Nothing
R/08-SE.methods.R
In mirt: Multidimensional Item Response Theory
Defines functions
SE.Fisher
SE.Oakes
SE.simple
SE.SEM
SE.Numerical
SE.Numerical <- function(pars, Theta, theta, dentype, itemloc, PrepList, ESTIMATE, constrain, Ls,
CUSTOM.IND, specific=NULL, sitems=NULL, EHPrior = NULL, warn, Data, type,
delta, lrPars, omp_threads){
longpars <- ESTIMATE$longpars
rlist <- ESTIMATE$rlist
infological=ESTIMATE$infological
ngroups <- length(pars)
J <- length(pars[[1L]]) - 1L
est <- c()
for(g in seq_len(ngroups))
for(j in seq_len(J+1L))
est <- c(est, pars[[g]][[j]]@est)
shortpars <- longpars[est]
gstructgrouppars <- vector('list', ngroups)
for(g in seq_len(ngroups))
gstructgrouppars[[g]] <- ExtractGroupPars(pars[[g]][[J+1L]])
for(g in seq_len(ngroups)){
for(i in seq_len(J)){
tmp <- c(itemloc[i]:(itemloc[i+1L] - 1L))
pars[[g]][[i]]@dat <- rlist[[g]]$r1[, tmp]
}
}
if(length(lrPars)){
est <- c(est, lrPars@est)
shortpars <- longpars[est]
}
hess <- numerical_deriv(shortpars, BL.LL, est=est, longpars=longpars, lrPars=lrPars,
pars=pars, ngroups=ngroups, J=J, itemloc=itemloc,
Theta=Theta, PrepList=PrepList, dentype=dentype,
constrain=constrain,
specific=specific, sitems=sitems, CUSTOM.IND=CUSTOM.IND,
EHPrior=EHPrior, Data=Data, theta=theta, type=type,
delta = delta, omp_threads=omp_threads, gradient = FALSE)
Hess <- matrix(0, length(longpars), length(longpars))
Hess[est, est] <- -hess
Hess <- updateHess(h=Hess, L=Ls$L)
info <- as.matrix(Hess[infological, infological])
ESTIMATE <- loadESTIMATEinfo(info=info, ESTIMATE=ESTIMATE, constrain=constrain, warn=warn)
return(ESTIMATE)
}
SE.SEM <- function(index, estmat, pars, constrain, Ls, PrepList, list, Theta, theta, dentype, ESTIMATE, DERIV,
collectLL, from, to, is.latent, Data, solnp_args, control){
est <- estmat[,index]
lrPars <- list$lrPars
full <- list$full
TOL <- list$TOL
dentype <- list$dentype
itemloc <- list$itemloc
J <- length(itemloc) - 1L
L <- Ls$L
Moptim <- list$Moptim
sitems <- list$sitems
specific <- list$specific
ngroups <- ESTIMATE$ngroups
NCYCLES <- ESTIMATE$cycles
if(NCYCLES <= 5L) stop('SEM can not be computed due to short EM history', call.=FALSE)
prior <- rlist <- vector('list', ngroups)
estpars <- ESTIMATE$estpars
redun_constr <- ESTIMATE$redun_constr
EMhistory <- ESTIMATE$EMhistory
MLestimates <- EMhistory[nrow(EMhistory), ]
UBOUND <- ESTIMATE$UBOUND
LBOUND <- ESTIMATE$LBOUND
estindex <- estpars
estindex[estpars] <- est
rij <- 1
prodlist <- PrepList[[1L]]$prodlist
nfact <- ncol(Theta)
ANY.PRIOR <- rep(FALSE, ngroups)
converged <- logical(sum(estpars & !redun_constr))
rijfull <- rep(NA, length(converged))
if(length(prodlist))
Theta <- prodterms(Theta, prodlist)
gTheta <- vector('list', ngroups)
for(g in seq_len(ngroups)){
ANY.PRIOR[g] <- any(sapply(pars[[g]], function(x) x@any.prior))
gTheta[[g]] <- Theta
}
converged <- FALSE
for (cycles in from:to){
longpars <- MLestimates
longpars[estindex] <- EMhistory[cycles, estindex]
longpars <- longpars_constrain(longpars=longpars, constrain=constrain)
pars <- reloadPars(longpars=longpars, pars=pars, ngroups=ngroups, J=J)
tmp <- updatePrior(pars=pars, gTheta=gTheta, list=list, ngroups=ngroups,
nfact=nfact, lrPars=lrPars, J=J, dentype=dentype,
sitems=sitems, cycles=cycles, rlist=rlist, full=full, MC=list$method == 'QMC')
prior <- tmp$prior; Prior <- tmp$Prior; Priorbetween <- tmp$Priorbetween
#Estep
