sim_4pl: Simulate data for 1/2/3/4-pl model

In PP: Person Parameter Estimation

Simulate data for 1/2/3/4-pl model

Description

This function returns a dichotomous matrix of simulated responses under given item and person parameters.

Usage

sim_4pl(beta, alpha, lowerA, upperA, theta)

Arguments

beta	A numeric vector which contains the difficulty parameters for each item.
alpha	A numeric vector, which contains the slope parameters for each item.
lowerA	A numeric vector, which contains the lower asymptote parameters (kind of guessing parameter) for each item.
upperA	numeric vector, which contains the upper asymptote parameters for each item.
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. A person with NA as person parameter gets a row of NA.

Value

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

Author(s)

Manuel Reif

See Also

sim_gpcm, sim_mixed, PP_4pl

Examples

set.seed(1700)
theta <- rnorm(200)
b <- seq(-2, 2, length.out = 7)

# 1PL (Rasch) model: slopes 1, no asymptotes
x1 <- sim_4pl(beta = b, alpha = 1, lowerA = 0, upperA = 1, theta = theta)
colMeans(x1)

# 4PL model
x4 <- sim_4pl(beta = b, alpha = c(1, 1.1, 0.9, 0.9, 1.5, 1.1, 1),
              lowerA = c(0, 0, 0.2, 0.15, 0.04, 0, 0.21),
              upperA = c(0.9, 0.98, 0.97, 1, 1, 1, 0.97), theta = theta)
head(x4)

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