A simulation procedure for the generation of samples to evaluate goodness of fit indices in item response theory models.

The LISREL8.8/PRELIS2.81 program can carry out ordinal factorial analysis (OFA command), with full information maximum likelihood methods, in a data set containing n samples obtained by simulation. Nevertheless, when the replication number is greater than 1, an error command is produced, which impedes reaching solutions that can execute normal (NOR) and logistic (POM) functions. This paper proposes a new procedure of data simulation in PRELIS-LISREL. This procedure permits the generation of n replications and the calculation of the goodness of fit (GOF) indices in the item response theory (IRT) models for each replication, thus allowing the execution of the OFA command for Monte Carlo simulations. The solutions using underlying variable (weighted least squares (WLS) estimation method) and IRT approaches are compared.