for(g in seq_len(ngroups)){
if(dentype == 'bfactor'){
rlist[[g]] <- Estep.bfactor(pars=pars[[g]], tabdata=Data$tabdatalong, freq=Data$Freq[[g]],
Theta=Theta, prior=prior[[g]], wmiss=Data$wmiss,
Priorbetween=Priorbetween[[g]], specific=specific, sitems=sitems,
itemloc=itemloc, CUSTOM.IND=list$CUSTOM.IND, omp_threads=1L)
} else {
rlist[[g]] <- Estep.mirt(pars=pars[[g]], tabdata=Data$tabdatalong, freq=Data$Freq[[g]],
CUSTOM.IND=list$CUSTOM.IND, Theta=Theta, wmiss=Data$wmiss,
prior=Prior[[g]], itemloc=itemloc, full=full, omp_threads=1L)
}
}
for(g in seq_len(ngroups)){
for(i in 1L:J)
pars[[g]][[i]]@dat <- rlist[[g]]$r1[, c(itemloc[i]:(itemloc[i+1L] - 1L)),
drop=FALSE]
if(dentype == 'bfactor'){
pars[[g]][[J+1L]]@rrb <- rlist[[g]]$r2
pars[[g]][[J+1L]]@rrs <- rlist[[g]]$r3
} else pars[[g]][[J+1L]]@rr <- rlist[[g]]$r1g
}
longpars <- Mstep(pars=pars, est=estpars, longpars=longpars, ngroups=ngroups, J=J,
gTheta=gTheta, itemloc=itemloc, Prior=Prior, ANY.PRIOR=ANY.PRIOR,
PrepList=PrepList, L=L, UBOUND=UBOUND, LBOUND=LBOUND, nfact=nfact,
rlist=rlist, constrain=constrain, DERIV=DERIV, keep_vcov_PD=list$keep_vcov_PD,
CUSTOM.IND=list$CUSTOM.IND, SLOW.IND=list$SLOW.IND, dentype=dentype,
Moptim=Moptim, Mrate=1, TOL=list$MSTEPTOL, solnp_args=solnp_args, full=full,
lrPars=lrPars, control=control)
rijlast <- rij
denom <- (EMhistory[cycles, estindex] - MLestimates[estindex])
if(denom == 0){
converged <- FALSE
break
}
rij <- (longpars[estpars & !redun_constr] - MLestimates[estpars & !redun_constr]) / denom
diff <- abs(rij - rijlast) < TOL
converged <- diff | converged
which <- is.na(rijfull) & converged
rijfull[which] <- rij[which]
if(all(!is.na(rijfull))){
converged <- TRUE
break
}
} #END EM
rijfull[is.na(rijfull)] <- rij[is.na(rijfull)]
attr(rijfull, 'converged') <- converged
return(rijfull)
}
SE.simple <- function(PrepList, ESTIMATE, Theta, constrain, Ls, N, type,
CUSTOM.IND, SLOW.IND, warn, message, Data, complete){
pars <- ESTIMATE$pars
itemloc <- PrepList[[1L]]$itemloc
ngroups <- length(pars)
nitems <- length(pars[[1L]]) - 1L
L <- ESTIMATE$L
Prior <- ESTIMATE$Prior
prior <- ESTIMATE$prior
Priorbetween <- ESTIMATE$Priorbetween
isbifactor <- length(Priorbetween[[1L]]) > 0L
if(!isbifactor)
prior <- Priorbetween <- list(matrix(0))
sitems <- ESTIMATE$sitems
iscross <- ifelse(type %in% c('crossprod', 'sandwich'), TRUE, FALSE)
gitemtrace <- vector('list', ngroups)
for(g in seq_len(ngroups)){
gitemtrace[[g]] <- computeItemtrace(pars=pars[[g]], Theta=Theta,
itemloc=itemloc, CUSTOM.IND=CUSTOM.IND)
gp <- ExtractGroupPars(pars[[g]][[nitems+1L]])
pars[[g]][[nitems+1L]]@mu <- gp$gmeans
pars[[g]][[nitems+1L]]@sig <- gp$gcov
pars[[g]][[nitems+1L]]@invsig <- solve(gp$gcov)
pars[[g]][[nitems+1L]]@meanTheta <- colMeans(Theta)
}
npars <- ncol(L)
gPrior <- t(do.call(rbind, Prior))
rs <- do.call(rbind, Data$Freq)
whichitems <- unique(c(CUSTOM.IND, SLOW.IND))
infolist <- .Call("computeInfo", pars, Theta, gPrior, prior, do.call(rbind, Priorbetween),
Data$tabdatalong, rs, sitems, itemloc, gitemtrace, npars, Data$wmiss,
isbifactor, iscross)
Igrad <- infolist[["Igrad"]]; IgradP <- infolist[["IgradP"]]
if(length(whichitems)){
warning('Internal information matrix computations currently not supported for at
least one of the supplied items. Information matrix/standard errors not computed', call.=FALSE)
return(ESTIMATE)
}
if(type != 'Louis'){
