <- NA
result$EBIC <- NA
result$ESABIC <- NA}
} else {
rstar.off <- sum(residual^2 * np.obs) #weight the residuals by their sample size
r2.off <-(r*r * np.obs) #weight the original by sample size
r2.off <- sum(r2.off) -tr(r2.off)
result$chi <- rstar.off #this is the sample size weighted chi square
result$nh <- harmonic.mean(as.vector(np.obs)) #this is the sample weighted cell size
result$rms <- sqrt(rstar.off/(result$nh*n*(n-1))) #this is the sample size weighted square root average squared residual
if (result$dof > 0) {result$EPVAL <- pchisq(result$chi, result$dof, lower.tail = FALSE)
result$crms <- sqrt(rstar.off/(2*result$nh*result$dof) )
result$EBIC <- result$chi - result$dof * log(result$nh)
result$ESABIC <- result$chi - result$dof * log((result$nh+2)/24) } else { #added 2/28/2014
result$EPVAL <- NA
result$crms <- NA
result$EBIC <- NA
result$ESABIC <- NA
}
}
result$fit <-1-rstar2/r2
result$fit.off <- 1-rstar.off/r2.off
result$sd <- sd(as.vector(residual)) #this is the none sample size weighted root mean square residual
result$factors <- nfactors
result$complexity <- (apply(f,1,function(x) sum(x^2)))^2/apply(f,1,function(x)sum(x^4))
diag(model) <- diag(r)
model <- cor.smooth(model) #this replaces the next few lines with a slightly cleaner approach
if(smooth) {r <- cor.smooth(r) } #this makes sure that the correlation is positive semi-definite
#although it would seem that the model should always be positive semidefinite so this is probably not necessary
#cor.smooth approach added August 25,2011
# }
m.inv.r <- try(solve(model,r),silent=TRUE) #modified Oct 30, 2009 to perhaps increase precision -- #modified 2015/1/2 to use try
if(inherits(m.inv.r,"try-error")) {warning("the model inverse times the r matrix is singular, replaced with Identity matrix which means fits are wrong")
m.inv.r <- diag(1,n,n)}
if(is.na(n.obs)) {result$n.obs=NA
result$PVAL=NA} else {result$n.obs=n.obs}
result$dof <- n * (n-1)/2 - n * nfactors + (nfactors *(nfactors-1)/2)
result$objective <- sum(diag((m.inv.r))) - log(det(m.inv.r)) -n #this is what Tucker Lewis call F
if(is.infinite(result$objective)) {result$objective <- rstar2
message("The determinant of the smoothed correlation was zero.\nThis means the objective function is not defined.\nChi square is based upon observed residuals.")}
result$criteria <- c("objective"=result$objective,NA,NA)
if (!is.na(n.obs)) {result$STATISTIC <- chisq <- result$objective * ((n.obs-1) -(2 * n + 5)/6 -(2*nfactors)/3) #from Tucker and from factanal
# if (!is.na(n.obs)) {result$STATISTIC <- chisq <- result$objective * ((n.obs-1)) #from Fox and sem
if(!is.nan(result$STATISTIC)) if (result$STATISTIC <0) {result$STATISTIC <- 0}
if (result$dof > 0) {result$PVAL <- pchisq(result$STATISTIC, result$dof, lower.tail = FALSE)} else {result$PVAL <- NA}
}
result$Call <- cl
#find the Tucker Lewis Index of reliability
#Also known as the NNFI which is expressed in terms of Chisq
#NNFI <- (chisqNull/dfNull - chisq/df)/(chisqNull/dfNull - 1)
