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R/parallel.irt.r
In psych: Procedures for Psychological, Psychometric, and Personality Research
#revised August 31, 2012 to allow for estimation of all 0s or all 1s
#modified March 10, 2016 to allow for quasi Bayesian estimates using normal theory
#which doesn't seem to do what I want to do, so we are not doing it
#June 30-July 7 , 2016 Trying to make it faster by parallelizing the code and
#reducing the number of items to score when using keys.
#uses local minima -- problematic for small number of items
#corrected various problems with finding total (sum) scores 7/4/16
#starting to make parallel for speed
#seems to result in at least a factor of 2 improvement
#the function to do 2 parameter dichotomous IRT
"score.irt.2" <-
function(stats,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic") {
#find the person parameters in a 2 parameter model we use deltas and betas from irt.discrim and irt.person.rasch
#find the person parameter
#This does the normal fit
#has several internal functions
irt.2par.norm <- function(x,delta,beta,scores) {
fit <- -1*(log(scores*(1-pnorm(beta*(delta-x))) + (1-scores)*(1-pnorm(beta*(x-delta)))))
mean(fit,na.rm=TRUE)
}
#This does the logistic fit
irt.2par <- function(x,delta,beta,scores) {
fit <- -1*(log(scores/(1+exp(beta*(delta-x))) + (1-scores)/(1+exp(beta*(x-delta)))))
mean(fit,na.rm=TRUE)
}
###
#this is the the one to use when parallelized
bigFunction <- function(f,n.obs,stats,items,keys=NULL,cut=.3,bounds=c(-5,5),mod="logistic") {
nf <- length(stats$difficulty)
diff <- stats$difficulty[[f]]
cat <- dim(diff)[2]
if(nf < 2) {#discrim <- drop(stats$discrimination)
discrim <- stats$discrimination # although I need to check this with keys
if(!is.null(keys)) {discrim <- discrim * abs(keys)}
} else {discrim <- stats$discrimination[,f]
if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
}}
###
fit <- rep(NA,n.obs)
theta <- rep(NA,n.obs)
if(is.null(keys)) {#drop the items with discrim < cut
items.f <- items[,(abs(discrim[,f]) > cut) ,drop=FALSE] #get rid of the those items that are not being processed for this factor
diffi.f <- diff[(abs(discrim[,f]) > 0)] #and the redundant diffi
discrim.f <- discrim[(abs(discrim[,f]) > cut),drop=FALSE ] #and get rid of the unnecessary discrim values
} else { #the case of scoring with a keys vector
items.f <- items[,(abs(keys[,f]) > 0) ,drop=FALSE] #get rid of the those items that are not being processed for this factor
discrim.f <- discrim[(abs(keys[,f]) > 0),drop=FALSE ] #and get rid of the unnecessary discrim values
diffi.f <- diff[(abs(keys[,f]) > 0)] #and the redundant diffi
}
diffi.vect <- as.vector(t(diffi.f))
#discrim.F.vect <- rep(discrim.f,each=cat)
#discrim.f <- discrim[(abs(discrim > cut)),drop=FALSE]
discrim.F.vect <- as.vector(t(discrim.f))
if(is.matrix(discrim)) discrim.F.vect <- drop(discrim.F.vect)
total <- rowMeans(t(t(items.f)*sign(discrim.F.vect)),na.rm=TRUE)
count <- rowSums(!is.na(items.f))
#We can speed this up somewhat if we don't try to fit items with 0 discrim (i.e., items that do not load on the factor or are not keyed)
#do it for all subject for this factor
#now, lets parallelize this one as well
for (i in 1:n.obs) {
#First we consider the case of all right or all wrong
if (count[i] > 0) {if((sum(items.f[i,],na.rm=TRUE) ==0 ) | (prod(items.f[i,],na.rm=TRUE) == 1 )) {
if(sum(items.f[i,],na.rm=TRUE) ==0 ) {
if(mod=="logistic") {p <- log(1-(1-items.f[i,])/(1+exp(discrim.f*(diffi.f))) )} else { #logistic
p <- log(1-(pnorm(items.f[i,]*discrim.f*diffi.f))) } #normals
pall <- exp(sum(p,na.rm=TRUE))
# theta[i] <- qnorm(pnorm(qnorm(pall))/2) #the z value of 1/2 the quantile value of pall
theta[i] <- qnorm(pnorm(qnorm(pall))) #the z value of the quantile value of pall
fit[i] <- 0
# cat ("\nThe case of all wrong",i,theta[i])
} else { #the case of all right
if(mod == "logistic") { p <- log((items.f[i,])/(1+exp(discrim.f*(diffi.f))) )} else {
p <- log((items.f[i,])*(1 - pnorm(1- discrim.f*(diffi.f)) )) }
pall <- exp(sum(p,na.rm=TRUE))
# theta[i] <- qnorm(1-pnorm(qnorm(pall))/2) #the z value of 1/2 the quantile value of pall
theta[i] <- qnorm(1-pnorm(qnorm(pall))) #or, perhaps just hte z value of the quantile value of pall
fit[i] <- 0
}
} else { #cat("the normal case",i )
if(mod=="logistic") {
myfit <- optimize(irt.2par,bounds,beta=discrim.f,delta=diffi.f,scores=items.f[i,]) #how to do an apply?
