Longitudinal GJS regression models
Models for rates and proportions; GJS distribution; Longitudinal proportional data; Longitudinal GJS Regression Models; Mixed generalized linear models.
We extend the GJS regression model that contemplates a wide class of distributions with limited support based on the symmetric family to the case of correlated observations, such as those from repeated measures, longitudinal studies or with grouped data. The extension was carried out using the methodology of mixed generalized linear models. We include subject- or group-specific effects to implicitly model variability due to unobserved genetic, behavioral, environmental, or social factors. Gauss-Hermite quadrature was used to numerically integrate the joint density function with respect to random effects. The marginal maximum likelihood method was used to obtain estimates of the effects of covariates on the observed response using the numerical maximization algorithm known as BFGS, and predictors for random effects were obtained using empirical Bayes estimates.