#first find the null model
F0 <- sum(diag((r))) - log(det(r)) -n
if(is.infinite(F0)) {F0 <- r2
message("The determinant of the smoothed correlation was zero.\nThis means the objective function is not defined for the null model either.\nThe Chi square is thus based upon observed correlations.")}
Fm <- result$objective #objective function of model
Mm <- Fm/( n * (n-1)/2 - n * nfactors + (nfactors *(nfactors-1)/2))
M0 <- F0* 2 /(n*(n-1))
nm <- ((n.obs-1) -(2 * n + 5)/6 -(2*nfactors)/3) #
result$null.model <- F0
result$null.dof <- n * (n-1) /2
if (!is.na(n.obs)) {result$null.chisq <- F0 * ((n.obs-1) -(2 * n + 5)/6 )
result$TLI <- (M0 - Mm)/(M0 - 1/nm) #NNFI in Fox's sem
if(is.numeric(result$TLI) & !is.nan(result$TLI) & (result$TLI >1)) result$F0 <-1
#The estimatation of RMSEA and the upper and lower bounds are taken from John Fox's summary.sem with minor modifications
if(!is.null(result$objective) && (result$dof >0) &&(!is.na(result$objective))) {
# RMSEA <- sqrt(max(result$objective/result$dof - 1/(n.obs-1), 0)) #this is x2/(df*N ) - 1/(N-1) #put back 4/21/17
#however, this is not quite right and should be
RMSEA <- sqrt(max(chisq/(result$dof* n.obs) - 1/(n.obs-1), 0)) #this is x2/(df*N ) - 1/(N-1) #fixed 4/5/19
#note that the result$objective is not actually the chi square unless we adjust it ala Tucker
#thus, the RMSEA was slightly off. This was fixed October 29, 2016 to be
# RMSEA <- sqrt(max( (chisq/(result$dof * (n.obs))-1/(n.obs)),0)) #changed to this from above October 29, 2016 and then changed to N February 28, 2017
#Seem to have dropped the sqrt part of this at some point
tail <- conf.level/2 #this had been incorrectly listed as (1-conf.level)/2 which gave extraordinarily narrow confidence boundaries, fixed August 25, 2011
N <- max <- n.obs
df <- result$dof
#chi.sq.statistic <- RMSEA^2 * df * (N - 1) + df
#why isn't this just chi.sq?
chi.sq.statistic <- chisq
max <- max(n.obs,chi.sq.statistic) +2* n.obs
#the alternative to this is to use the uniroot technique of Yves Rosseel in lavaan
#### from Hao Wu
# LB<-function(T){
# + if (pchisq(df=df,q=T)<=0.95) return(0) else
# + sqrt(uniroot(function(x) {pchisq(df=df,ncp=x,q=T)-0.95},c(0,10000))$root/nstar/df)
# + }
#
# > UB<-function(T){
# + if (pchisq(df=df,q=T)<=0.05) return(0) else
# + sqrt(uniroot(function(x) {pchisq(df=df,ncp=x,q=T)-0.05},c(0,10000))$root/nstar/df)
# + }
##
#Finally implement February 2017
# upperlambda <- function(lam) {tail - pchisq(chi.sq.statistic, df, ncp=lam)^2 }
RMSEA.U <- 0 #in case we can not find it
if(pchisq(df=result$dof,q=result$STATISTIC) > tail){ RMSEA.U <- try( sqrt(uniroot(function(x) {pchisq(df=result$dof,ncp=x,q=result$STATISTIC)- tail},c(0,max))$root/(n.obs-1)/result$dof),silent=TRUE)
if(inherits( RMSEA.U,"try-error")) {if(RMSEA <= 0 ) {RMSEA.U <- 0} else {message("In factor.stats, I could not find the RMSEA upper bound . Sorry about that")
#if the fit is super good, then the chisq is too small to get an upper bound. Report it as 0.
