Comparison between conditional and marginal maximum likelihood estimation for a class of ordinal item response models

In the literature on latent variable models, there is a considerable interest in estimation methods that do not require parametric assumptions on the latent distri- bution. In this paper, we focus on a class of item response theory models for ordinal responses, named graded response models, taking into account a constrained version with constant discriminating indices. In this class of models, we introduce a conditional likelihood estimator, which requires no assumptions on the latent distribution. Through a Monte Carlo study, we compare the behavior of the proposed estimator with that of two competitors, based on the maximization of the marginal likelihood, which is computed assuming the normality of the latent variable in one case, and the discreteness of the la- tent variable in the other case. The method also allows us to implement a Hausman test to compare the marginal and conditional likelihood estimators, which results in a test for the normality assumption on the latent distribution. We conclude with an application based on data coming from the administration of a questionnaire on the perception of science and technology.