Nothing

```
## convenience function to set up sampling function
## based on parameter specifications
make_rnorm_fun <- function(par) {
m <- par[1L]
s <- par[2L]
function(n) rnorm(n, mean = m, sd = s)
}
make_sample_fun <- function(par) {
x <- if(is.null(dim(par))) par[1L] else par[, 1L]
p <- if(is.null(dim(par))) par[2L] else par[, 2L]
if(isTRUE(all.equal(sum(p), 1))) {
function(n) x[sample.int(length(x), size = n, prob = p, replace = TRUE)]
} else {
function(n) {
np <- n * p / sum(p)
stopifnot(isTRUE(all.equal(np, round(np))))
rep(x, round(np))[sample.int(round(sum(np)))]
}
}
}
simRaschmix <- function(design, extremes = FALSE, attributes = TRUE,...) {
if(!(is.list(design) && length(design) == 2L & all(names(design) %in%
c("ability", "difficulty")))){
## character specification
if(is.character(design)) {
nobs <- 1800
switch(match.arg(design, c("rost1", "rost2", "rost3")),
## Rost gives item easiness parameter which are converted to
## item difficulty parameters here.
"rost1" = {
weights <- 1
ability <- array(c(cbind(c(-2.7, -0.9, 0.9, 2.7), rep(1, 4))),
dim = c(4, 2, 1))
difficulty <- matrix(c(2.7,2.1,1.5,0.9,0.3,-0.3,-0.9,-1.5,-2.1,-2.7), ncol = 1)
},
"rost2" = {
weights <- c(1,1)
ability <- array(c(cbind(c(-2.7, -0.9, 0.9, 2.7), rep(1, 4)),
cbind(c(-2.7, -0.9, 0.9, 2.7), rep(1, 4))),
dim = c(4, 2, 2))
difficulty <- cbind(c(2.7,2.1,1.5,0.9,0.3,-0.3,-0.9,-1.5,-2.1,-2.7),
c(-2.7,-2.1,-1.5,-0.9,-0.3,0.3,0.9,1.5,2.1,2.7))
},
"rost3" = {
weights <- c(4,2,3)
ab.c3 <- numeric(4)
ab.c3[sample.int(4, size = 1, prob = rep(1,4)/4)] <- 1
ability <- array(c(cbind(c(-2.7, -0.9, 0.9, 2.7), rep(1, 4)),
cbind(c(-2.7, -0.9, 0.9, 2.7), rep(1, 4)),
cbind(c(-2.7, -0.9, 0.9, 2.7), ab.c3)),
dim = c(4, 2, 3))
difficulty <- cbind(c(2.7,2.1,1.5,0.9,0.3,-0.3,-0.9,-1.5,-2.1,-2.7),
c(-2.7,-2.1,-1.5,-0.9,-0.3,0.3,0.9,1.5,2.1,2.7),
c(-0.5,0.5,-0.5,0.5,-0.5,0.5,-0.5,0.5,-0.5,0.5))
})
} else if(is.list(design) & length(design) == 4L & all(names(design) %in% c("ability", "difficulty", "nobs", "weights"))) {
nobs <- design$nobs
weights <- design$weights
ability <- design$ability
difficulty <- design$difficulty
}
## process weights, can be in three formats:
## (1) function(n)
## (2) vector of probabilities (summing to 1)
## (3) vector of integer weights (summing to n, or an integer division thereof)
## reduce (2)/(3) to case (1)
if(!is.function(weights)) weights <- make_sample_fun(cbind(seq_along(weights), weights))
## set up weights
cluster <- weights(nobs)
weights <- table(cluster)
k <- length(weights)
## ability specification (in three clusters?), can be in three formats:
## (1) list(k) of function(n)
## (2) matrix(2, k) with means and standard deviations per cluster
## (3) array(., 2, k) with abilities per weights/probabilities per cluster
## reduce (2)/(3) to case (1)
if(!(is.list(ability) && all(sapply(ability, is.function)))) {
if(length(dim(ability)) == 2L & dim(ability)[1L] == 2L & dim(ability)[2L] == k) {
ability <- lapply(1:k, function(i) make_rnorm_fun(ability[, i]))
} else if(length(dim(ability)) == 3L & dim(ability)[2L] == 2L & dim(ability)[3L] == k) {
ability <- lapply(1:k, function(i) make_sample_fun(ability[, , i]))
} else {
stop("unknown ability specification")
}
}
## set up ability within each cluster
ab <- numeric(nobs)
for(i in 1:k) ab[cluster == i] <- ability[[i]](weights[i])
ability <- ab
## difficulty specification, can be in 2 formats
## (1) matrix(n, .) with difficulties per person
## (2) matrix(., k) with difficulties per cluster
if(!(length(dim(difficulty)) == 2L & dim(difficulty)[1L] == nobs)){
if(length(dim(difficulty)) == 2L && dim(difficulty)[2L] == k){
## transform from per cluster to per person
difficulty.o <- difficulty
dif <- matrix(NA, nrow = nobs, ncol = dim(difficulty)[1L])
for (i in 1:k) dif[cluster == i,] <- rep(difficulty[,i], each = weights[i])
difficulty <- dif
}
else {
stop("unknown difficulty specification")
}
}
} else {
ability <- design$ability
difficulty <- design$difficulty
cluster <- NULL
}
## generate response
stopifnot(NROW(ability) == NROW(difficulty))
linpred <- ability - difficulty
prob <- plogis(linpred)
rval <- rbinom(n = length(prob), prob = prob, size = 1)
dim(rval) <- dim(prob)
## remove observations with extreme raw scores
if (!extremes){
w <- which(rowSums(rval) == 0 | rowSums(rval) == ncol(rval))
if (length(w) > 0){
rval <- rval[-w,]
ability <- ability[-w]
cluster <- cluster[-w]
}
}
## attach attributes
if(attributes) {
attr(rval, "ability") <- ability
#if(exists("difficulty.o")) attr(rval, "difficulty") <- difficulty.o
attr(rval, "difficulty") <- if(exists("difficulty.o")) difficulty.o else difficulty
attr(rval, "cluster") <- cluster
}
## return
return(rval)
}
```

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