RMSEA.U <- NA}}
}
# lam.U <- NA} else {lam.U <- res}
# # if (is.null(res) || is.na(res$objective) || res$objective < 0){
# # max <- 0
# # warning("cannot find upper bound of RMSEA")
# # break
# # }
#
# lowerlambda <- function(lam) {1- tail - pchisq(chi.sq.statistic, df, ncp=lam)^2 }
RMSEA.L <- 0 #in case we can not find it
if(pchisq(df=result$dof,q=result$STATISTIC) > (1-tail)) { RMSEA.L <- try( sqrt(uniroot(function(x) {pchisq(df=result$dof,ncp=x,q=result$STATISTIC)-1 + tail},c(0,max))$root/(n.obs-1)/result$dof) ,silent=TRUE)
if(inherits(RMSEA.L,"try-error")) {#message("In factor.stats, I could not find the RMSEA lower bound . Sorry about that")
RMSEA.L <- NA}
} else {RMSEA.L <- 0}
# lam.L <- 0} else {lam.L <- res}
# # if (is.null(res) || is.na(res$objective) || res$objective < 0){
# # max <- 0
# # warning("cannot find lower bound of RMSEA")
# # break
# # }
#However, this was giving the wrong results and so I implemented the following
#suggested by Hao Wu April, 2017
#RMSEA.U <- sqrt(uniroot(function(x) {pchisq(df=result$dof,ncp=x,q=result$STATISTIC)- alpha},c(0,10000))$root/(n.obs-1)/result$dof)
#RMSEA.L <- sqrt(uniroot(function(x) {pchisq(df=result$dof,ncp=x,q=result$STATISTIC)-1 + alpha},c(0,10000))$root/(n.obs-1)/result$dof)
# while (max > 1){
# res <- try(optimize(function(lam) (tail - pchisq(chi.sq.statistic, df, ncp=lam))^2, interval=c(0, max)),silent=TRUE)
# if(class(res)=="try-error") {message("In factor.stats, I could not find the RMSEA upper bound . Sorry about that")
# res <- NULL}
# if (is.null(res) || is.na(res$objective) || res$objective < 0){
# max <- 0
# warning("cannot find upper bound of RMSEA")
# break
# }
# if (sqrt(res$objective) < tail/100) break
# max <- max/2
# }
# lam.U <- if (max <= 1) NA else res$minimum
# # max <- max(max,lam.U)
# max <- lam.U
# if(is.na(max)) max <- N
# while (max > 1){# this just iterates in to get a value
# res <- try(optimize(function(lam) (1 - tail - pchisq(chi.sq.statistic, df, ncp=lam))^2, interval=c(0, max)),silent=TRUE)
# if(class(res)=="try-error") {message("In factor.stats, I could not find the RMSEA lower bound. Sorry about that")
# res <- NULL}
# if (is.null(res)) {break}
# if (sqrt(res$objective) < tail/100) break
# max <- max/2
# if (is.na(res$objective) || res$objective < 0){
# max <- 0
# warning("cannot find lower bound of RMSEA")
# break
# }
# }
#
#
# lam.L <- if (max <= 1) NA else res$minimum #lam is the ncp
# this RMSEA calculation is probably not right because it will sometimes (but rarely) give cis that don't include the estimate
# RMSEA.U <- sqrt(lam.U/((N)*df) ) #lavaan uses sqrt(lam.U/((N)*df) ) sem uses sqrt(lam.U/((N-1)*df) )
# RMSEA.L <- min(sqrt(lam.L/((N)*df) ),RMSEA)
if(!is.na(RMSEA.U) && RMSEA.U < RMSEA) RMSEA.U <- NA
if(!is.na(RMSEA.L) && RMSEA.L > RMSEA) RMSEA.L <- NA
result$RMSEA <- c(RMSEA, RMSEA.L, RMSEA.U, 1-conf.level)
names(result$RMSEA) <- c("RMSEA","lower","upper","confidence")
result$BIC <- chisq - df * log(N)
result$SABIC <- chisq - df * log((N+2)/24) # added 1/27/2014
}
}
#now, find the correlations of the factor scores, even if not estimated, with the factors
#this repeats what was done in factor.scores and does not take in\to account the options in factor.scores
