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`person.parameter.eRm` <- function(object){
# estimation of the person parameters with jml
# object of class eRm
# se... whether standard errors should be computed
se <- TRUE
interpolation <- TRUE
X <- object$X
#collapse X
#X.full <- object$X
max.it <- apply(X, 2L, max, na.rm = TRUE) #maximum item raw score without NA
rp <- rowSums(X, na.rm = TRUE) #person raw scores
maxrp <- apply(X, 1L, function(x.i){ sum(max.it[!is.na(x.i)]) }) #maximum item raw score for person i
TFrow <- ((rp==maxrp) | (rp==0))
pers.exe <- (1L:nrow(X))[TFrow] #persons excluded from estimation due to 0/full
pers.exe.names <- rownames(X)[pers.exe]
pers.in <- (1L:nrow(X))[-pers.exe] #persons in estimation
if(length(pers.exe) > 0L){ #data matrix persons (full/0) excluded)
X.ex <- object$X[-pers.exe,]
} else {
X.ex <- object$X
}
if(any(is.na(X))){
dichX <- ifelse(is.na(X), 1, 0)
strdata <- apply(dichX, 1L, function(x){ paste(x, collapse="") })
gmemb.X <- as.vector(data.matrix(data.frame(strdata)))
} else {
gmemb.X <- rep(1L, nrow(X))
}
if(length(pers.exe) > 0L) X <- X[-pers.exe,]
X.dummy <- X
if(any(is.na(X))){
dichX <- ifelse(is.na(X), 1, 0)
strdata <- apply(dichX, 1L, function(x){ paste(x, collapse="") })
gmemb <- as.vector(data.matrix(data.frame(strdata)))
gmemb1 <- gmemb
} else {
gmemb <- rep(1L, nrow(X))
gmemb1 <- gmemb
}
#mt_vek <- apply(X, 2L, max, na.rm = TRUE) #number of categories - 1 for each item
mt_vek <- apply(object$X, 2L, max, na.rm = TRUE) ## FIX: to be tested
mt_ind <- rep(1L:length(mt_vek), mt_vek) #index i for items
indvec <- NULL #establish matrix with unique raw scores
for(i in unique(gmemb)){
gmemb.ind <- which(gmemb == i)
collapse.vec <- which(!duplicated(rowSums(rbind(X[gmemb==i,]), na.rm = TRUE)))
indvec <- c(indvec, gmemb.ind[collapse.vec])
}
#for (i in unique(gmemb)) indvec <- c(indvec,!duplicated(rowSums(rbind(X[gmemb==i,]),na.rm = TRUE)))
indvec <- sort(indvec)
X <- X[indvec,] #collapsing X
beta.all <- object$betapar
if(!is.null(object$ngroups)){
if(object$ngroups > 1L) stop("Estimation of person parameters for models with group contrasts not possible!")
}
if(is.null(object$mpoints)){
mpoints <- 1L
} else {
mpoints <- object$mpoints
}
r.pall <- rowSums(X, na.rm = TRUE) #person raw scores
X01 <- object$X01
if(length(pers.exe) > 0L) X01 <- X01[-pers.exe,] #if persons excluded due to 0/full response
X01 <- X01[indvec,] #collapsed version
gmemb <- gmemb[indvec] #collapsed version
rownames(X01) <- rownames(X)
rowvec <- 1L:nrow(X01)
fitlist <- tapply(rowvec, gmemb, function(rind){ #list with nlm outputs
if(length(rind) > 1L){
ivec <- !is.na(X[rind[1],]) #non-NA elements
r.i <- colSums(X[rind, ivec], na.rm = TRUE) #item raw scores
} else { #if only one person belongs to raw score group
ivec <- !is.na(X[rind[1],])
r.i <- X[rind, ivec]
# r.i <- X[rind,]
# r.i[is.na(r.i)] <- 0
}
#r.i <- colSums(object$X[rind,],na.rm=TRUE) #item raw scores
r.p <- r.pall[rind] #person raw scores for current NA group
X01g <- rbind(X01[rind,])
beta <- beta.all[!is.na(X01g[1L,])]
X01beta <- rbind(X01g, beta.all) #matrix with unique 0/1 response patterns and beta vector in the last row
theta <- rep(0L, length(r.p))
#==================== ML routines ===================================
jml.rasch <- function(theta){ #fast ML for RM only
ksi <- exp(theta)
denom <- 1/exp(-beta) #-beta instead of beta since beta are easiness parameter
