rmvlogis {ltm}R Documentation

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.

Details

The binary variates can be simulated under the following parameterizations for the probability of correctly responding in the ith item. If IRT = TRUE

π_i = c_i + (1 - c_i) g(beta_{2i} (z - beta_{1i})),

whereas if IRT = FALSE

π_i = c_i + (1 - c_i) g(beta_{1i} + beta_{2i} z),

z denotes the latent variable, β_{1i} and β_{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.

Value

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

Note

For options distr = "logistic", distr = "log-normal" and distr = "uniform" the simulated random variates for z simulated under the Logistic distribution with location = 0 and scale = 1, the log-Normal distribution with meanlog = 0 and sdlog = 1 and the Uniform distribution with min = -3.5 and max = 3.5, respectively. Then, the simulated z variates are standardized, using the theoretical mean and variance of the Logistic, log-Normal and Uniform distribution, respectively.

Author(s)

Dimitris Rizopoulos dimitris.rizopoulos@med.kuleuven.be

See Also

ltm, rasch, tpm

Examples


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


[Package ltm version 0.8-4 Index]