sirt: sim.raschtype – R documentation

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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 θ
`b`	Vector of item difficulties b
`alpha1`	Parameter α_1 in generalized logistic link function
`alpha2`	Parameter α_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: α_1=0 and α_2=0
probit link function: α_1=0.165 and α_2=0.165
loglog link function: α_1=-0.037 and α_2=0.62
cloglog link function: α_1=0.62 and α_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.

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 )

sirt

Supplementary Item Response Theory Models

v3.10-118

GPL (>= 2)

Authors

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>)

Initial release

2021-09-22 17:45:34