if(!is.null(phi)) f <- f %*% phi #convert the pattern to structure coefficients
if(smooth) {r <- cor.smooth(r)}
# w <- try(solve(r,f) ,silent=TRUE) #these are the regression factor weights
w <- Pinv(r)%*%f #use the Pseudo inverse #added 4/22/23
if(inherits(w,"try-error")) {message("In factor.stats, the correlation matrix is singular, an approximation is used")
ev <- eigen(r)
if(is.complex(ev$values)) {warning("complex eigen values detected by factor stats, results are suspect")
} else {
ev$values[ev$values < .Machine$double.eps] <- 100 * .Machine$double.eps
r <- ev$vectors %*% diag(ev$values) %*% t(ev$vectors)
diag(r) <- 1
# w <- try(solve(r,f) ,silent=TRUE)
w <- Pinv(r)%*% r #use the Pseudo inverse #these are the factor weights
if(inherits(w,"try-error")) {warning("In factor.stats, the correlation matrix is singular, and we could not calculate the beta weights for factor score estimates")
w <- diag(1,dim(r)[1])
} #these are the beta weights
}}
R2 <- diag(t(w) %*% f) #but, we actually already found this in factor scores -- these are the Thurstone values
if(is.null(fm)) {
if(prod(R2,na.rm=TRUE) < 0 ) {message("In factor.stats: The factor scoring weights matrix is probably singular -- Factor score estimate results are likely incorrect.\n Try a different factor score estimation method\n")
R2[abs(R2) > 1] <- NA
R2[R2 <= 0] <- NA
}
if ((max(R2,na.rm=TRUE) > (1 + .Machine$double.eps)) ) {warning("The estimated weights for the factor scores are probably incorrect. Try a different factor score estimation method.")}
}
r.scores <- cov2cor(t(w) %*% r %*% w)
result$r.scores <- r.scores
result$R2 <- R2 #this is the multiple R2 of the scores with the factors
# result$R2.corrected <- factor.indeterm(r,f)
# result$R2.total <- R2.cor$R2
# result$beta.total <- R2.cor$beta.total
#coarse coding
if(coarse){ keys <- factor2cluster(f) #added the not coarse option 8/25/23
covar <- t(keys) %*% r %*% keys
if((nfactors >1) && (dim(covar)[2] >1 )) {
sd.inv <- diag(1/sqrt(diag(covar)))
cluster.correl <- sd.inv %*% covar %*% sd.inv #this is just cov2cor(covar)
valid <- t(f) %*% keys %*% sd.inv
result$valid <- diag(valid)
if(NCOL(cluster.correl) < NCOL(r.scores)) {#we need to pad out the cluster.correl matrix so that fa.organize does not choke 9/2/20
temp <- cluster.correl
n.temp <- NROW(temp)
cluster.correl <- matrix(NA,ncol(r.scores),nrow(r.scores))
cluster.correl[1:n.temp,1:n.temp] <- temp
}
result$score.cor <- cluster.correl} else {sd.inv <- 1/sqrt(covar)
if(dim(sd.inv)[1] == 1) sd.inv <- diag(sd.inv)
valid <- try(t(f) %*% keys * sd.inv)
result$valid <- valid}
} else {
result$score.cor <-NULL
result$valid <- NULL}
result$weights <- w #the beta weights for factor scores
class(result) <- c("psych","stats")
return(result)
}
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#added the coarse option (defaulting to TRUE) 8/25/23
"factor.stats" <-
function(r=NULL,f,phi=NULL,n.obs=NA,np.obs=NULL,alpha=.1,fm=NULL,smooth=TRUE, coarse=TRUE) {
fa.stats(r=r,f=f,phi=phi,n.obs=n.obs,np.obs=np.obs,alpha=alpha,fm=fm,smooth=smooth,coarse=coarse)}
"fa.stats" <-
function(r=NULL,f,phi=NULL,n.obs=NA,np.obs=NULL,alpha=.05,fm=NULL,smooth=TRUE,coarse=TRUE) {
#revised June 21, 2010 to add RMSEA etc.
