Simulate data for the gpcm model

This function returns an integer matrix of simulated responses under given item and person parameters.

sim_gpcm(thres, alpha, theta)

Arguments

thres

An numeric matrix which contains threshold parameters for each item. The first row must contain zeroes only!

alpha

A numeric vector, which contains the slope parameters - one parameter per item is expected.

theta

A numeric vector which contains person parameters.

See also

sim_4pl, PP_gpcm

Examples

################# simulate GPCM ###############################################

set.seed(1750)

THRES  <- matrix(c(-2,-1.23,1.11,3.48,1
                   ,2,-1,-0.2,0.5,1.3,-0.8,1.5),nrow=2)
# slopes
sl     <- c(0.5,1,1.5,1.1,1,0.98)

THRESx <- rbind(0,THRES)

THETA  <- rnorm(100)

simdat_gpcm <- sim_gpcm(thres = THRESx,alpha = sl,theta = THETA)

head(simdat_gpcm)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    2    0    0    0    0    1
#> [2,]    2    1    0    1    0    0
#> [3,]    2    0    1    2    1    1
#> [4,]    2    0    1    2    1    1
#> [5,]    1    0    1    2    2    2
#> [6,]    1    0    1    1    2    0


### simulate with a different number of categories


THRES1 <- rbind(THRESx,c(NA,NA,NA,NA,1.7,1))
THRES1 # last 2 items have +1 category
#>       [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]  0.00 0.00    0  0.0  0.0  0.0
#> [2,] -2.00 1.11    1 -1.0  0.5 -0.8
#> [3,] -1.23 3.48    2 -0.2  1.3  1.5
#> [4,]    NA   NA   NA   NA  1.7  1.0

simdat_gpcm2 <- sim_gpcm(thres = THRES1,alpha = sl,theta = THETA)

head(simdat_gpcm2)
#>      [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,]    2    0    0    0    0    0
#> [2,]    1    1    0    2    0    2
#> [3,]    2    0    0    1    2    2
#> [4,]    2    1    1    2    2    0
#> [5,]    2    1    1    2    3    3
#> [6,]    2    0    0    2    0    1

# check the maximum category
apply(simdat_gpcm2,2,max)
#> [1] 2 2 2 2 3 3