Influence Diagnostics for Skew-Normal Linear Mixed Models

Abstract

Normality (symmetry) of the random effects is a routine assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. We relax this assumption by assuming that the random effects density is skew-normal, considered as an extension of the univariate version proposed by Sahu, Dey and Branco (CJS, 2003). Following Zhu and Lee (JRSSB, 2001), we implement an EM-type algorithm to parameter estimation and then using the related conditional expectation of the complete-data log-likelihood function, develop diagnostic measures for implementing the local influence approach under four model perturbation schemes. Results obtained from simulated and real data sets are reported illustrating the usefulness of the approach. AMS (2000) subject classification. Primary 62H12, 60E05.