} else {myfit <- optimize(irt.2par.norm,bounds,beta=discrim.f,delta=diffi.f,scores=items.f[i,])} #do a normal fit function
theta[i] <- myfit$minimum
fit[i] <- myfit$objective #fit of optimizing program
}} else {#cat("\nno items",i)
theta[i] <- NA
fit[i] <- NA
} #end if count ... else
} #end subject loop
theta [theta < bounds[1]] <- bounds[1]
theta[theta > bounds[2]] <- bounds[2]
# if((!is.null(keys)) & (all(keys[,f] == -1) || (sign(cor(discrim,keys[,f],use="pairwise")) < 0) )) {theta <- -theta
#if((!is.null(keys)) & (all(keys[,f] == -1) )) {theta <- -theta
# total <- -total}
nf <- length(stats$difficulty)
n.obs <- dim(items)[1]
nvar <- dim(items)[2]
# scores <- matrix(NaN,nrow=n.obs,ncol=nf*3)
scores <- list(nf*3)
scores <- list(theta,total,fit)
return(scores)
} # end of bigFunction
#we now start score.irt.2 proper
#this finds scores using multiple cores if they are available
nf <- length(stats$difficulty)
n.obs <- dim(items)[1]
#nvar <- dim(items)[2]
# if(nf < 2) {#discrim <- drop(stats$discrimination)
# discrim <- stats$discrimination
# if(!is.null(keys)) {discrim <- discrim * abs(keys) }
# } else {discrim <- stats$discrimination[,f]
# if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
# }}
#{for (f in 1:nf) { #note that only items that load on this factor need to be considered
#discrim <- stats$discrimination[,f]
# if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
# }
#use mapply for debugging, mcmapply for parallel processing
scores <- mapply(bigFunction,c(1:nf),MoreArgs=list(n.obs=n.obs,items=items,stats=stats,keys=keys, cut=cut, bounds=bounds, mod=mod))
nf <- length(stats$difficulty)
scores <- matrix(unlist(scores),ncol=nf*3)
scores <- scores[,c(seq(1,nf*3,3),seq(2,nf*3+1,3),seq(3,nf*3 +2,3))]
colnames(scores) <- paste(rep(c("theta","total","fit"),each=nf),1:nf,sep="")
return(scores)
}#end of score.irt.2
#############
"score.irt.poly" <-
function(stats,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic") {
#find the person parameters in a 2 parameter model we use deltas and betas from irt.discrim and irt.person.rasch
#find the person parameter
#created July 4, 2011
irt.2par.poly <- function(x,delta,beta,scores) {
fit <- -1*(log(scores/(1+exp(beta*(delta-x))) + (1-scores)/(1+exp(beta*(x-delta)))))
mean(fit,na.rm=TRUE)
}
####The function that is parallelized
big.poly <- function(f,n.obs,stats,items,keys=NULL,cut=.3,bounds=c(-5,5),mod="logistic") {
nf <- ncol(stats$discrimination)
#for (f in 1:nf) { #do it for every factor/scale
diff <- stats$difficulty[[f]]
if(nf < 2) {discrim <- stats$discrimination
if(!is.null(keys)) {discrim <- discrim * abs(keys)
} } else {discrim <- stats$discrimination[,f]
if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
}
}
cat <- dim(diff)[2]
fit <- rep(NA,n.obs)
theta <- rep(NA,n.obs)
item.f <- t(items)
item.f[abs(discrim) < cut] <- NA #this does not change the item, just the temp version of the item
item.f <- t(item.f)
###
item.f <- item.f[,(abs(keys[,f])>0) ,drop=FALSE] #get rid of the those items that are not being processed for this factor
discrim.f <- discrim[(abs(keys[,f]) >0),drop=FALSE ] #and get rid of the unnecessary discrim values
#diffi.f <- diff[(abs(keys[,f]) > 0),drop=FALSE] #and the redundant diffi
diffi.f <- diff[(abs(keys[,f])>0),byrows=TRUE]
#diffi.vect <- as.vector(t(diffi.f))
#diffi.vect <- as.vector(diffi.f)
diffi.vect <- as.vector(t(diff[(abs(keys[,f])>0),byrows=TRUE]))
discrim.F.vect <- rep(discrim.f,each=cat)
## notice that this is vectorized and does it all subjects
#seem to have solved the problem of missing items which are reversed.
