On Comparisons of Frequentist to Bayesian Estimation for Item Response Theory Models in the Presence of Dichotomous Response.

Abstract

Item response theory (IRT) is a family of mathematical models that attempt to explain the relationship between latent traits and their manifestations. They are widely used in education to calibrate and evaluate items in tests, questionnaires, and similar instructions, measuring abilities, attitudes, or other variables. The most frequent method for estimating latent traits called Maximum Likelihood (ML) can either fail to converge or produce biased estimates in complex latent traits models due to co-linearity of explanatory variables. Bayesian estimation approach provides a better alternative to ML (frequentist) for IRT in this case. This study compared the Bayesian against ML estimators for IRT models. The same data set were analysed using both Bayesian and ML estimations. The findings suggest that ML method is a reasonable choice for one and two-parameter logistic IRT models while Bayesian estimation is more appropriate for three-parameter IRT to circumvent nonconvergence of ML estimation procedure.