Iprior <- matrix(0, nrow(Igrad), ncol(Igrad))
ind1 <- 1L
for(group in seq_len(length(pars))){
for (i in seq_len(length(pars[[group]]))){
np <- length(pars[[group]][[i]]@par)
deriv <- DerivativePriors(x=pars[[group]][[i]], grad=numeric(np),
hess=matrix(0, np, np))
ind2 <- ind1 + np - 1L
Iprior[ind1:ind2, ind1:ind2] <- deriv$hess
ind1 <- ind2 + 1L
}
}
Iprior <- -updateHess(Iprior, L=Ls$L)
Iprior <- Iprior[ESTIMATE$estindex_unique, ESTIMATE$estindex_unique]
}
Igrad <- updateHess(Igrad, L=Ls$L)
IgradP <- updateHess(IgradP, L=Ls$L)
Igrad <- Igrad[ESTIMATE$estindex_unique, ESTIMATE$estindex_unique]
IgradP <- IgradP[ESTIMATE$estindex_unique, ESTIMATE$estindex_unique]
Ihess <- complete
if(type == 'Louis'){
info <- -Ihess - IgradP + Igrad
} else if(type == 'crossprod'){
info <- Igrad + Iprior
} else if(type == 'sandwich.Louis'){
tmp <- solve(-Ihess - IgradP + Igrad)
info <- solve(tmp %*% (Igrad + Iprior) %*% tmp)
} else if(type == 'sandwich'){
tmp <- -solve(ESTIMATE$hess)
info <- solve(tmp %*% (Igrad + Iprior) %*% tmp)
}
info <- as.matrix(info)
colnames(info) <- rownames(info) <- names(ESTIMATE$correction)
ESTIMATE <- loadESTIMATEinfo(info=info, ESTIMATE=ESTIMATE, constrain=constrain, warn=warn)
return(ESTIMATE)
}
SE.Oakes <- function(pick, pars, L, constrain, est, shortpars, longpars,
gTheta, list, ngroups, J, dentype, sitems,
rlist, full, Data, specific, itemloc, CUSTOM.IND,
delta, prior, Prior, Priorbetween, nfact, mixtype,
PrepList, ANY.PRIOR, DERIV, SLOW.IND, Norder, omp_threads,
zero_g = NULL){
r <- 1L
Richardson <- if(Norder > 2L) TRUE else FALSE
if(Richardson){
delta <- delta * 10
r <- Norder
Norder <- 2L
R <- array(0, dim = c(length(shortpars), r, 2L))
}
if(is.null(zero_g)){
grad <- matrix(0, 2L, length(shortpars))
signs <- c(-1, 1)
} else {
grad <- matrix(0, 2L, length(shortpars))
grad[1L, ] <- zero_g
signs <- 1
}
for(rr in 0L:(r-1L)){
row <- ifelse(is.null(zero_g), 1L, 2L)
for(sign in signs){
longpars_old <- longpars
d <- sign * delta
longpars[which(est)[pick]] <- shortpars[pick] + d
longpars <- longpars_constrain(longpars, constrain)
pars <- reloadPars(longpars=longpars, pars=pars,
ngroups=ngroups, J=J)
tmp <- updatePrior(pars=pars, gTheta=gTheta,
list=list, ngroups=ngroups, nfact=nfact,
J=J, dentype=dentype, sitems=sitems, cycles=100L,
rlist=rlist, full=full, MC=list$method == 'QMCEM')
prior <- tmp$prior; Prior <- tmp$Prior; Priorbetween <- tmp$Priorbetween
Elist <- Estep(pars=pars, Data=Data, gTheta=gTheta, prior=prior, Prior=Prior,
Priorbetween=Priorbetween, specific=specific, sitems=sitems,
ngroups=ngroups, itemloc=itemloc, CUSTOM.IND=CUSTOM.IND,
dentype=dentype, rlist=rlist, full=full, Etable=list$Etable,
omp_threads=omp_threads)
rlist <- Elist$rlist
longpars <- longpars_old
pars <- reloadPars(longpars=longpars, pars=pars,
ngroups=ngroups, J=J)
if(pars[[1L]][[J + 1L]]@itemclass == -1L){
for(g in seq_len(length(pars))){
gp <- pars[[g]][[J + 1L]]
pars[[g]][[J + 1L]]@density <- gp@safe_den(gp, gTheta[[g]])
}
}
for(g in seq_len(ngroups)){
for(i in 1L:J)
pars[[g]][[i]]@dat <- rlist[[g]]$r1[ , c(itemloc[i]:(itemloc[i+1L] - 1L)),
drop=FALSE]
if(dentype == 'bfactor'){
pars[[g]][[J+1L]]@rrb <- rlist[[g]]$r2
pars[[g]][[J+1L]]@rrs <- rlist[[g]]$r3
} else pars[[g]][[J+1L]]@rr <- rlist[[g]]$r1g
}
g <- .Call('computeDPars', pars, gTheta, matrix(0L, 1L, J), length(est), 0L, 0L, 1L, TRUE)$grad
if(length(SLOW.IND)){
