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

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.

Value

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

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.

See also

sim_gpcm, sim_mixed, PP_4pl

Author

Manuel Reif

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)
#> [1] 0.820 0.755 0.700 0.430 0.365 0.265 0.120

# 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)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    0    1    1    1    0    0    1
#> [2,]    1    1    1    0    0    0    0
#> [3,]    0    1    1    1    0    0    0
#> [4,]    1    1    0    0    0    0    0
#> [5,]    1    0    1    0    1    0    1
#> [6,]    1    1    1    0    1    0    0