ltm (version 0.8-9)

rmvlogis: Generate Random Responses Patterns under Dichotomous IRT models

Description

Produces Bernoulli random variates under the Rasch, two-parameter and three parameter logistic models.

Usage

rmvlogis(n, thetas, IRT = TRUE, link = c("logit", "probit"), 
         distr = c("normal", "logistic", "log-normal", "uniform"), 
         z.vals = NULL)

Arguments

n

a scalar indicating the number of response patterns to simulate.

thetas

a numeric matrix with rows representing the items and columns the parameters. See Details for more info.

IRT

logical; if TRUE thetas are under the IRT parameterization. See Details for more info.

link

a character string indicating the link function to use. Options are logit and probit.

distr

a character string indicating the distribution of the latent variable. Options are Normal, Logistic, log-Normal, and Uniform.

z.vals

a numeric vector of length n providing the values of the latent variable (ability) to be used in the simulation of the dichotomous responses; if specified the value of distr is ignored.

Value

• a numeric matrix with n rows and columns the number of items, containing the simulated binary variates.

Details

The binary variates can be simulated under the following parameterizations for the probability of correctly responding in the $i$th item. If IRT = TRUE $$\pi_i = c_i + (1 - c_i) g(\beta_{2i} (z - \beta_{1i})),$$ whereas if IRT = FALSE $$\pi_i = c_i + (1 - c_i) g(\beta_{1i} + \beta_{2i} z),$$ $z$ denotes the latent variable, $\beta_{1i}$ and $\beta_{2i}$ are the first and second columns of thetas, respectively, and $g()$ is the link function. If thetas is a three-column matrix then the third column should contain the guessing parameters $c_i$'s.

See Also

ltm, rasch, tpm

Examples

# 10 response patterns under a Rasch model
# with 5 items
rmvlogis(10, cbind(seq(-2, 2, 1), 1))