sim_mixed: Simulate data for mixed tests (4PL and GPCM items)

In PP: Person Parameter Estimation

Simulate data for mixed tests (4PL and GPCM items)

Description

This function returns an integer matrix of simulated responses for a test with dichotomous (1/2/3/4-PL) and polytomous (GPCM) items, with the item parameters in the layout of PPall.

Usage

sim_mixed(thres, alpha = NULL, lowerA = NULL, upperA = NULL, theta)

Arguments

thres	A numeric matrix with the thresholds of each item in its columns, as in PPall: for a 4PL item the difficulty, for a GPCM item its thresholds, NA below the last one. Items with one threshold are 4PL items, the others GPCM items. The first row may contain zeroes only; otherwise a row of zeroes is added.
alpha	A numeric vector of slope parameters. If NULL (default), all slopes are 1.
lowerA	A numeric vector of lower asymptotes (4PL items). If NULL (default), 0.
upperA	A numeric vector of upper asymptotes (4PL items). If NULL (default), 1.
theta	A numeric vector which contains person parameters.

Details

alpha, lowerA and upperA may also be single numbers, which are then used for every item. lowerA and upperA only apply to the 4PL items. A person with NA as person parameter gets a row of NA. The data of a pure 4PL or GPCM test are the same as those of sim_4pl or sim_gpcm with the same seed.

Value

An integer matrix with one row per person and one column per item.

See Also

sim_4pl, sim_gpcm, PPall

Examples

set.seed(1800)
# four 3PL items and two GPCM items with three categories
thres <- rbind(0, c(-1, -0.3, 0.4, 1.2, -0.5, 0.2), c(NA, NA, NA, NA, 0.8, 1.4))
x <- sim_mixed(thres = thres, alpha = c(1, 1.2, 0.8, 1.1, 1, 0.9),
               lowerA = c(0.2, 0.1, 0.15, 0.2, 0, 0), theta = rnorm(300))
head(x)

# and back: estimate the persons with the same parameters
res <- PPall(x, thres = thres, slopes = c(1, 1.2, 0.8, 1.1, 1, 0.9),
             lowerA = c(0.2, 0.1, 0.15, 0.2, 0, 0))
summary(res$estimates$estimate)

PP documentation built on Oct. 15, 2026, 1:06 a.m.