This paper examines and compares various estimation methods for generalized linear latent variable models for multidimensional longitudinal binary data. In such cases, likelihood-based methods are problematic due to the high dimensional integrals involved, which lack analytical solution. Among the methods proposed in the literature to address this issue, we focus on approximate likelihood and composite likelihood methods. Specifically, within the first class, we examine the dimension-wise quadrature, while within the second class, we consider composite likelihood methods based on bivariate densities. The properties of these methods are evaluated through a comprehensive simulation study.