total <- rowMeans(t(t(item.f )* as.vector(sign(discrim.f))),na.rm=TRUE) #fixed 11/11/11 to be as.vector
# total.positive <- rowMeans(t(t(item.f)* as.vector(sign(discrim.f) > 0)),na.rm=TRUE)
# total.negative <- rowMeans(t(t(item.f)* as.vector(sign(discrim.f) < 0)),na.rm=TRUE)
##
num.keyed <- rowSums(!is.na(item.f))
num.reversed <- rowSums(!is.na(item.f[,discrim.f <0,drop=FALSE]))
total <- total + num.reversed * (max.item- min.item+1)/num.keyed + min.item
count <- rowSums(!is.na(item.f))
#but now, we need to the next step one at a time (I think)
for (subj in 1:n.obs) {
if (count[subj]>0) {
newscore <- NULL
score <- item.f[subj,] #just the items to be scored
for (i in 1:ncol(item.f)) { #Treat the items as a series of 1 or 0 responses
if(is.na(score[i])) {newscore <- c(newscore,rep(NA,cat)) } else {
if(score[i] == cat) {newscore <- c(newscore,rep(1,score[i]))
} else {
newscore <- c(newscore,rep(1,score[i]),rep(0,cat-score[i])) }}
}
#check for all lowest responses or all highest responses
if((sum(newscore,na.rm=TRUE) ==0 ) | (prod(newscore,na.rm=TRUE) == 1) | (total[subj]==min.item) | (total [subj]== (max.item+min.item)) ) {
if((sum(newscore,na.rm=TRUE) ==0) | (total[subj]== min.item)) {
if(mod=="logistic") {p <- log(1-(1-newscore)/(1+exp(abs(discrim.f)*(diffi.f))) )} else { #logistic
p <- log(1-(pnorm(newscore*abs(discrim.f)*diffi.f))) } #normals
pall <- exp(sum(p,na.rm=TRUE))
# theta[i] <- qnorm(pnorm(qnorm(pall))/2) #the z value of 1/2 the quantile value of pall
theta[i] <- qnorm(pnorm(qnorm(pall))) #just the z value of the quantile of pall
fit[i] <- 0
# cat ("\nThe case of all wrong",i,theta[i])
} else { #the case of all right
if(mod == "logistic") { p <- log(1/(1+exp(abs(discrim.f)*(diffi.f))) )} else {
p <- log((1)*(1 - pnorm(1- abs(discrim.f)*(diffi.f)) )) }
pall <- exp(sum(p,na.rm=TRUE))
theta[subj] <- qnorm(1-pnorm(qnorm(pall))) #the z value of the quantile value of pall
fit[subj] <- 0 } } else {
myfit <- optimize(irt.2par.poly,bounds,beta=discrim.F.vect,delta=diffi.vect,scores=newscore)
theta[subj] <- myfit$minimum
fit[subj] <- myfit$objective #fit of optimizing program
}
} else {
fit[subj] <- NA
theta[subj] <- NA
} #end if else
}
if((!is.null(keys)) & (all(keys[,f] == -1) )) {theta <- -theta
total <- -total}
theta[theta<bounds[1]] <- bounds[1]
theta[theta > bounds[2]] <- bounds[2]
scores <- list(theta,total, fit)
return(scores)
} #end of big function
##the start of the irt.poly.function after setting up the various subfunctions
min.item <- min(items,na.rm=TRUE) #uses local minima --probably problematic for small number of items
items <- items - min.item #this converts scores to positive values from 0 up
max.item <- max(items,na.rm=TRUE) #we use this when reverse score -- but note that this is not the original max value. We will adjust this in total
nf <- length(stats$difficulty)
n.obs <- dim(items)[1]
nvar <- dim(items)[2]
#mcmapply for parallel, mappy for debugging
scores <- mcmapply(big.poly,1:nf,MoreArgs=list(n.obs=n.obs,stats=stats,items=items,keys=keys,cut=.3,bounds=bounds,mod=mod))
scores <- matrix(unlist(scores),ncol=nf*3)
scores <- scores[,c(seq(1,nf*3,3),seq(2,nf*3+1,3),seq(3,nf*3 +2,3))]
colnames(scores) <- paste(rep(c("theta","total","fit"),each=nf),1:nf,sep="")
return(scores)
} #end of score.irt.poly
#added the tau option in switch in case we have already done irt.tau 6/29/16
"score.irt" <- function(stats=NULL,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic") {
if(!is.null(keys) && (is.vector(keys))) keys <- matrix(keys)
if (length(class(stats)) > 1) {
if(!is.null(keys) && is.vector(keys)) keys <- as.matrix(keys)
obnames <- cs(irt.poly, irt.fa, fa,tau)
value <- inherits(stats, obnames, which=TRUE)
if (any(value > 1)) {value <- obnames[which(value >0)]} else {value <- "none"}
switch(value,
irt.poly = {scores <- score.irt.poly(stats$irt,items,keys,cut,bounds=bounds,mod=mod) },
irt.fa = {scores <- score.irt.2(stats$irt,items,keys,cut,bounds=bounds,mod=mod)},
fa = {tau <- irt.tau(items) #this is the case of a factor analysis to be applied to irt
nf <- dim(stats$loadings)[2]
diffi <- list()
for (i in 1:nf) {diffi[[i]] <- tau/sqrt(1-stats$loadings[,i]^2) }
discrim <- stats$loadings/sqrt(1-stats$loadings^2)
class(diffi) <- NULL
class(discrim) <- NULL