lnL <- sum(r.p*theta) - sum(r.i*(-beta)) - sum(log(1 + outer(ksi,denom)))
return(-lnL)
}
jml <- function(theta){ #ML for all other models
t1t2.list <- tapply(1L:ncol(X01beta), mt_ind, function(xin){
#xb <- (t(X01beta)[xin,])
xb <- rbind(t(X01beta)[xin,]) #0/1 responses and beta parameters for one item
beta.i <- c(0.0, xb[,ncol(xb)]) #item parameter with 0
#person responses (row-wise) on each category for current item
if((nrow(xb) > 1L) && (length(xin == 1L))){
x01.i <- as.matrix(xb[,1L:(ncol(xb) - 1L)])
} else {
x01.i <- rbind(xb[,1L:(ncol(xb) - 1L)]) #0/1 matrix for item i without beta
}
cat0 <- rep(0L, ncol(x01.i))
cat0[colSums(x01.i) == 0L] <- 1 #those with 0 on the 1-kth category get a 1
x01.i0 <- rbind(cat0, x01.i) #appending response vector for 0th category
ind.h <- 0L:(length(beta.i)-1L)
theta.h <- ind.h %*% t(theta) #n. categories times theta
term1 <- (theta.h + beta.i) * x01.i0 #category-person matrix
t1.i <- sum(colSums(term1)) #sum over categories and persons
#print(t1.i)
term2 <- exp(theta.h+beta.i)
t2.i <- sum(log(colSums(term2))) #sum over categories and persons
#print(t2.i)
return(c(t1.i,t2.i))
})
termlist <- matrix(unlist(t1t2.list), ncol = 2L, byrow = TRUE)
termlist <- termlist[!is.na(rowSums(termlist)),]
st1st2 <- colSums(termlist, na.rm = TRUE) #sum term1, term2
lnL <- st1st2[1] - st1st2[2]
return(-lnL)
}
#==================== end ML routines ================================
#==================== call optimizer =================================
if (object$model == "RM") {
fit <- nlm(jml.rasch, theta, hessian = se, iterlim = 1000L)
} else {
fit <- nlm(jml, theta, hessian = se, iterlim = 1000)
}
#fit2 <- optim(theta, jml.rasch, method="BFGS", hessian=TRUE)
#=================== end call optimizer ==============================
loglik <- -fit$minimum
niter <- fit$iterations
thetapar <- fit$estimate
if(se){
se <- sqrt(diag(solve(fit$hessian)))
} else {
se <- NA
fit$hessian <- NA
}
return(list("loglik" = loglik,
"niter" = niter,
"thetapar" = thetapar,
"se" = se,
"hessian" = fit$hessian))
})
loglik <- niter <- npar <- numeric(length(fitlist))
thetapar <- se.theta <- hessian <- vector(mode = "list", length = length(fitlist))
for(i in seq_along(fitlist)){
loglik[i] <- fitlist[[i]]$loglik
niter[i] <- fitlist[[i]]$niter
npar[i] <- length(fitlist[[i]]$thetapar)
thetapar[[i]] <- fitlist[[i]]$thetapar
se.theta[[i]] <- fitlist[[i]]$se
hessian[[i]] <- fitlist[[i]]$hessian
}
if(interpolation){ #cubic spline interpolation for 0 and full raw scores
x <- rowSums(X, na.rm = TRUE)
xlist <- split(x, gmemb)
splineMessage <- FALSE # to display the spline-failure message only once
max.rs.NAgroups <- lapply(sort(unique(gmemb.X)), function(i){ ## MM 2012-02-01
sum(max.it[!is.na(object$X[which(gmemb.X == i)[1],])]) # get the max. raw score per NA-group
})
NAgroups.min <- tapply(rowSums(object$X, na.rm=T), gmemb.X, min, na.rm = TRUE)
NAgroups.max <- tapply(rowSums(object$X, na.rm=T), gmemb.X, max, na.rm = TRUE)
NAgroup_exclude <- numeric()
for(i in seq_along(unique(gmemb.X))){ # delete groups with 0/full patterns from max.rs.NAgroups, NAgroups.min, NAgroups.max
if(all(rowSums(object$X, na.rm=TRUE)[gmemb.X == i] %in% c(0, max.rs.NAgroups[[i]]))) NAgroup_exclude <- c(NAgroup_exclude, i)
}
if(length(NAgroup_exclude) > 0L){
splineMessage <- TRUE # so that the message is only printed once
max.rs.NAgroups <- max.rs.NAgroups[-NAgroup_exclude]