for(group in seq_len(ngroups)){
for (i in SLOW.IND){
deriv <- if(i == (J + 1L)){
Deriv(pars[[group]][[i]], Theta=gTheta[[group]])
} else {
DERIV[[group]][[i]](x=pars[[group]][[i]], Theta=gTheta[[group]])
}
g[pars[[group]][[i]]@parnum] <- deriv$grad
}
}
}
if(dentype == 'mixture'){
mixtype$par <- sapply(1L:length(pars),
function(g) sum(pars[[g]][[J+1L]]@par[length(pars[[g]][[J+1L]]@par)]))
mixtype$dat <- matrix(sapply(1L:length(pars),
function(g) sum(pars[[g]][[J+1L]]@rr)), 1L)
deriv <- Deriv.mix(mixtype)
g[mixtype$parnum] <- deriv$grad
}
tmp <- g %*% L
if(pick == 0L) return(tmp[est])
grad[row, ] <- tmp[est]
row <- row + 1L
}
cfs <- get_deriv_coefs(order=Norder)
ret <- colSums(cfs * grad) / delta
if(!Richardson) return(ret)
delta <- delta / 2
if(rr == 0L){
R[, 1L, 1L] <- ret
} else {
R[ ,1L, 2L] <- ret
for (j in 1L:rr)
R[ ,j + 1L, 2L] <- (4^j*R[ , j, 2L] - R[, j, 1L])/(4^j - 1)
R[ , , 1L] <- R[ , , 2L]
}
}
R[ , r, 2L]
}
SE.Fisher <- function(PrepList, ESTIMATE, Theta, constrain, Ls, CUSTOM.IND,
SLOW.IND, warn, Data, full, omp_threads){
pars <- ESTIMATE$pars
Ns <- table(Data$group)
itemloc <- PrepList[[1L]]$itemloc
ngroups <- length(pars)
nitems <- length(pars[[1L]]) - 1L
L <- Ls$L
DX <- numeric(ncol(L))
Prior <- ESTIMATE$Prior
tabdata <- Data$tabdatalong
K <- Data$K
resp <- vector('list', nitems)
for(i in seq_len(nitems))
resp[[i]] <- 0L:(K[i]-1L)
resp <- expand.grid(resp)
stringfulldata <- apply(resp, 1L, paste, sep='', collapse = '/')
stringtabdata <- unique(stringfulldata)
tabdata2 <- lapply(strsplit(stringtabdata, split='/'), as.integer)
tabdata2 <- do.call(rbind, tabdata2)
tabdata2[tabdata2 == 99999L] <- NA
tabdata <- matrix(0L, nrow(tabdata2), sum(K))
for(i in seq_len(nitems)){
uniq <- sort(na.omit(unique(tabdata2[,i])))
if(length(uniq) < K[i]) uniq <- 0L:(K[i]-1L)
for(j in seq_len(length(uniq)))
tabdata[,itemloc[i] + j - 1L] <- as.integer(tabdata2[,i] == uniq[j])
}
gTheta <- vector('list', ngroups)
for(g in seq_len(ngroups)){
PrepList[[g]]$tabdata <- tabdata
gTheta[[g]] <- Theta
}
info_list <- vector('list', ngroups)
for(g in seq_len(ngroups)){
info <- 0
# reset
for(gg in seq_len(ngroups)){
for(i in seq_len(nitems)){
tmp <- c(itemloc[i]:(itemloc[i+1L] - 1L))
pars[[gg]][[i]]@dat <- pars[[gg]][[i]]@itemtrace <-
matrix(0, nrow(Theta), length(tmp))
}
pars[[gg]][[nitems + 1L]]@rr <-
numeric(length(pars[[gg]][[nitems + 1L]]@rr))
}
for(pat in seq_len(nrow(tabdata))){
gtabdata <- PrepList[[g]]$tabdata[pat, , drop=FALSE]
rlist <- Estep.mirt(pars=pars[[g]], tabdata=gtabdata, freq=1L,
CUSTOM.IND=CUSTOM.IND, full=full, wmiss=1,
Theta=Theta, prior=Prior[[g]], itemloc=itemloc,
deriv=TRUE, omp_threads=omp_threads)
for(i in seq_len(nitems)){
tmp <- c(itemloc[i]:(itemloc[i+1L] - 1L))
pars[[g]][[i]]@dat <- rlist$r1[, tmp]
pars[[g]][[i]]@itemtrace <- rlist$itemtrace[, tmp]
}
pars[[g]][[nitems + 1L]]@rr <- rlist$r1g
DX <- .Call('computeDPars', pars, gTheta, matrix(0L, 1L, nitems),
ncol(L), 0L, 0L, 1L, TRUE)$grad
info <- info + DX %*% t(DX) * rlist$expected
}
info_list[[g]] <- Ns[g] * info
}
info <- Reduce("+", info_list)
info <- as.matrix(updateHess(info, L=Ls$L)[ESTIMATE$estindex_unique,
ESTIMATE$estindex_unique])
colnames(info) <- rownames(info) <- names(ESTIMATE$correction)
ESTIMATE <- loadESTIMATEinfo(info=info, ESTIMATE=ESTIMATE,
constrain=constrain, warn=warn)
return(ESTIMATE)
}
