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library(ggplot2)
library(OpenMx)
library(rpf)
library(pROC)
mkmodel <- function(numItems, numPeople, genCond, fitCond, numBad) {
spec <- list()
trueFit <- rep(FALSE, numBad)
trueFit <- c(trueFit, rep(TRUE, numItems - length(trueFit)))
if (genCond == "2pl") {
spec[1:numItems] <- rpf.grm()
correct <- sapply(spec, rpf.rparam)
correct['a', trueFit==TRUE] <- 1
data <- rpf.sample(numPeople, spec, correct)
if (fitCond == "1pl") {
spec[1:numItems] <- rpf.grm()
ip.mat <- mxMatrix(name="ItemParam", nrow=2, ncol=numItems,
values=c(1,0),
free=c(FALSE, TRUE),
dimnames=list(rownames(correct), colnames(data)))
} else { stop(fitCond) }
}
if (genCond == "3pl") {
spec[1:numItems] <- rpf.drm()
correct <- sapply(spec, rpf.rparam)
correct['g',trueFit==TRUE] <- logit(0)
correct['u',trueFit==TRUE] <- logit(1)
correct['u',trueFit==FALSE] <- logit(.5)
correct['u',trueFit==FALSE] <- logit(1)
data <- rpf.sample(numPeople, spec, correct)
if (fitCond == "2pl") {
spec[1:numItems] <- rpf.drm()
ip.mat <- mxMatrix(name="ItemParam", nrow=4, ncol=numItems,
values=c(1,0, logit(0), logit(1)),
free=c(TRUE, TRUE, FALSE, FALSE),
dimnames=list(rownames(correct), colnames(data)))
} else { stop(fitCond) }
}
if (genCond == "nom2") {
spec[1:numItems] <- rpf.nrm(outcomes=4)
correct <- sapply(spec, rpf.rparam)
half <- numItems/2
correct[c('alf2', 'alf3'), trueFit==TRUE] <- 0
data <- rpf.sample(numPeople, spec, correct)
if (fitCond == "grm") {
spec[1:numItems] <- rpf.grm(outcomes=4)
ip.mat <- mxMatrix(name="ItemParam", nrow=4, ncol=numItems,
values=rpf.rparam(spec[[1]]),
free=TRUE,
dimnames=list(names(rpf.rparam(spec[[1]])), colnames(data)))
} else { stop(fitCond) }
}
m.mat <- mxMatrix(name="mean", nrow=1, ncol=1, values=0, free=FALSE, dimnames=list("a","a"))
cov.mat <- mxMatrix(name="cov", nrow=1, ncol=1, values=1, free=FALSE, dimnames=list("a","a"))
m1 <- mxModel(model="ot2k", ip.mat, m.mat, cov.mat,
mxData(observed=data, type="raw"),
mxExpectationBA81(ItemSpec=spec, ItemParam="ItemParam",
mean="mean", cov="cov"),
mxFitFunctionML(),
mxComputeEM('expectation', 'scores', mxComputeNewtonRaphson()))
list(model=m1, trueFit=trueFit)
}
trial <- function(numItems, numPeople, genCond, fitCond, numBad) {
got <- mkmodel(numItems, numPeople, genCond, fitCond, numBad)
model <- got$model
trueFit <- got$trueFit
model <- mxRun(model, silent=TRUE)
grp <- list(spec=model$expectation$ItemSpec,
param=model$ItemParam$values,
mean=model$mean$values,
cov=model$cov$values,
data=model$data$observed)
result <- expand.grid(method=c("pearson", "rms"), alt=c(TRUE, FALSE), item=1:numItems, trueFit=NA, pval=NA)
result <- result[!(result$method=="rms" & result$alt),]
for (ix in 1:numItems) {
result[result$item == ix, 'trueFit'] <- trueFit[ix]
}
got <- rpf.SitemFit(grp, method="pearson")
mask <- result$method=="pearson" & !result$alt
result[mask,'pval'] <- sapply(got, function(x) x$pval)
got <- rpf.SitemFit(grp, method="pearson", alt=TRUE)
mask <- result$method=="pearson" & result$alt
result[mask,'pval'] <- sapply(got, function(x) x$pval)
got <- rpf.SitemFit(grp, method="rms")
mask <- result$method=="rms" & !result$alt
result[mask,'pval'] <- sapply(got, function(x) x$pval)
result
}
result <- NULL
for (replication in 1:20) {
result <- rbind(result, trial(20, 500, "nom2", "grm", 20))
result <- rbind(result, trial(20, 500, "nom2", "grm", 0))
# result <- rbind(result, trial(10, 1000, "3pl", "2pl", 1))
}
alphaPlot <- function(result) {
aResult <- expand.grid(method=unique(result$method), alt=unique(result$alt), alpha=seq(.01,.1, .005), got=0)
aResult$label <- paste(aResult$method, aResult$alt, sep="+")
# need at least 10/min(alpha) replications for good accuracy
minRows <- 10/min(aResult$alpha)
for (r in 1:nrow(aResult)) {
mre <- subset(result, method==aResult$method[r] & alt==aResult$alt[r] & trueFit)
if (aResult$alpha[r] == min(aResult$alpha) &&
nrow(mre) && nrow(mre) < minRows) {
warning(paste("Only", nrow(mre),"rows for", aResult$label[r], "need", minRows))
}
aResult$got[r] <- sum(mre$pval < aResult$alpha[r]) / nrow(mre)
}
aResult <- aResult[is.finite(aResult$got),]
ggplot(aResult, aes(alpha, got, color=label)) + geom_line() +
geom_abline(intercept=0, slope=1, color="green") +
labs(x="expected alpha", y="empirical alpha") + ylim(0,max(aResult$got))
}
if (0) {
numItems = 20
numPeople = 1000
genCond = "3pl"
fitCond = "2pl"
roc(trueFit ~ pval, subset(result, method=="pearson" & !alt), plot=TRUE, ci=TRUE)
roc(trueFit ~ pval, subset(result, method=="rms" & !alt), plot=TRUE, ci=TRUE)
roc(trueFit ~ pval, subset(result, method=="pearson" & alt), plot=TRUE, ci=TRUE) # difference at small # of items
alphaPlot(result)
}
# bad items make other items bad so there are two feasible ways to compose the items,
# 100% bad, 100% good
# 1 bad and the rest good
# rms has no advantage in all good vs all bad, dichotomous
# rms has less power but better alpha level (who cares?)
# pearson & alt=TRUE has slightly less power than pearson & alt=FALSE with less than 10 items
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