sim.raschtype.Rd
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.
sim.raschtype(theta, b, alpha1=0, alpha2=0, fixed.a=NULL, fixed.c=NULL, fixed.d=NULL)
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 \(d\) |
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.
Data frame with simulated item responses
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.
############################################################################# ## 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 )