#revised August 25, 2011 to add cor.smooth for smoothing
#revised November 10, 2012 to add stats for the minchi option of factoring
#revised February 28, 2014 to emphasize empirical chi 2 and report empirical BIC
#revised March 9, 2015 to report NA if RMSEA values are not in the confidence intervals
cl <- match.call()
conf.level <- alpha
if((!is.matrix(f)) && (!is.data.frame(f))) {#do a number of things that use f as list
if(is.null(r) && (!is.null(f$r)) ) r <- f$r #we found the correlation while factoring
#if(is.na(n.obs) && (!is.null(f$np.obs))) {np.obs <- f$np.obs}
f <- as.matrix(f$loadings)} else {f <- as.matrix(f)}
n <- dim(r)[2] #number of variables
if(dim(r)[1] !=n ) {n.obs = dim(r)[1]
r <- cor(r,use="pairwise")
}
if(is.data.frame(r)) r <- as.matrix(r)
nfactors <- dim(f)[2] # number of factors
if(is.null(phi)) {model <- f %*% t(f)} else {model <- f %*% phi %*% t(f)}
residual<- r - model
r2 <- sum(r*r)
rstar2 <- sum(residual*residual)
result <- list(residual = residual)
result$dof <- dof <- n * (n-1)/2 - n * nfactors + (nfactors *(nfactors-1)/2)
#r2.off <- r
#diag(r2.off) <- 0
# r2.off <- sum(r2.off^2)
r2.off <- r2 - tr(r)
diag(residual) <- 0
if(is.null(np.obs)) {rstar.off <- sum(residual^2)
result$ENull <- r2.off * n.obs #the empirical null model
result$chi <- rstar.off * n.obs #this is the empirical chi square
result$rms <- sqrt(rstar.off/(n*(n-1))) #this is the empirical rmsea
result$nh <- n.obs
if (result$dof > 0) {result$EPVAL <- pchisq(result$chi, result$dof, lower.tail = FALSE)
result$crms <- sqrt(rstar.off/(2*result$dof) )
result$EBIC <- result$chi - result$dof * log(n.obs)
result$ESABIC <- result$chi - result$dof * log((n.obs+2)/24) } else {result$EPVAL <- NA
result$crms <- NA
result$EBIC <- NA
result$ESABIC <- NA}
} else {
rstar.off <- sum(residual^2 * np.obs) #weight the residuals by their sample size
r2.off <-(r*r * np.obs) #weight the original by sample size
r2.off <- sum(r2.off) -tr(r2.off)
result$chi <- rstar.off #this is the sample size weighted chi square
result$nh <- harmonic.mean(as.vector(np.obs)) #this is the sample weighted cell size
result$rms <- sqrt(rstar.off/(result$nh*n*(n-1))) #this is the sample size weighted square root average squared residual
if (result$dof > 0) {result$EPVAL <- pchisq(result$chi, result$dof, lower.tail = FALSE)
result$crms <- sqrt(rstar.off/(2*result$nh*result$dof) )
result$EBIC <- result$chi - result$dof * log(result$nh)
result$ESABIC <- result$chi - result$dof * log((result$nh+2)/24) } else { #added 2/28/2014
result$EPVAL <- NA
result$crms <- NA
result$EBIC <- NA
result$ESABIC <- NA
}
}
result$fit <-1-rstar2/r2
result$fit.off <- 1-rstar.off/r2.off
result$sd <- sd(as.vector(residual)) #this is the none sample size weighted root mean square residual
result$factors <- nfactors
result$complexity <- (apply(f,1,function(x) sum(x^2)))^2/apply(f,1,function(x)sum(x^4))
diag(model) <- diag(r)
model <- cor.smooth(model) #this replaces the next few lines with a slightly cleaner approach
if(smooth) {r <- cor.smooth(r) } #this makes sure that the correlation is positive semi-definite
#although it would seem that the model should always be positive semidefinite so this is probably not necessary
#cor.smooth approach added August 25,2011
# }
m.inv.r <- try(solve(model,r),silent=TRUE) #modified Oct 30, 2009 to perhaps increase precision -- #modified 2015/1/2 to use try
if(inherits(m.inv.r,"try-error")) {warning("the model inverse times the r matrix is singular, replaced with Identity matrix which means fits are wrong")
m.inv.r <- diag(1,n,n)}
if(is.na(n.obs)) {result$n.obs=NA
result$PVAL=NA} else {result$n.obs=n.obs}
result$dof <- n * (n-1)/2 - n * nfactors + (nfactors *(nfactors-1)/2)
result$objective <- sum(diag((m.inv.r))) - log(det(m.inv.r)) -n #this is what Tucker Lewis call F
if(is.infinite(result$objective)) {result$objective <- rstar2
