Assessing the goodness of fit of a latent variable model for ordinal data

摘要

Latent variable models are used to explain the interrelationships among a set of observed variables through a smaller set of latent variables. In this paper we deal with the goodness of fit evaluation of a latent variable model with ordinal observed variables in presence of sparse data. In this situation the evaluation of the model can be obstructed by the fact that the true distribution of usual goodness of fit statistics is badly approximated by the X~2 distribution. A test based on residuals associated to the marginal distributions of the observed variables is developed as possible solution to this problem. It represents an extension of a test proposed by Reiser (1966) for a model with binary data. Through a Monte Carlo simulation study the performance of this test is compared with the classical tests.