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

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

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.

See also

sim_gpcm, PP_4pl

Author

Manuel Reif

Examples

################# simulate 4PL ###############################################

set.seed(1700)
 
# simulate 1-PL model ----------

thetas <- c(0.231,-1.313,1.772,1.601,1.733,-2.001,0.443,3.111,-4.156)
sl <- c(1,1.1,0.9,0.89,1.5,1.1,1)
la <- c(0,0,0.2,0.15,0.04,0,0.21)
ua <- c(0.9,0.98,0.97,1,1,1,0.97)

simdat1pl <- sim_4pl(beta=seq(-4,4,length.out=7), alpha=rep(1,7),
                  lowerA=rep(0,7), upperA=rep(1,7), theta=thetas)


head(simdat1pl)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    1    1    1    0    0    0    0
#> [2,]    1    1    1    0    0    0    0
#> [3,]    1    1    1    1    0    1    0
#> [4,]    1    1    1    0    1    0    0
#> [5,]    1    1    1    1    1    0    0
#> [6,]    1    1    1    0    0    0    0


# simulate 2-PL model ----------

simdat2pl <- sim_4pl(beta=seq(-4,4,length.out=7), alpha=sl,
                  lowerA=rep(0,7), upperA=rep(1,7), theta=thetas)


head(simdat2pl)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    1    1    0    0    0    0    0
#> [2,]    1    1    0    0    0    0    0
#> [3,]    1    1    1    1    0    0    0
#> [4,]    1    1    1    1    0    1    0
#> [5,]    1    1    1    0    0    0    0
#> [6,]    1    1    1    0    0    0    0


# simulate 3-PL model ----------

simdat3pl <- sim_4pl(beta=seq(-4,4,length.out=7), alpha=sl,
                     lowerA=la, upperA=rep(1,7), theta=thetas)


head(simdat3pl)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    1    1    1    1    0    0    0
#> [2,]    1    1    1    0    0    0    0
#> [3,]    1    1    1    1    1    1    0
#> [4,]    1    1    1    1    0    0    0
#> [5,]    1    1    1    0    1    0    0
#> [6,]    1    1    1    1    0    0    0


# simulate 4-PL model ----------

simdat4pl <- sim_4pl(beta=seq(-4,4,length.out=7), alpha=sl,
                     lowerA=la, upperA=ua, theta=thetas)


head(simdat4pl)
#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,]    0    1    1    1    0    0    1
#> [2,]    1    1    1    1    0    0    0
#> [3,]    1    1    1    1    0    0    0
#> [4,]    1    1    1    1    1    0    0
#> [5,]    1    1    1    1    1    0    0
#> [6,]    1    1    0    0    1    0    0