message("The determinant of the smoothed correlation was zero.\nThis means the objective function is not defined.\nChi square is based upon observed residuals.")}
result$criteria <- c("objective"=result$objective,NA,NA)
if (!is.na(n.obs)) {result$STATISTIC <- chisq <- result$objective * ((n.obs-1) -(2 * n + 5)/6 -(2*nfactors)/3) #from Tucker and from factanal
# if (!is.na(n.obs)) {result$STATISTIC <- chisq <- result$objective * ((n.obs-1)) #from Fox and sem
if(!is.nan(result$STATISTIC)) if (result$STATISTIC <0) {result$STATISTIC <- 0}
if (result$dof > 0) {result$PVAL <- pchisq(result$STATISTIC, result$dof, lower.tail = FALSE)} else {result$PVAL <- NA}
}
result$Call <- cl
#find the Tucker Lewis Index of reliability
#Also known as the NNFI which is expressed in terms of Chisq
#NNFI <- (chisqNull/dfNull - chisq/df)/(chisqNull/dfNull - 1)
#first find the null model
F0 <- sum(diag((r))) - log(det(r)) -n
if(is.infinite(F0)) {F0 <- r2
message("The determinant of the smoothed correlation was zero.\nThis means the objective function is not defined for the null model either.\nThe Chi square is thus based upon observed correlations.")}
Fm <- result$objective #objective function of model
Mm <- Fm/( n * (n-1)/2 - n * nfactors + (nfactors *(nfactors-1)/2))
M0 <- F0* 2 /(n*(n-1))
nm <- ((n.obs-1) -(2 * n + 5)/6 -(2*nfactors)/3) #
result$null.model <- F0
result$null.dof <- n * (n-1) /2
if (!is.na(n.obs)) {result$null.chisq <- F0 * ((n.obs-1) -(2 * n + 5)/6 )
result$TLI <- (M0 - Mm)/(M0 - 1/nm) #NNFI in Fox's sem
if(is.numeric(result$TLI) & !is.nan(result$TLI) & (result$TLI >1)) result$F0 <-1
#The estimatation of RMSEA and the upper and lower bounds are taken from John Fox's summary.sem with minor modifications
if(!is.null(result$objective) && (result$dof >0) &&(!is.na(result$objective))) {
# RMSEA <- sqrt(max(result$objective/result$dof - 1/(n.obs-1), 0)) #this is x2/(df*N ) - 1/(N-1) #put back 4/21/17
#however, this is not quite right and should be
RMSEA <- sqrt(max(chisq/(result$dof* n.obs) - 1/(n.obs-1), 0)) #this is x2/(df*N ) - 1/(N-1) #fixed 4/5/19
#note that the result$objective is not actually the chi square unless we adjust it ala Tucker
#thus, the RMSEA was slightly off. This was fixed October 29, 2016 to be
# RMSEA <- sqrt(max( (chisq/(result$dof * (n.obs))-1/(n.obs)),0)) #changed to this from above October 29, 2016 and then changed to N February 28, 2017
#Seem to have dropped the sqrt part of this at some point
tail <- conf.level/2 #this had been incorrectly listed as (1-conf.level)/2 which gave extraordinarily narrow confidence boundaries, fixed August 25, 2011
N <- max <- n.obs
df <- result$dof
#chi.sq.statistic <- RMSEA^2 * df * (N - 1) + df
#why isn't this just chi.sq?
chi.sq.statistic <- chisq
max <- max(n.obs,chi.sq.statistic) +2* n.obs
#the alternative to this is to use the uniroot technique of Yves Rosseel in lavaan
#### from Hao Wu
# LB<-function(T){
# + if (pchisq(df=df,q=T)<=0.95) return(0) else
# + sqrt(uniroot(function(x) {pchisq(df=df,ncp=x,q=T)-0.95},c(0,10000))$root/nstar/df)
# + }
#
# > UB<-function(T){
# + if (pchisq(df=df,q=T)<=0.05) return(0) else
# + sqrt(uniroot(function(x) {pchisq(df=df,ncp=x,q=T)-0.05},c(0,10000))$root/nstar/df)
# + }
##
#Finally implement February 2017
# upperlambda <- function(lam) {tail - pchisq(chi.sq.statistic, df, ncp=lam)^2 }
RMSEA.U <- 0 #in case we can not find it
if(pchisq(df=result$dof,q=result$STATISTIC) > tail){ RMSEA.U <- try( sqrt(uniroot(function(x) {pchisq(df=result$dof,ncp=x,q=result$STATISTIC)- tail},c(0,max))$root/(n.obs-1)/result$dof),silent=TRUE)
if(inherits( RMSEA.U,"try-error")) {if(RMSEA <= 0 ) {RMSEA.U <- 0} else {message("In factor.stats, I could not find the RMSEA upper bound . Sorry about that")
#if the fit is super good, then the chisq is too small to get an upper bound. Report it as 0.
