Inferences in semi-parametric dynamic mixed models for longitudinal count data
In this paper, the generalized linear longitudinal mixed model (GLLMM) for count data is extended to a semiparametric setup. The proposed model is referred to as the semiparametric GLLMM (SGLLMM). A quasi-likelihood estimation approach to this model is developed, assuming that the repeated count data are generated following an \(\mathrm{AR}(1)\) Poisson mixed model. The main regression effects and the overdispersion parameter are estimated using true correlation structure-based semiparametric generalized quasi-likelihood. The nonparametric function is estimated using semiparametric quasi-likelihood. The longitudinal correlations are estimated using the semiparametric method of moments. Proofs for the consistency properties of the estimators of the nonparametric function, regression parameters, variance of the random effects, and autocorrelation structure of the model are derived along with their convergence rates. Simulation studies are conducted to examine estimation effects when the nonparametric function is ignored and in the presence of the nonparametric function, including its estimation as well.
scientific article; zbMATH DE number 6836005
scientific article