new.stats <- list(difficulty=diffi,discrimination=discrim)
scores <- score.irt.poly(new.stats,items,keys,cut,bounds=bounds)},
tau = {tau <- stats #get the tau stats from a prior run
if(is.matrix(keys)) {nf <- dim(keys)[2]} else {nf <-1}
diffi <- list()
for (i in 1:nf) {diffi[[i]] <- tau }
discrim <- keys
class(diffi) <- NULL
class(discrim) <- NULL
new.stats <- list(difficulty=diffi,discrimination=discrim)
if(dim(tau)[2] ==1) {scores <- score.irt.2(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)} else {
scores <- score.irt.poly(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)}
}
)
#we should have a null case
} else {#input is a keys matrix
tau <- irt.tau(items) #this is the case of a using a scoring matrix to be applied to irt
if(is.matrix(keys)) {nf <- dim(keys)[2]} else {nf <-1}
diffi <- list()
for (i in 1:nf) {diffi[[i]] <- tau }
if(!is.null(keys)) {discrim <- keys} else {stop("I am sorry, you specified tau but not keys.")}
class(diffi) <- NULL
class(discrim) <- NULL
new.stats <- list(difficulty=diffi,discrimination=discrim)
if(dim(tau)[2] ==1) {scores <- score.irt.2(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)} else {
scores <- score.irt.poly(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)}
}
scores <- data.frame(scores)
return(scores)
}
#find tau from dichotomous or polytomous data without bothering to find the correlations
#useful for score.irt
"irt.tau" <- function(x) {
x <-as.matrix(x)
nvar <- dim(x)[2]
xt <- table(x)
nvalues <- length(xt) #find the number of response alternatives
if(nvalues ==2) {tau <- -qnorm(colMeans(x,na.rm=TRUE))
tau <- as.matrix(tau)
rownames(tau) <- colnames(x)} else {
if(nvalues > 10) stop("You have more than 10 categories for your items, polychoric is probably not needed")
xmin <- min(x,na.rm=TRUE)
xfreq <- apply(x- xmin+ 1,2,tabulate,nbins=nvalues)
n.obs <- colSums(xfreq)
xfreq <- t(t(xfreq)/n.obs)
tau <- qnorm(apply(xfreq,2,cumsum))[1:(nvalues-1),] #these are the normal values of the cuts
if(!is.matrix(tau)) tau <- matrix(tau,ncol=nvar)
rownames(tau) <- names(xt)[1:(nvalues-1)]
colnames(tau) <- colnames(x)
if(dim(tau)[1] < dim(tau)[2]) tau <- t(tau) #rows are variables, columns are subjects
}
class(tau) <- c("psych","tau") #added the tau class so score.irt can use the tau values
return(tau)
}
#added August 6, 2012
"irt.responses" <-
function(theta,items, breaks = 11,show.missing=FALSE,show.legend=TRUE,legend.location="topleft",colors=NULL,...) {
#if(is.null(colors)) colors =c("gray0", "blue3", "red3", "darkgreen", "gold2", "gray50", "cornflowerblue", "mediumorchid2")
if(is.null(colors)) colors =c("black", "blue", "red", "darkgreen", "gold2", "gray50", "cornflowerblue", "mediumorchid2")
#legend.location <- c("bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right", "center","none")
#uniqueitems <- unique(as.vector(unlist(items)))
item.counts <- names(table(as.vector(unlist(items))))
uniqueitems <- as.numeric(item.counts)
nalt <- length(uniqueitems) + 1 #include the missing value from response.frequencies
nvar <- ncol(items)
theta.min <- min(theta,na.rm=TRUE)
theta.max <- max(theta,na.rm=TRUE)
binrange <- cut(theta, breaks = breaks)
binnums <- as.numeric(binrange)
items <- as.matrix(items)
stats <- by(items,binnums,function(x) response.frequencies(x,uniqueitems=uniqueitems))
stats.m <- unlist(stats)
stats.m <- matrix(stats.m,ncol=nvar*nalt,byrow=TRUE)
theta <- seq(theta.min,theta.max,length.out=breaks)
for (i in 1:nvar) {
plot(theta,stats.m[,i],ylim=c(0,1),typ="l",xlab="theta",ylab="P(response)",main=paste(colnames(items)[i]),col=colors[1],...)
for(j in 1:(nalt-2+show.missing)) {
points(theta,stats.m[,i+nvar*j],typ="l",lty=(j+1),col=colors[j+1 ],...)
}
if(show.legend) { legend(legend.location, paste(item.counts[1:(nalt-1 + show.missing)]), text.col = colors[1:(nalt-1+show.missing)], lty = 1:(nalt-1+show.missing), ncol=4,bty="n")}
}}
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#revised August 31, 2012 to allow for estimation of all 0s or all 1s
#modified March 10, 2016 to allow for quasi Bayesian estimates using normal theory
#which doesn't seem to do what I want to do, so we are not doing it
#June 30-July 7 , 2016 Trying to make it faster by parallelizing the code and
#reducing the number of items to score when using keys.
