LIKELIHOOD BASED INFERENCE FOR SKEW-NORMAL INDEPENDENT LINEAR MIXED MODELS

Linear mixed models with normally distributed response are routinely used in longitudinal data. However, the accuracy of the assumed normal distribution is crucial for valid inference of the parameters We present a new class of asymmetric linear mixed models that provides for an efficient estimation of the parameters in the analysis of longitudinal data We assume that, marginally. the random effects follow a multivariate skew-normal/independent distribution (Branco and Dey (2001)) and that the random errors follow a symmetric normal/independent distribution (Lange and Sinsheimer (1993)), providing an appealing robust alternative to the usual symmetric normal distribution in linear mixed models Specific distributions examined include the skew-normal, the skew-t, the skew-slash, and the skew-contaminated normal distribution We present all efficient EM-type algorithm algorithm for the computation of maximum likelihood estimation of parameters The technique for the prediction of future responses under this class of distributions is also investigated The methodology is illustrated through an applications to Framingham cholesterol data and a. simulation study.