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sim.2pl <- function(persons, items, discrim = 0.25, seed = NULL, cutpoint = "randomized")
{
# simulation of Birnbaum's 2-PL (non-parallel ICCs)
# violation is steered by the standard deviation sdlog.
# meanlog in rlnorm is 0 which implies that the random numbers lie asymmetrically around 1. If sdlog = 0 the data are Rasch homogeneous.
# For IRT applications, values up to 0.5 should be considered.
if (length(items) == 1) {
if (!is.null(seed)) set.seed(seed)
schwierig <- rnorm(items) #standard normal distributed
n.items <- items
} else {
schwierig <- items
n.items <- length(items)
}
if (length(persons) == 1) {
if (!is.null(seed)) set.seed(seed)
faehig <- rnorm(persons)
n.persons <- persons
} else {
faehig <- persons
n.persons <- length(persons)
}
if (length(discrim) > 1) {
alpha <- discrim
} else {
if (!is.null(seed)) set.seed(seed)
alpha <- rlnorm(n.items, 0, sdlog = discrim) #discrimination parameter
}
psolve <- matrix(0, n.persons, n.items)
for (i in 1:n.persons)
for (j in 1:n.items)
psolve[i,j]<-exp(alpha[j]*(faehig[i]-schwierig[j]))/(1+exp(alpha[j]*(faehig[i]-schwierig[j])))
if (cutpoint == "randomized") {
if (!is.null(seed)) set.seed(seed)
R <-(matrix(runif(n.items*n.persons),n.persons,n.items) < psolve)*1
} else {
R <- (cutpoint < psolve)*1
}
return(R)
}
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