sim.raschtype: Simulate from Generalized Logistic Item Response Model

Description

This function simulates dichotomous item responses from a generalized logistic item response model (Stukel, 1988). The four-parameter logistic item response model (Loken & Rulison, 2010) is a special case. See rasch.mml2 for more details.

Usage

sim.raschtype(theta, b, alpha1 = 0, alpha2 = 0, fixed.a = NULL,  fixed.c = NULL, fixed.d = NULL)

Arguments

theta

Unidimensional ability vector $\theta$

Vector of item difficulties $b$

alpha1

Parameter $\alpha_1$ in generalized logistic link function

alpha2

Parameter $\alpha_2$ in generalized logistic link function

fixed.a

Vector of item slopes $a$

fixed.c

Vector of lower item asymototes $c$

fixed.d

Vector of lower item asymototes $d$

Details

The class of generalized logistic link functions contain the most important link functions using the specifications (Stukel, 1988):

logistic link function: $\alpha_1=0$ and $\alpha_2=0$ probit link function: $\alpha_1=0.165$ and $\alpha_2=0.165$ loglog link function: $\alpha_1=-0.037$ and $\alpha_2=0.62$ cloglog link function: $\alpha_1=0.62$ and $\alpha_2=-0.037$

See pgenlogis for exact transformation formulas of the mentioned link functions.

References

Loken, E., & Rulison, K. L. (2010). Estimation of a four-parameter item response theory model. British Journal of Mathematical and Statistical Psychology, 63, 509-525.

Stukel, T. A. (1988). Generalized logistic models. Journal of the American Statistical Association, 83, 426-431.

Examples

Run this code

#############################################################################
## EXAMPLE 1: Simulation of data from a Rasch model (alpha_1 = alpha_2 = 0)
#############################################################################	

base::set.seed(9765)	
N <- 500    # number of persons
I <- 11     # number of items
b <- base::seq( -2 , 2 , length=I )
dat <- sim.raschtype( stats::rnorm( N ) , b )
base::colnames(dat) <- base::paste0( "I" , 1:I )