The dimension-wise quadrature estimation of dynamic latent variable models for count data

When dynamic latent variable models are specified for discrete and/or mixed observations, problems related to the integration of the likelihood function arise since analytical solutions do not exist. A recently developed dimension-wise quadrature is applied to deal with these likelihoods with high-dimensional integrals. A comparison is performed with the pairwise likelihood method, one of the most often used remedies. Both a real data application and a simulation study show the superior performance of the dimension-wise quadrature with respect to the pairwise likelihood in estimating the parameters of the latent autoregressive process.