ABSTRACT
Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 8.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.7.1 Appendix A: Densities of some specific NI distributions 175 8.7.2 Appendix B: Conditional posterior distributions . . . . . . . 176 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
in Bayesian
Longitudinal data abounds in bio-statistical research, leading to exploration of a wide variety of statistical models with varying complexity. Linear mixed effects (LME) models [see e.g. 18, 31, 32] are routinely used to analyze these data, allowing researchers to capture correlations between responses that exhibit multivariate, clustered, multilevel, spatially-referenced and various other data structures. The LME model for continuous responses assumes normal distributions for the between-subject random effects and the within-subject random errors. However, this may lack robustness in parameter estimation under departures from normality (namely, heavy tails) and/or outliers [24]. To deal with this issue, some proposals in the literature consider replacing the normality assumption with a more flexible class of distributions. For example, [24] proposed a multivariate Student-t LME model in the presence of outliers. [20] and [21] developed some additional tools for the t-LME model from a Bayesian perspective. [28] advocated the use of a subclass of elliptical distributions, called normal/independent (NI) distributions [22], and adopted a Bayesian framework to carry out posterior analysis for heavy-tailed LME (NI-LME) models. [1, 2] proposed extensions of the normal LME to deal with both asymmetry and outliers, with the LME as a particular case.
