Estimating a Noncompensatory IRT Model Using Metropolis Within Gibbs Sampling

Relatively little research has been conducted with the noncompensatory class of multidimensional item response theory (MIRT) models. A Monte Carlo simulation study was conducted exploring the estimation of a two-parameter noncompensatory item response theory (IRT) model. The estimation method used was a Metropolis-Hastings within Gibbs algorithm that accepted or rejected new parameters in a bivariate fashion. Results showed that acceptable estimation of the noncompensatory model required a sample size of 4,000 people, six unidimensional items per dimension, and latent traits that are not highly correlated. Although the data requirements to estimate this model are a bit daunting, future advances in methodology could make this model valuable for modeling multidimensional data where the latent traits are not expected to be highly correlated.