R: Generate Random Responses Patterns under Dichotomous and...
rmvlogis
R Documentation
Generate Random Responses Patterns under Dichotomous and Polytomous IRT models
Description
Produces Bernoulli or Multinomial random variates under the Rasch, the two-parameter logistic, the three parameter,
the graded response, and the generalized partial credit models.
a scalar indicating the number of response patterns to simulate.
thetas
for rmvlogis() a numeric matrix with rows representing the items and columns the parameters.
For rmvordlogis() a list with numeric vector elements, with first the threshold parameters and last the discrimination
parameter. See Details for more info.
IRT
logical; if TRUEthetas are under the IRT parameterization.
See Details for more info.
model
from which model to simulate.
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
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.
The ordinal variates are simulated according to the generalized partial credit model or the graded response model depending
on the value of the model argument. Check gpcm and grm to see how these models are defined,
under both parameterizations.
Value
a numeric matrix with n rows and columns the number of items, containing the simulated binary or ordinal 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.
# 10 response patterns under a Rasch model
# with 5 items
rmvlogis(10, cbind(seq(-2, 2, 1), 1))
# 10 response patterns under a GPCM model
# with 5 items, with 3 categories each
thetas <- lapply(1:5, function(u) c(seq(-1, 1, len = 2), 1.2))
rmvordlogis(10, thetas)