Maximum-likelihood estimation and influence analysis in multivariate skew-normal reproductive dispersion mixed models for longitudinal data

Various mixed models were developed to capture the features of between- and within-individual variation for longitudinal data under the normality assumption of the random effect and the within-individual random error. However, the normality assumption may be violated in some applications. To this end, this article assumes that the random effect follows a skew-normal distribution and the within-individual error is distributed as a reproductive dispersion model. An expectation conditional maximization (ECME) algorithm together with the Metropolis-Hastings (MH) algorithm within the Gibbs sampler is presented to simultaneously obtain estimates of parameters and random effects. Several diagnostic measures are developed to identify the potentially influential cases and assess the effect of minor perturbation to model assumptions via the case-deletion method and local influence analysis. To reduce the computational burden, we derive the first-order approximations to case-deletion diagnostics. Several simulation studies and a real data example are presented to illustrate the newly developed methodologies.