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Defines functions SE.Fisher SE.Oakes SE.simple SE.SEM SE.Numerical
SE.Numerical <- function(pars, Theta, theta, dentype, itemloc, PrepList, ESTIMATE, constrain, Ls,
CUSTOM.IND, specific=NULL, sitems=NULL, EHPrior = NULL, warn, Data, type,
delta, lrPars, omp_threads){
longpars <- ESTIMATE$longpars
rlist <- ESTIMATE$rlist
infological=ESTIMATE$infological
ngroups <- length(pars)
J <- length(pars[[1L]]) - 1L
est <- c()
for(g in seq_len(ngroups))
for(j in seq_len(J+1L))
est <- c(est, pars[[g]][[j]]@est)
shortpars <- longpars[est]
gstructgrouppars <- vector('list', ngroups)
for(g in seq_len(ngroups))
gstructgrouppars[[g]] <- ExtractGroupPars(pars[[g]][[J+1L]])
for(g in seq_len(ngroups)){
for(i in seq_len(J)){
tmp <- c(itemloc[i]:(itemloc[i+1L] - 1L))
pars[[g]][[i]]@dat <- rlist[[g]]$r1[, tmp]
}
}
if(length(lrPars)){
est <- c(est, lrPars@est)
shortpars <- longpars[est]
}
hess <- numerical_deriv(shortpars, BL.LL, est=est, longpars=longpars, lrPars=lrPars,
pars=pars, ngroups=ngroups, J=J, itemloc=itemloc,
Theta=Theta, PrepList=PrepList, dentype=dentype,
constrain=constrain,
specific=specific, sitems=sitems, CUSTOM.IND=CUSTOM.IND,
EHPrior=EHPrior, Data=Data, theta=theta, type=type,
delta = delta, omp_threads=omp_threads, gradient = FALSE)
Hess <- matrix(0, length(longpars), length(longpars))
Hess[est, est] <- -hess
Hess <- updateHess(h=Hess, L=Ls$L)
info <- as.matrix(Hess[infological, infological])
ESTIMATE <- loadESTIMATEinfo(info=info, ESTIMATE=ESTIMATE, constrain=constrain, warn=warn)
return(ESTIMATE)
}
SE.SEM <- function(index, estmat, pars, constrain, Ls, PrepList, list, Theta, theta, dentype, ESTIMATE, DERIV,
collectLL, from, to, is.latent, Data, solnp_args, control){
est <- estmat[,index]
lrPars <- list$lrPars
full <- list$full
TOL <- list$TOL
dentype <- list$dentype
itemloc <- list$itemloc
J <- length(itemloc) - 1L
L <- Ls$L
Moptim <- list$Moptim
sitems <- list$sitems
specific <- list$specific
ngroups <- ESTIMATE$ngroups
NCYCLES <- ESTIMATE$cycles
if(NCYCLES <= 5L) stop('SEM can not be computed due to short EM history', call.=FALSE)
prior <- rlist <- vector('list', ngroups)
estpars <- ESTIMATE$estpars
redun_constr <- ESTIMATE$redun_constr
EMhistory <- ESTIMATE$EMhistory
MLestimates <- EMhistory[nrow(EMhistory), ]
UBOUND <- ESTIMATE$UBOUND
LBOUND <- ESTIMATE$LBOUND
estindex <- estpars
estindex[estpars] <- est
rij <- 1
prodlist <- PrepList[[1L]]$prodlist
nfact <- ncol(Theta)
ANY.PRIOR <- rep(FALSE, ngroups)
converged <- logical(sum(estpars & !redun_constr))
rijfull <- rep(NA, length(converged))
if(length(prodlist))
Theta <- prodterms(Theta, prodlist)
gTheta <- vector('list', ngroups)
for(g in seq_len(ngroups)){
ANY.PRIOR[g] <- any(sapply(pars[[g]], function(x) x@any.prior))
gTheta[[g]] <- Theta
}
converged <- FALSE
for (cycles in from:to){
longpars <- MLestimates
longpars[estindex] <- EMhistory[cycles, estindex]
longpars <- longpars_constrain(longpars=longpars, constrain=constrain)
pars <- reloadPars(longpars=longpars, pars=pars, ngroups=ngroups, J=J)
tmp <- updatePrior(pars=pars, gTheta=gTheta, list=list, ngroups=ngroups,
nfact=nfact, lrPars=lrPars, J=J, dentype=dentype,
sitems=sitems, cycles=cycles, rlist=rlist, full=full, MC=list$method == 'QMC')
prior <- tmp$prior; Prior <- tmp$Prior; Priorbetween <- tmp$Priorbetween
#Estep
for(g in seq_len(ngroups)){
