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"factor.scores" <- function(x,f,Phi=NULL,method=c("Thurstone","tenBerge","Anderson","Bartlett","Harman","components"),rho=NULL,missing=FALSE,impute="none") {
#the normal case is f is the structure matrix and Phi is not specified
#Note that the Grice formulas distinguish between Pattern and Structure matrices
#I need to confirm that I am doing this
if(length(method) > 1) method <- "tenBerge" #the default
if(method=="regression") method <- "Thurstone"
if(method %in% c("tenberge", "Tenberge","tenBerge","TenBerge")) method <- "tenBerge"
if(length(class(f)) > 1) { if(inherits(f[2] ,"irt.fa" )) f <- f$fa }
if(!is.matrix(f)) {Phi <- f$Phi
f <- loadings(f)
if(ncol(f)==1) {method <- "Thurstone"}
}
nf <- dim(f)[2]
if(is.null(Phi)) Phi <- diag(1,nf,nf)
if(dim(x)[1] == dim(f)[1]) {r <- as.matrix(x)
square <- TRUE} else {
square <- FALSE
if(!is.null(rho)) {r <- rho } else {
r <- cor(x,use="pairwise") #find the correlation matrix from the data
}}
S <- f %*% Phi #the Structure matrix
switch(method,
"Thurstone" = { w <- try(solve(r,S),silent=TRUE ) #these are the factor weights (see Grice eq. 5)
if(inherits(w,"try-error")) {message("In factor.scores, the correlation matrix is singular, the pseudo inverse is used")
# r <- cor.smooth(r)
w <- Pinv(r) %*% S }
# w <- try(solve(r,S),silent=TRUE) #redudant, this will fail again (pointed out by Chanlder McClellan 4/4/23)
# if(inherits(w,"try-error")) {message("I was unable to calculate the factor score weights, factor loadings used instead")
# w <- f}
colnames(w) <- colnames(f)
rownames(w) <- rownames(f)
},
"tenBerge" = { #Following Grice equation 8 to estimate scores for oblique solutions (with a correction to the second line where r should r.inv
L <- f %*% matSqrt(Phi)
r.5 <- invMatSqrt(r)
r <- cor.smooth(r)
inv.r <- try(solve(r),silent=TRUE)
if(inherits(inv.r, as.character("try-error"))) {warning("The tenBerge based scoring could not invert the correlation matrix, regression scores found instead")
ev <- eigen(r)
ev$values[ev$values < .Machine$double.eps] <- 100 * .Machine$double.eps
r <- ev$vectors %*% diag(ev$values) %*% t(ev$vectors)
diag(r) <- 1
w <- solve(r,f)} else {
C <- r.5 %*% L %*% invMatSqrt(t(L) %*% inv.r %*% L) #note that this is the correct formula, per Grice personal communication
w <- r.5 %*% C %*% matSqrt(Phi)}
colnames(w) <- colnames(f)
rownames(w) <- rownames(f)
},
"Harman" = { #Grice equation 10 --
# m <- t(f) %*% f #factor intercorrelations
m <- f %*% t(S) #should be this (the model matrix) Revised August 31, 2017
diag(m) <- 1 #Grice does not say this, but it is necessary to make it work!
inv.m <- solve(m)
# w <- f %*%inv.m
w <- inv.m %*% f
},
"Anderson" = { #scores for orthogonal factor solution will be orthogonal Grice Eq 7 and 8
I <- diag(1,nf,nf)
h2 <- diag( f %*% Phi %*% t(f))
U2 <- 1 - h2
inv.U2 <- diag(1/U2)
w <- inv.U2 %*% f %*% invMatSqrt(t(f) %*% inv.U2 %*% r %*% inv.U2 %*% f)
colnames(w) <- colnames(f)
rownames(w) <- rownames(f)
},
"Bartlett" = { #Grice eq 9 # f should be the pattern, not the structure
I <- diag(1,nf,nf)
h2 <- diag( f %*% Phi %*% t(f))
U2 <- 1 - h2
inv.U2 <- diag(1/U2)
w <- inv.U2 %*% f %*% (solve(t(f) %*% inv.U2 %*% f))
colnames(w) <- colnames(f)
rownames(w) <- rownames(f)
},
"none" = {w <- NULL},
"components" = {w <- try(solve(r,f),silent=TRUE ) #basically, just do the regression/Thurstone approach for components
w <- f }
)
#now find a few fit statistics
if(is.null(w)) {results <- list(scores=NULL,weights=NULL)} else {
R2 <- diag(t(w) %*% S) #this had been R2 <- diag(t(w) %*% f) Corrected Sept 1, 2017
if(any(R2 > 1) || (prod(!is.nan(R2)) <1) || (prod(R2) < 0) ) {#message("The matrix is probably singular -- Factor score estimate results are likely incorrect")
R2[abs(R2) > 1] <- NA
R2[R2 <= 0] <- NA
}
#if ((max(R2,na.rm=TRUE) > (1 + .Machine$double.eps)) ) {message("The estimated weights for the factor scores are probably incorrect. Try a different factor extraction method.")}
r.scores <- cov2cor(t(w) %*% r %*% w) #what actually is this?
if(square) { #that is, if given the correlation matrix
class(w) <- NULL
results <- list(scores=NULL,weights=w)
results$r.scores <- r.scores
results$R2 <- R2 #this is the multiple R2 of the scores with the factors
} else {
#missing <- rowSums(is.na(x))
if(missing && (impute !="none")) {
x <- data.matrix(x)
miss <- which(is.na(x),arr.ind=TRUE)
if(impute=="mean") {
item.means <- colMeans(x,na.rm=TRUE) #replace missing values with means
x[miss]<- item.means[miss[,2]]} else {
item.med <- apply(x,2,median,na.rm=TRUE) #replace missing with medians
x[miss]<- item.med[miss[,2]]} #this only works if items is a matrix
}
if(method !="components") {if(impute!="none") {scores <- factorScoresSapa(weights=w, items = scale(x))} else {
scores <- scale(x) %*% w }} else { #standardize the data before doing the regression if using factors,
scores <- x %*% w} # for components, the data have already been zero centered and, if appropriate, scaled
results <- list(scores=scores,weights=w)
results$r.scores <- r.scores
results$missing <- missing
results$R2 <- R2 #this is the multiple R2 of the scores with the factors
}
}
return(results) }
#how to treat missing data? see score.item
"matSqrt" <- function(x) {
e <- eigen(x)
e$values[e$values < 0] <- .Machine$double.eps
sqrt.ev <- sqrt(e$values) #need to put in a check here for postive semi definite
result <- e$vectors %*% diag(sqrt.ev) %*% t(e$vectors)
result}
"invMatSqrt" <- function(x) {
e <- eigen(x)
if(is.complex(e$values)) {warning("complex eigen values detected by invMatSqrt, results are suspect")
result <- x
} else {
e$values[e$values < .Machine$double.eps] <- 100 * .Machine$double.eps
inv.sqrt.ev <- 1/sqrt(e$values) #need to put in a check here for postive semi definite
result <- e$vectors %*% diag(inv.sqrt.ev) %*% t(e$vectors) }
result}
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