#uses local minima -- problematic for small number of items
#corrected various problems with finding total (sum) scores 7/4/16
#starting to make parallel for speed
#seems to result in at least a factor of 2 improvement
#the function to do 2 parameter dichotomous IRT
"score.irt.2" <-
function(stats,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic") {
#find the person parameters in a 2 parameter model we use deltas and betas from irt.discrim and irt.person.rasch
#find the person parameter
#This does the normal fit
#has several internal functions
irt.2par.norm <- function(x,delta,beta,scores) {
fit <- -1*(log(scores*(1-pnorm(beta*(delta-x))) + (1-scores)*(1-pnorm(beta*(x-delta)))))
mean(fit,na.rm=TRUE)
}
#This does the logistic fit
irt.2par <- function(x,delta,beta,scores) {
fit <- -1*(log(scores/(1+exp(beta*(delta-x))) + (1-scores)/(1+exp(beta*(x-delta)))))
mean(fit,na.rm=TRUE)
}
###
#this is the the one to use when parallelized
bigFunction <- function(f,n.obs,stats,items,keys=NULL,cut=.3,bounds=c(-5,5),mod="logistic") {
nf <- length(stats$difficulty)
diff <- stats$difficulty[[f]]
cat <- dim(diff)[2]
if(nf < 2) {#discrim <- drop(stats$discrimination)
discrim <- stats$discrimination # although I need to check this with keys
if(!is.null(keys)) {discrim <- discrim * abs(keys)}
} else {discrim <- stats$discrimination[,f]
if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
}}
###
fit <- rep(NA,n.obs)
theta <- rep(NA,n.obs)
if(is.null(keys)) {#drop the items with discrim < cut
items.f <- items[,(abs(discrim[,f]) > cut) ,drop=FALSE] #get rid of the those items that are not being processed for this factor
diffi.f <- diff[(abs(discrim[,f]) > 0)] #and the redundant diffi
discrim.f <- discrim[(abs(discrim[,f]) > cut),drop=FALSE ] #and get rid of the unnecessary discrim values
} else { #the case of scoring with a keys vector
items.f <- items[,(abs(keys[,f]) > 0) ,drop=FALSE] #get rid of the those items that are not being processed for this factor
discrim.f <- discrim[(abs(keys[,f]) > 0),drop=FALSE ] #and get rid of the unnecessary discrim values
diffi.f <- diff[(abs(keys[,f]) > 0)] #and the redundant diffi
}
diffi.vect <- as.vector(t(diffi.f))
#discrim.F.vect <- rep(discrim.f,each=cat)
#discrim.f <- discrim[(abs(discrim > cut)),drop=FALSE]
discrim.F.vect <- as.vector(t(discrim.f))
if(is.matrix(discrim)) discrim.F.vect <- drop(discrim.F.vect)
total <- rowMeans(t(t(items.f)*sign(discrim.F.vect)),na.rm=TRUE)
count <- rowSums(!is.na(items.f))
#We can speed this up somewhat if we don't try to fit items with 0 discrim (i.e., items that do not load on the factor or are not keyed)
#do it for all subject for this factor
#now, lets parallelize this one as well
for (i in 1:n.obs) {
#First we consider the case of all right or all wrong
if (count[i] > 0) {if((sum(items.f[i,],na.rm=TRUE) ==0 ) | (prod(items.f[i,],na.rm=TRUE) == 1 )) {
if(sum(items.f[i,],na.rm=TRUE) ==0 ) {
if(mod=="logistic") {p <- log(1-(1-items.f[i,])/(1+exp(discrim.f*(diffi.f))) )} else { #logistic
p <- log(1-(pnorm(items.f[i,]*discrim.f*diffi.f))) } #normals
pall <- exp(sum(p,na.rm=TRUE))
# theta[i] <- qnorm(pnorm(qnorm(pall))/2) #the z value of 1/2 the quantile value of pall
theta[i] <- qnorm(pnorm(qnorm(pall))) #the z value of the quantile value of pall
fit[i] <- 0
# cat ("\nThe case of all wrong",i,theta[i])
} else { #the case of all right
if(mod == "logistic") { p <- log((items.f[i,])/(1+exp(discrim.f*(diffi.f))) )} else {
p <- log((items.f[i,])*(1 - pnorm(1- discrim.f*(diffi.f)) )) }
pall <- exp(sum(p,na.rm=TRUE))
# theta[i] <- qnorm(1-pnorm(qnorm(pall))/2) #the z value of 1/2 the quantile value of pall
theta[i] <- qnorm(1-pnorm(qnorm(pall))) #or, perhaps just hte z value of the quantile value of pall
fit[i] <- 0
}
} else { #cat("the normal case",i )
if(mod=="logistic") {
myfit <- optimize(irt.2par,bounds,beta=discrim.f,delta=diffi.f,scores=items.f[i,]) #how to do an apply?