RMSEA.U <- NA}}
}
# lam.U <- NA} else {lam.U <- res}
# # if (is.null(res) || is.na(res$objective) || res$objective < 0){
# # max <- 0
# # warning("cannot find upper bound of RMSEA")
# # break
# # }
#
# lowerlambda <- function(lam) {1- tail - pchisq(chi.sq.statistic, df, ncp=lam)^2 }
RMSEA.L <- 0 #in case we can not find it
if(pchisq(df=result$dof,q=result$STATISTIC) > (1-tail)) { RMSEA.L <- try( sqrt(uniroot(function(x) {pchisq(df=result$dof,ncp=x,q=result$STATISTIC)-1 + tail},c(0,max))$root/(n.obs-1)/result$dof) ,silent=TRUE)
if(inherits(RMSEA.L,"try-error")) {#message("In factor.stats, I could not find the RMSEA lower bound . Sorry about that")
RMSEA.L <- NA}
} else {RMSEA.L <- 0}
# lam.L <- 0} else {lam.L <- res}
# # if (is.null(res) || is.na(res$objective) || res$objective < 0){
# # max <- 0
# # warning("cannot find lower bound of RMSEA")
# # break
# # }
#However, this was giving the wrong results and so I implemented the following
#suggested by Hao Wu April, 2017
#RMSEA.U <- sqrt(uniroot(function(x) {pchisq(df=result$dof,ncp=x,q=result$STATISTIC)- alpha},c(0,10000))$root/(n.obs-1)/result$dof)
#RMSEA.L <- sqrt(uniroot(function(x) {pchisq(df=result$dof,ncp=x,q=result$STATISTIC)-1 + alpha},c(0,10000))$root/(n.obs-1)/result$dof)
# while (max > 1){
# res <- try(optimize(function(lam) (tail - pchisq(chi.sq.statistic, df, ncp=lam))^2, interval=c(0, max)),silent=TRUE)
# if(class(res)=="try-error") {message("In factor.stats, I could not find the RMSEA upper bound . Sorry about that")
# res <- NULL}
# if (is.null(res) || is.na(res$objective) || res$objective < 0){
# max <- 0
# warning("cannot find upper bound of RMSEA")
# break
# }
# if (sqrt(res$objective) < tail/100) break
# max <- max/2
# }
# lam.U <- if (max <= 1) NA else res$minimum
# # max <- max(max,lam.U)
# max <- lam.U
# if(is.na(max)) max <- N
# while (max > 1){# this just iterates in to get a value
# res <- try(optimize(function(lam) (1 - tail - pchisq(chi.sq.statistic, df, ncp=lam))^2, interval=c(0, max)),silent=TRUE)
# if(class(res)=="try-error") {message("In factor.stats, I could not find the RMSEA lower bound. Sorry about that")
# res <- NULL}
# if (is.null(res)) {break}
# if (sqrt(res$objective) < tail/100) break
# max <- max/2
# if (is.na(res$objective) || res$objective < 0){
# max <- 0
# warning("cannot find lower bound of RMSEA")
# break
# }
# }
#
#
# lam.L <- if (max <= 1) NA else res$minimum #lam is the ncp
# this RMSEA calculation is probably not right because it will sometimes (but rarely) give cis that don't include the estimate
# RMSEA.U <- sqrt(lam.U/((N)*df) ) #lavaan uses sqrt(lam.U/((N)*df) ) sem uses sqrt(lam.U/((N-1)*df) )
# RMSEA.L <- min(sqrt(lam.L/((N)*df) ),RMSEA)
if(!is.na(RMSEA.U) && RMSEA.U < RMSEA) RMSEA.U <- NA
if(!is.na(RMSEA.L) && RMSEA.L > RMSEA) RMSEA.L <- NA
result$RMSEA <- c(RMSEA, RMSEA.L, RMSEA.U, 1-conf.level)
names(result$RMSEA) <- c("RMSEA","lower","upper","confidence")
result$BIC <- chisq - df * log(N)
result$SABIC <- chisq - df * log((N+2)/24) # added 1/27/2014