if(dentype == 'bfactor'){
rlist[[g]] <- Estep.bfactor(pars=pars[[g]], tabdata=Data$tabdatalong, freq=Data$Freq[[g]],
Theta=Theta, prior=prior[[g]], wmiss=Data$wmiss,
Priorbetween=Priorbetween[[g]], specific=specific, sitems=sitems,
itemloc=itemloc, CUSTOM.IND=list$CUSTOM.IND, omp_threads=1L)
} else {
rlist[[g]] <- Estep.mirt(pars=pars[[g]], tabdata=Data$tabdatalong, freq=Data$Freq[[g]],
CUSTOM.IND=list$CUSTOM.IND, Theta=Theta, wmiss=Data$wmiss,
prior=Prior[[g]], itemloc=itemloc, full=full, omp_threads=1L)
}
}
for(g in seq_len(ngroups)){
for(i in 1L:J)
pars[[g]][[i]]@dat <- rlist[[g]]$r1[, c(itemloc[i]:(itemloc[i+1L] - 1L)),
drop=FALSE]
if(dentype == 'bfactor'){
pars[[g]][[J+1L]]@rrb <- rlist[[g]]$r2
pars[[g]][[J+1L]]@rrs <- rlist[[g]]$r3
} else pars[[g]][[J+1L]]@rr <- rlist[[g]]$r1g
}
longpars <- Mstep(pars=pars, est=estpars, longpars=longpars, ngroups=ngroups, J=J,
gTheta=gTheta, itemloc=itemloc, Prior=Prior, ANY.PRIOR=ANY.PRIOR,
PrepList=PrepList, L=L, UBOUND=UBOUND, LBOUND=LBOUND, nfact=nfact,
rlist=rlist, constrain=constrain, DERIV=DERIV, keep_vcov_PD=list$keep_vcov_PD,
CUSTOM.IND=list$CUSTOM.IND, SLOW.IND=list$SLOW.IND, dentype=dentype,
Moptim=Moptim, Mrate=1, TOL=list$MSTEPTOL, solnp_args=solnp_args, full=full,
lrPars=lrPars, control=control)
rijlast <- rij
denom <- (EMhistory[cycles, estindex] - MLestimates[estindex])
if(denom == 0){
converged <- FALSE
break
}
rij <- (longpars[estpars & !redun_constr] - MLestimates[estpars & !redun_constr]) / denom
diff <- abs(rij - rijlast) < TOL
converged <- diff | converged
which <- is.na(rijfull) & converged
rijfull[which] <- rij[which]
if(all(!is.na(rijfull))){
converged <- TRUE
break
}
} #END EM
rijfull[is.na(rijfull)] <- rij[is.na(rijfull)]
attr(rijfull, 'converged') <- converged
return(rijfull)
}
SE.simple <- function(PrepList, ESTIMATE, Theta, constrain, Ls, N, type,
CUSTOM.IND, SLOW.IND, warn, message, Data, complete){
pars <- ESTIMATE$pars
itemloc <- PrepList[[1L]]$itemloc
ngroups <- length(pars)
nitems <- length(pars[[1L]]) - 1L
L <- ESTIMATE$L
Prior <- ESTIMATE$Prior
prior <- ESTIMATE$prior
Priorbetween <- ESTIMATE$Priorbetween
isbifactor <- length(Priorbetween[[1L]]) > 0L
if(!isbifactor)
prior <- Priorbetween <- list(matrix(0))
sitems <- ESTIMATE$sitems
iscross <- ifelse(type %in% c('crossprod', 'sandwich'), TRUE, FALSE)
gitemtrace <- vector('list', ngroups)
for(g in seq_len(ngroups)){
gitemtrace[[g]] <- computeItemtrace(pars=pars[[g]], Theta=Theta,
itemloc=itemloc, CUSTOM.IND=CUSTOM.IND)
gp <- ExtractGroupPars(pars[[g]][[nitems+1L]])
pars[[g]][[nitems+1L]]@mu <- gp$gmeans
pars[[g]][[nitems+1L]]@sig <- gp$gcov
pars[[g]][[nitems+1L]]@invsig <- solve(gp$gcov)
pars[[g]][[nitems+1L]]@meanTheta <- colMeans(Theta)
}
npars <- ncol(L)
gPrior <- t(do.call(rbind, Prior))
rs <- do.call(rbind, Data$Freq)
whichitems <- unique(c(CUSTOM.IND, SLOW.IND))
infolist <- .Call("computeInfo", pars, Theta, gPrior, prior, do.call(rbind, Priorbetween),
Data$tabdatalong, rs, sitems, itemloc, gitemtrace, npars, Data$wmiss,
isbifactor, iscross)
Igrad <- infolist[["Igrad"]]; IgradP <- infolist[["IgradP"]]
if(length(whichitems)){
warning('Internal information matrix computations currently not supported for at
least one of the supplied items. Information matrix/standard errors not computed', call.=FALSE)
return(ESTIMATE)
}
if(type != 'Louis'){
Iprior <- matrix(0, nrow(Igrad), ncol(Igrad))
