Comparison Between Different Estimation Methods of Factor Models for Longitudinal Ordinal Data

Latent variable models represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In presence of many latent variables/random effects, problems related to the integration of the likelihood function can arise since analytical solutions do not exist. In literature, different remedies have been proposed to overcome these problems. Among these, the composite likelihoods method and, more recently, the dimension-wise quadrature have been shown to produce estimators with desirable properties. We compare the performance of the two methods in the case of longitudinal ordinal data through a simulation study and an empirical application. Both the methods perform similarly, but the dimension-wise quadrature results less computational demanding. Indeed, for the specific model under investigation, it involves integrals of smaller dimensions than those involved in the computation of the pairwise likelihood, with a better performance than the latter in terms of accuracy of the estimates.