}
}
#now, find the correlations of the factor scores, even if not estimated, with the factors
#this repeats what was done in factor.scores and does not take in\to account the options in factor.scores
if(!is.null(phi)) f <- f %*% phi #convert the pattern to structure coefficients
if(smooth) {r <- cor.smooth(r)}
# w <- try(solve(r,f) ,silent=TRUE) #these are the regression factor weights
w <- Pinv(r)%*%f #use the Pseudo inverse #added 4/22/23
if(inherits(w,"try-error")) {message("In factor.stats, the correlation matrix is singular, an approximation is used")
ev <- eigen(r)
if(is.complex(ev$values)) {warning("complex eigen values detected by factor stats, results are suspect")
} else {
ev$values[ev$values < .Machine$double.eps] <- 100 * .Machine$double.eps
r <- ev$vectors %*% diag(ev$values) %*% t(ev$vectors)
diag(r) <- 1
# w <- try(solve(r,f) ,silent=TRUE)
w <- Pinv(r)%*% r #use the Pseudo inverse #these are the factor weights
if(inherits(w,"try-error")) {warning("In factor.stats, the correlation matrix is singular, and we could not calculate the beta weights for factor score estimates")
w <- diag(1,dim(r)[1])
} #these are the beta weights
}}
R2 <- diag(t(w) %*% f) #but, we actually already found this in factor scores -- these are the Thurstone values
if(is.null(fm)) {
if(prod(R2,na.rm=TRUE) < 0 ) {message("In factor.stats: The factor scoring weights matrix is probably singular -- Factor score estimate results are likely incorrect.\n Try a different factor score estimation method\n")
R2[abs(R2) > 1] <- NA
R2[R2 <= 0] <- NA
}
if ((max(R2,na.rm=TRUE) > (1 + .Machine$double.eps)) ) {warning("The estimated weights for the factor scores are probably incorrect. Try a different factor score estimation method.")}
}
r.scores <- cov2cor(t(w) %*% r %*% w)
result$r.scores <- r.scores
result$R2 <- R2 #this is the multiple R2 of the scores with the factors
# result$R2.corrected <- factor.indeterm(r,f)
# result$R2.total <- R2.cor$R2
# result$beta.total <- R2.cor$beta.total
#coarse coding
if(coarse){ keys <- factor2cluster(f) #added the not coarse option 8/25/23
covar <- t(keys) %*% r %*% keys
if((nfactors >1) && (dim(covar)[2] >1 )) {
sd.inv <- diag(1/sqrt(diag(covar)))
cluster.correl <- sd.inv %*% covar %*% sd.inv #this is just cov2cor(covar)
valid <- t(f) %*% keys %*% sd.inv
result$valid <- diag(valid)
if(NCOL(cluster.correl) < NCOL(r.scores)) {#we need to pad out the cluster.correl matrix so that fa.organize does not choke 9/2/20
temp <- cluster.correl
n.temp <- NROW(temp)
cluster.correl <- matrix(NA,ncol(r.scores),nrow(r.scores))
cluster.correl[1:n.temp,1:n.temp] <- temp
}
result$score.cor <- cluster.correl} else {sd.inv <- 1/sqrt(covar)
if(dim(sd.inv)[1] == 1) sd.inv <- diag(sd.inv)
valid <- try(t(f) %*% keys * sd.inv)
result$valid <- valid}
} else {
result$score.cor <-NULL
result$valid <- NULL}
result$weights <- w #the beta weights for factor scores
class(result) <- c("psych","stats")
return(result)
}
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