ind1 <- 1L
for(group in seq_len(length(pars))){
for (i in seq_len(length(pars[[group]]))){
np <- length(pars[[group]][[i]]@par)
deriv <- DerivativePriors(x=pars[[group]][[i]], grad=numeric(np),
hess=matrix(0, np, np))
ind2 <- ind1 + np - 1L
Iprior[ind1:ind2, ind1:ind2] <- deriv$hess
ind1 <- ind2 + 1L
}
}
Iprior <- -updateHess(Iprior, L=Ls$L)
Iprior <- Iprior[ESTIMATE$estindex_unique, ESTIMATE$estindex_unique]
}
Igrad <- updateHess(Igrad, L=Ls$L)
IgradP <- updateHess(IgradP, L=Ls$L)
Igrad <- Igrad[ESTIMATE$estindex_unique, ESTIMATE$estindex_unique]
IgradP <- IgradP[ESTIMATE$estindex_unique, ESTIMATE$estindex_unique]
Ihess <- complete
if(type == 'Louis'){
info <- -Ihess - IgradP + Igrad
} else if(type == 'crossprod'){
info <- Igrad + Iprior
} else if(type == 'sandwich.Louis'){
tmp <- solve(-Ihess - IgradP + Igrad)
info <- solve(tmp %*% (Igrad + Iprior) %*% tmp)
} else if(type == 'sandwich'){
tmp <- -solve(ESTIMATE$hess)
info <- solve(tmp %*% (Igrad + Iprior) %*% tmp)
}
info <- as.matrix(info)
colnames(info) <- rownames(info) <- names(ESTIMATE$correction)
ESTIMATE <- loadESTIMATEinfo(info=info, ESTIMATE=ESTIMATE, constrain=constrain, warn=warn)
return(ESTIMATE)
}
SE.Oakes <- function(pick, pars, L, constrain, est, shortpars, longpars,
gTheta, list, ngroups, J, dentype, sitems,
rlist, full, Data, specific, itemloc, CUSTOM.IND,
delta, prior, Prior, Priorbetween, nfact, mixtype,
PrepList, ANY.PRIOR, DERIV, SLOW.IND, Norder, omp_threads,
zero_g = NULL){
r <- 1L
Richardson <- if(Norder > 2L) TRUE else FALSE
if(Richardson){
delta <- delta * 10
r <- Norder
Norder <- 2L
R <- array(0, dim = c(length(shortpars), r, 2L))
}
if(is.null(zero_g)){
grad <- matrix(0, 2L, length(shortpars))
signs <- c(-1, 1)
} else {
grad <- matrix(0, 2L, length(shortpars))
grad[1L, ] <- zero_g
signs <- 1
}
for(rr in 0L:(r-1L)){
row <- ifelse(is.null(zero_g), 1L, 2L)
for(sign in signs){
longpars_old <- longpars
d <- sign * delta
longpars[which(est)[pick]] <- shortpars[pick] + d
longpars <- longpars_constrain(longpars, constrain)
pars <- reloadPars(longpars=longpars, pars=pars,
ngroups=ngroups, J=J)
tmp <- updatePrior(pars=pars, gTheta=gTheta,
list=list, ngroups=ngroups, nfact=nfact,
J=J, dentype=dentype, sitems=sitems, cycles=100L,
rlist=rlist, full=full, MC=list$method == 'QMCEM')
prior <- tmp$prior; Prior <- tmp$Prior; Priorbetween <- tmp$Priorbetween
Elist <- Estep(pars=pars, Data=Data, gTheta=gTheta, prior=prior, Prior=Prior,
Priorbetween=Priorbetween, specific=specific, sitems=sitems,
ngroups=ngroups, itemloc=itemloc, CUSTOM.IND=CUSTOM.IND,
dentype=dentype, rlist=rlist, full=full, Etable=list$Etable,
omp_threads=omp_threads)
rlist <- Elist$rlist
longpars <- longpars_old
pars <- reloadPars(longpars=longpars, pars=pars,
ngroups=ngroups, J=J)
if(pars[[1L]][[J + 1L]]@itemclass == -1L){
for(g in seq_len(length(pars))){
gp <- pars[[g]][[J + 1L]]
pars[[g]][[J + 1L]]@density <- gp@safe_den(gp, gTheta[[g]])
}
}
for(g in seq_len(ngroups)){
for(i in 1L:J)
pars[[g]][[i]]@dat <- rlist[[g]]$r1[ , c(itemloc[i]:(itemloc[i+1L] - 1L)),
drop=FALSE]
if(dentype == 'bfactor'){
pars[[g]][[J+1L]]@rrb <- rlist[[g]]$r2
pars[[g]][[J+1L]]@rrs <- rlist[[g]]$r3
} else pars[[g]][[J+1L]]@rr <- rlist[[g]]$r1g
}
g <- .Call('computeDPars', pars, gTheta, matrix(0L, 1L, J), length(est), 0L, 0L, 1L, TRUE)$grad
if(length(SLOW.IND)){
for(group in seq_len(ngroups)){