} else {myfit <- optimize(irt.2par.norm,bounds,beta=discrim.f,delta=diffi.f,scores=items.f[i,])} #do a normal fit function
theta[i] <- myfit$minimum
fit[i] <- myfit$objective #fit of optimizing program
}} else {#cat("\nno items",i)
theta[i] <- NA
fit[i] <- NA
} #end if count ... else
} #end subject loop
theta [theta < bounds[1]] <- bounds[1]
theta[theta > bounds[2]] <- bounds[2]
# if((!is.null(keys)) & (all(keys[,f] == -1) || (sign(cor(discrim,keys[,f],use="pairwise")) < 0) )) {theta <- -theta
#if((!is.null(keys)) & (all(keys[,f] == -1) )) {theta <- -theta
# total <- -total}
nf <- length(stats$difficulty)
n.obs <- dim(items)[1]
nvar <- dim(items)[2]
# scores <- matrix(NaN,nrow=n.obs,ncol=nf*3)
scores <- list(nf*3)
scores <- list(theta,total,fit)
return(scores)
} # end of bigFunction
#we now start score.irt.2 proper
#this finds scores using multiple cores if they are available
nf <- length(stats$difficulty)
n.obs <- dim(items)[1]
#nvar <- dim(items)[2]
# if(nf < 2) {#discrim <- drop(stats$discrimination)
# discrim <- stats$discrimination
# if(!is.null(keys)) {discrim <- discrim * abs(keys) }
# } else {discrim <- stats$discrimination[,f]
# if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
# }}
#{for (f in 1:nf) { #note that only items that load on this factor need to be considered
#discrim <- stats$discrimination[,f]
# if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
# }
#use mapply for debugging, mcmapply for parallel processing
scores <- mapply(bigFunction,c(1:nf),MoreArgs=list(n.obs=n.obs,items=items,stats=stats,keys=keys, cut=cut, bounds=bounds, mod=mod))
nf <- length(stats$difficulty)
scores <- matrix(unlist(scores),ncol=nf*3)
scores <- scores[,c(seq(1,nf*3,3),seq(2,nf*3+1,3),seq(3,nf*3 +2,3))]
colnames(scores) <- paste(rep(c("theta","total","fit"),each=nf),1:nf,sep="")
return(scores)
}#end of score.irt.2
#############
"score.irt.poly" <-
function(stats,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic") {
#find the person parameters in a 2 parameter model we use deltas and betas from irt.discrim and irt.person.rasch
#find the person parameter
#created July 4, 2011
irt.2par.poly <- function(x,delta,beta,scores) {
fit <- -1*(log(scores/(1+exp(beta*(delta-x))) + (1-scores)/(1+exp(beta*(x-delta)))))
mean(fit,na.rm=TRUE)
}
####The function that is parallelized
big.poly <- function(f,n.obs,stats,items,keys=NULL,cut=.3,bounds=c(-5,5),mod="logistic") {
nf <- ncol(stats$discrimination)
#for (f in 1:nf) { #do it for every factor/scale
diff <- stats$difficulty[[f]]
if(nf < 2) {discrim <- stats$discrimination
if(!is.null(keys)) {discrim <- discrim * abs(keys)
} } else {discrim <- stats$discrimination[,f]
if(!is.null(keys)) {discrim <- discrim * abs(keys[,f])
}
}
cat <- dim(diff)[2]
fit <- rep(NA,n.obs)
theta <- rep(NA,n.obs)
item.f <- t(items)
item.f[abs(discrim) < cut] <- NA #this does not change the item, just the temp version of the item
item.f <- t(item.f)
###
item.f <- item.f[,(abs(keys[,f])>0) ,drop=FALSE] #get rid of the those items that are not being processed for this factor
discrim.f <- discrim[(abs(keys[,f]) >0),drop=FALSE ] #and get rid of the unnecessary discrim values
#diffi.f <- diff[(abs(keys[,f]) > 0),drop=FALSE] #and the redundant diffi
diffi.f <- diff[(abs(keys[,f])>0),byrows=TRUE]
#diffi.vect <- as.vector(t(diffi.f))
#diffi.vect <- as.vector(diffi.f)
diffi.vect <- as.vector(t(diff[(abs(keys[,f])>0),byrows=TRUE]))
discrim.F.vect <- rep(discrim.f,each=cat)
## notice that this is vectorized and does it all subjects
#seem to have solved the problem of missing items which are reversed.
