sim.raschtype {sirt}

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

b

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 asymptotes c

fixed.d

Vector of lower item asymptotes 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.

Value

Data frame with simulated item responses

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.

See Also

rasch.mml2, pgenlogis

Examples

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

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