for (i in SLOW.IND){
deriv <- if(i == (J + 1L)){
Deriv(pars[[group]][[i]], Theta=gTheta[[group]])
} else {
DERIV[[group]][[i]](x=pars[[group]][[i]], Theta=gTheta[[group]])
}
g[pars[[group]][[i]]@parnum] <- deriv$grad
}
}
}
if(dentype == 'mixture'){
mixtype$par <- sapply(1L:length(pars),
function(g) sum(pars[[g]][[J+1L]]@par[length(pars[[g]][[J+1L]]@par)]))
mixtype$dat <- matrix(sapply(1L:length(pars),
function(g) sum(pars[[g]][[J+1L]]@rr)), 1L)
deriv <- Deriv.mix(mixtype)
g[mixtype$parnum] <- deriv$grad
}
tmp <- g %*% L
if(pick == 0L) return(tmp[est])
grad[row, ] <- tmp[est]
row <- row + 1L
}
cfs <- get_deriv_coefs(order=Norder)
ret <- colSums(cfs * grad) / delta
if(!Richardson) return(ret)
delta <- delta / 2
if(rr == 0L){
R[, 1L, 1L] <- ret
} else {
R[ ,1L, 2L] <- ret
for (j in 1L:rr)
R[ ,j + 1L, 2L] <- (4^j*R[ , j, 2L] - R[, j, 1L])/(4^j - 1)
R[ , , 1L] <- R[ , , 2L]
}
}
R[ , r, 2L]
}
SE.Fisher <- function(PrepList, ESTIMATE, Theta, constrain, Ls, CUSTOM.IND,
SLOW.IND, warn, Data, full, omp_threads){
pars <- ESTIMATE$pars
Ns <- table(Data$group)
itemloc <- PrepList[[1L]]$itemloc
ngroups <- length(pars)
nitems <- length(pars[[1L]]) - 1L
L <- Ls$L
DX <- numeric(ncol(L))
Prior <- ESTIMATE$Prior
tabdata <- Data$tabdatalong
K <- Data$K
resp <- vector('list', nitems)
for(i in seq_len(nitems))
resp[[i]] <- 0L:(K[i]-1L)
resp <- expand.grid(resp)
stringfulldata <- apply(resp, 1L, paste, sep='', collapse = '/')
stringtabdata <- unique(stringfulldata)
tabdata2 <- lapply(strsplit(stringtabdata, split='/'), as.integer)
tabdata2 <- do.call(rbind, tabdata2)
tabdata2[tabdata2 == 99999L] <- NA
tabdata <- matrix(0L, nrow(tabdata2), sum(K))
for(i in seq_len(nitems)){
uniq <- sort(na.omit(unique(tabdata2[,i])))
if(length(uniq) < K[i]) uniq <- 0L:(K[i]-1L)
for(j in seq_len(length(uniq)))
tabdata[,itemloc[i] + j - 1L] <- as.integer(tabdata2[,i] == uniq[j])
}
gTheta <- vector('list', ngroups)
for(g in seq_len(ngroups)){
PrepList[[g]]$tabdata <- tabdata
gTheta[[g]] <- Theta
}
info_list <- vector('list', ngroups)
for(g in seq_len(ngroups)){
info <- 0
# reset
for(gg in seq_len(ngroups)){
for(i in seq_len(nitems)){
tmp <- c(itemloc[i]:(itemloc[i+1L] - 1L))
pars[[gg]][[i]]@dat <- pars[[gg]][[i]]@itemtrace <-
matrix(0, nrow(Theta), length(tmp))
}
pars[[gg]][[nitems + 1L]]@rr <-
numeric(length(pars[[gg]][[nitems + 1L]]@rr))
}
for(pat in seq_len(nrow(tabdata))){
gtabdata <- PrepList[[g]]$tabdata[pat, , drop=FALSE]
rlist <- Estep.mirt(pars=pars[[g]], tabdata=gtabdata, freq=1L,
CUSTOM.IND=CUSTOM.IND, full=full, wmiss=1,
Theta=Theta, prior=Prior[[g]], itemloc=itemloc,
deriv=TRUE, omp_threads=omp_threads)
for(i in seq_len(nitems)){
tmp <- c(itemloc[i]:(itemloc[i+1L] - 1L))
pars[[g]][[i]]@dat <- rlist$r1[, tmp]
pars[[g]][[i]]@itemtrace <- rlist$itemtrace[, tmp]
}
pars[[g]][[nitems + 1L]]@rr <- rlist$r1g
DX <- .Call('computeDPars', pars, gTheta, matrix(0L, 1L, nitems),
ncol(L), 0L, 0L, 1L, TRUE)$grad
info <- info + DX %*% t(DX) * rlist$expected
}
info_list[[g]] <- Ns[g] * info
}
info <- Reduce("+", info_list)
info <- as.matrix(updateHess(info, L=Ls$L)[ESTIMATE$estindex_unique,
ESTIMATE$estindex_unique])
colnames(info) <- rownames(info) <- names(ESTIMATE$correction)
ESTIMATE <- loadESTIMATEinfo(info=info, ESTIMATE=ESTIMATE,
constrain=constrain, warn=warn)
return(ESTIMATE)
}
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