Estimation issues in multivariate panel data

atent variable models are a powerful tool in various research fields when the constructs of interest are not directly observable. However, the likelihood-based model estimation can be problematic when dealing with many latent variables and/or random effects since the integrals involved in the likelihood function do not have analytical solutions. In the literature, several approaches have been proposed to overcome this issue. Among them, the pairwise likelihood method and the dimension-wise quadrature have emerged as effective solutions that produce estimators with desirable properties. In this study, we compare a weighted version of the pairwise likelihood method with the dimension-wise quadrature for a latent variable model for binary longitudinal data by means of a simulation study.