NAgroups.min <- NAgroups.min[-NAgroup_exclude]
NAgroups.max <- NAgroups.max[-NAgroup_exclude]
gmemb_reduced <- unique(gmemb.X[-which(gmemb.X %in% NAgroup_exclude)])
}
pred.list <- Map(function(xx, yy, rs, NAmin, NAmax){ # Map(...) is mapply(..., SIMPLFY = FALSE)
y <- tapply(yy, xx, function(xy){ xy[1] })
x <- unique(sort(xx))
from <- ifelse(NAmin == 0, 0, min(x))
to <- ifelse(NAmax == rs, rs, max(x))
if((length(x) > 3) || (length(y) > 3)){ #otherwise splinereg is not admissible
fm1 <- interpSpline(x,y)
if((from == 0) | (to == rs)){
pred.val <- unclass(predict(fm1, unique(c(from, x, to))))
} else {
list(x=unname(x),y=unname(y)) #MM2012-02-01
}
} else {
splineMessage <- TRUE # so that the message is only printed once
rval <- list(x=unname(x),y=unname(y)) #MM2012-02-01
if(from == 0){ rval$x <- c(0, rval$x)
rval$y <- c(NA, rval$y) }
if(to == rs){ rval$x <- c(rval$x, rs)
rval$y <- c(rval$y, NA) }
rval
}
}, xlist, thetapar, max.rs.NAgroups, NAgroups.min, NAgroups.max)
X.n <- object$X
# if (any(sapply(pred.list,is.null))) pred.list <- NULL #no spline interpolation applicable #MM2012-02-01
if(splineMessage) message("Spline interpolation in some subgroups not performed!\n Less than 4 different person parameters estimable!\n Perhaps NAs in subgroup(s).")
}
names(thetapar) <- names(se.theta) <- paste("NAgroup", 1L:length(thetapar), sep="")
#---------expand theta and se.theta, labeling -------------------
for(i in unique(gmemb)){
o.r <- rowSums(rbind(X.dummy[gmemb1==i,]), na.rm = TRUE) #orginal raw scores
names(o.r) <- rownames(X.dummy)[gmemb1 == i]
c.r <- rowSums(rbind(X[gmemb==i,]), na.rm = TRUE) #collapsed raw scores
match.ind <- match(o.r, c.r)
thetapar[[i]] <- thetapar[[i]][match.ind] #de-collapse theta's
se.theta[[i]] <- se.theta[[i]][match.ind] #de-collapse se's
names(thetapar[[i]]) <- names(se.theta[[i]]) <- names(o.r)
}
#--------------- end expand, labeling ---------------------------
#---------------------- theta.table new ----------------------
if(length(NAgroup_exclude) > 0L){
selector <- gmemb.X %in% gmemb_reduced
} else {
selector <- rep(TRUE, length(gmemb.X))
}
gmemb.X_final <- gmemb.X[selector]
while(any(diff(sort(unique(gmemb.X_final))) > 1L) | (min(gmemb.X_final) > 1L)){
if(!any(gmemb.X_final == 1L)){ gmemb.X_final <- gmemb.X_final - 1L; next }
for(i in 1:max(gmemb.X_final)){
if(sum(gmemb.X_final == i) == 0) gmemb.X_final[gmemb.X_final == (i+1L)] <- gmemb.X_final[gmemb.X_final == (i+1L)] - 1L
}
}
theta.table <- data.frame("Person Parameter" = rep(NA, nrow(object$X)),
"NAgroup" = NA,
"Interpolated" = FALSE,
row.names=rownames(object$X),
check.names = FALSE)
theta.table[selector, "Person Parameter"] <- mapply(function(rs, NAgroup){
pred.list[[NAgroup]]$y[which(pred.list[[NAgroup]]$x == rs)]
}, rowSums(object$X, na.rm=T)[selector], gmemb.X_final)
theta.table[selector, "NAgroup"] <- gmemb.X_final
if(length(pers.exe) > 0) theta.table[pers.exe,"Interpolated"] <- TRUE
result <- list(X = X.n, X01 = object$X01, X.ex = X.ex, W = object$W, model = object$model,
loglik = loglik, loglik.cml = object$loglik, npar = npar, iter = niter, betapar = object$betapar,
thetapar = thetapar, se.theta = se.theta, theta.table = theta.table,
pred.list = pred.list, hessian = hessian, mpoints = mpoints,
pers.ex = pers.exe, gmemb = gmemb1)
class(result) <- "ppar"
return(result)
}
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