total <- rowMeans(t(t(item.f )* as.vector(sign(discrim.f))),na.rm=TRUE) #fixed 11/11/11 to be as.vector
# total.positive <- rowMeans(t(t(item.f)* as.vector(sign(discrim.f) > 0)),na.rm=TRUE)
# total.negative <- rowMeans(t(t(item.f)* as.vector(sign(discrim.f) < 0)),na.rm=TRUE)
##
num.keyed <- rowSums(!is.na(item.f))
num.reversed <- rowSums(!is.na(item.f[,discrim.f <0,drop=FALSE]))
total <- total + num.reversed * (max.item- min.item+1)/num.keyed + min.item
count <- rowSums(!is.na(item.f))
#but now, we need to the next step one at a time (I think)
for (subj in 1:n.obs) {
if (count[subj]>0) {
newscore <- NULL
score <- item.f[subj,] #just the items to be scored
for (i in 1:ncol(item.f)) { #Treat the items as a series of 1 or 0 responses
if(is.na(score[i])) {newscore <- c(newscore,rep(NA,cat)) } else {
if(score[i] == cat) {newscore <- c(newscore,rep(1,score[i]))
} else {
newscore <- c(newscore,rep(1,score[i]),rep(0,cat-score[i])) }}
}
#check for all lowest responses or all highest responses
if((sum(newscore,na.rm=TRUE) ==0 ) | (prod(newscore,na.rm=TRUE) == 1) | (total[subj]==min.item) | (total [subj]== (max.item+min.item)) ) {
if((sum(newscore,na.rm=TRUE) ==0) | (total[subj]== min.item)) {
if(mod=="logistic") {p <- log(1-(1-newscore)/(1+exp(abs(discrim.f)*(diffi.f))) )} else { #logistic
p <- log(1-(pnorm(newscore*abs(discrim.f)*diffi.f))) } #normals
pall <- exp(sum(p,na.rm=TRUE))
# theta[i] <- qnorm(pnorm(qnorm(pall))/2) #the z value of 1/2 the quantile value of pall
theta[i] <- qnorm(pnorm(qnorm(pall))) #just the z value of the quantile of pall
fit[i] <- 0
# cat ("\nThe case of all wrong",i,theta[i])
} else { #the case of all right
if(mod == "logistic") { p <- log(1/(1+exp(abs(discrim.f)*(diffi.f))) )} else {
p <- log((1)*(1 - pnorm(1- abs(discrim.f)*(diffi.f)) )) }
pall <- exp(sum(p,na.rm=TRUE))
theta[subj] <- qnorm(1-pnorm(qnorm(pall))) #the z value of the quantile value of pall
fit[subj] <- 0 } } else {
myfit <- optimize(irt.2par.poly,bounds,beta=discrim.F.vect,delta=diffi.vect,scores=newscore)
theta[subj] <- myfit$minimum
fit[subj] <- myfit$objective #fit of optimizing program
}
} else {
fit[subj] <- NA
theta[subj] <- NA
} #end if else
}
if((!is.null(keys)) & (all(keys[,f] == -1) )) {theta <- -theta
total <- -total}
theta[theta<bounds[1]] <- bounds[1]
theta[theta > bounds[2]] <- bounds[2]
scores <- list(theta,total, fit)
return(scores)
} #end of big function
##the start of the irt.poly.function after setting up the various subfunctions
min.item <- min(items,na.rm=TRUE) #uses local minima --probably problematic for small number of items
items <- items - min.item #this converts scores to positive values from 0 up
max.item <- max(items,na.rm=TRUE) #we use this when reverse score -- but note that this is not the original max value. We will adjust this in total
nf <- length(stats$difficulty)
n.obs <- dim(items)[1]
nvar <- dim(items)[2]
#mcmapply for parallel, mappy for debugging
scores <- mcmapply(big.poly,1:nf,MoreArgs=list(n.obs=n.obs,stats=stats,items=items,keys=keys,cut=.3,bounds=bounds,mod=mod))
scores <- matrix(unlist(scores),ncol=nf*3)
scores <- scores[,c(seq(1,nf*3,3),seq(2,nf*3+1,3),seq(3,nf*3 +2,3))]
colnames(scores) <- paste(rep(c("theta","total","fit"),each=nf),1:nf,sep="")
return(scores)
} #end of score.irt.poly
#added the tau option in switch in case we have already done irt.tau 6/29/16
"score.irt" <- function(stats=NULL,items,keys=NULL,cut=.3,bounds=c(-4,4),mod="logistic") {
if(!is.null(keys) && (is.vector(keys))) keys <- matrix(keys)
if (length(class(stats)) > 1) {
if(!is.null(keys) && is.vector(keys)) keys <- as.matrix(keys)
obnames <- cs(irt.poly, irt.fa, fa,tau)
value <- inherits(stats, obnames, which=TRUE)
if (any(value > 1)) {value <- obnames[which(value >0)]} else {value <- "none"}
switch(value,
irt.poly = {scores <- score.irt.poly(stats$irt,items,keys,cut,bounds=bounds,mod=mod) },
irt.fa = {scores <- score.irt.2(stats$irt,items,keys,cut,bounds=bounds,mod=mod)},
fa = {tau <- irt.tau(items) #this is the case of a factor analysis to be applied to irt
nf <- dim(stats$loadings)[2]
diffi <- list()
for (i in 1:nf) {diffi[[i]] <- tau/sqrt(1-stats$loadings[,i]^2) }
discrim <- stats$loadings/sqrt(1-stats$loadings^2)
class(diffi) <- NULL
class(discrim) <- NULL
new.stats <- list(difficulty=diffi,discrimination=discrim)
scores <- score.irt.poly(new.stats,items,keys,cut,bounds=bounds)},
tau = {tau <- stats #get the tau stats from a prior run
if(is.matrix(keys)) {nf <- dim(keys)[2]} else {nf <-1}
diffi <- list()
for (i in 1:nf) {diffi[[i]] <- tau }
discrim <- keys
class(diffi) <- NULL
class(discrim) <- NULL
new.stats <- list(difficulty=diffi,discrimination=discrim)
if(dim(tau)[2] ==1) {scores <- score.irt.2(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)} else {
scores <- score.irt.poly(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)}
}
)
#we should have a null case
} else {#input is a keys matrix
tau <- irt.tau(items) #this is the case of a using a scoring matrix to be applied to irt
if(is.matrix(keys)) {nf <- dim(keys)[2]} else {nf <-1}
diffi <- list()
for (i in 1:nf) {diffi[[i]] <- tau }
if(!is.null(keys)) {discrim <- keys} else {stop("I am sorry, you specified tau but not keys.")}
class(diffi) <- NULL
class(discrim) <- NULL
new.stats <- list(difficulty=diffi,discrimination=discrim)
if(dim(tau)[2] ==1) {scores <- score.irt.2(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)} else {
scores <- score.irt.poly(stats=new.stats,items=items,keys=keys,cut=cut,bounds=bounds)}
}
scores <- data.frame(scores)
return(scores)
}
#find tau from dichotomous or polytomous data without bothering to find the correlations
#useful for score.irt
"irt.tau" <- function(x) {
x <-as.matrix(x)
nvar <- dim(x)[2]
xt <- table(x)
nvalues <- length(xt) #find the number of response alternatives
if(nvalues ==2) {tau <- -qnorm(colMeans(x,na.rm=TRUE))
tau <- as.matrix(tau)
rownames(tau) <- colnames(x)} else {
if(nvalues > 10) stop("You have more than 10 categories for your items, polychoric is probably not needed")
xmin <- min(x,na.rm=TRUE)
xfreq <- apply(x- xmin+ 1,2,tabulate,nbins=nvalues)
n.obs <- colSums(xfreq)
xfreq <- t(t(xfreq)/n.obs)
tau <- qnorm(apply(xfreq,2,cumsum))[1:(nvalues-1),] #these are the normal values of the cuts
if(!is.matrix(tau)) tau <- matrix(tau,ncol=nvar)
rownames(tau) <- names(xt)[1:(nvalues-1)]
colnames(tau) <- colnames(x)
if(dim(tau)[1] < dim(tau)[2]) tau <- t(tau) #rows are variables, columns are subjects
}
class(tau) <- c("psych","tau") #added the tau class so score.irt can use the tau values
return(tau)
}
#added August 6, 2012
"irt.responses" <-
function(theta,items, breaks = 11,show.missing=FALSE,show.legend=TRUE,legend.location="topleft",colors=NULL,...) {
#if(is.null(colors)) colors =c("gray0", "blue3", "red3", "darkgreen", "gold2", "gray50", "cornflowerblue", "mediumorchid2")
if(is.null(colors)) colors =c("black", "blue", "red", "darkgreen", "gold2", "gray50", "cornflowerblue", "mediumorchid2")
#legend.location <- c("bottomright", "bottom", "bottomleft", "left", "topleft", "top", "topright", "right", "center","none")
#uniqueitems <- unique(as.vector(unlist(items)))
item.counts <- names(table(as.vector(unlist(items))))
uniqueitems <- as.numeric(item.counts)
nalt <- length(uniqueitems) + 1 #include the missing value from response.frequencies
nvar <- ncol(items)
theta.min <- min(theta,na.rm=TRUE)
theta.max <- max(theta,na.rm=TRUE)
binrange <- cut(theta, breaks = breaks)
binnums <- as.numeric(binrange)
items <- as.matrix(items)
stats <- by(items,binnums,function(x) response.frequencies(x,uniqueitems=uniqueitems))
stats.m <- unlist(stats)
stats.m <- matrix(stats.m,ncol=nvar*nalt,byrow=TRUE)
theta <- seq(theta.min,theta.max,length.out=breaks)
for (i in 1:nvar) {
plot(theta,stats.m[,i],ylim=c(0,1),typ="l",xlab="theta",ylab="P(response)",main=paste(colnames(items)[i]),col=colors[1],...)
for(j in 1:(nalt-2+show.missing)) {
points(theta,stats.m[,i+nvar*j],typ="l",lty=(j+1),col=colors[j+1 ],...)
}
if(show.legend) { legend(legend.location, paste(item.counts[1:(nalt-1 + show.missing)]), text.col = colors[1:(nalt-1+show.missing)], lty = 1:(nalt-1+show.missing), ncol=4,bty="n")}
}}
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