Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook's well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001 Zhu , H. , Lee , S. ( 2001 ). Local influence for incomplete-data models . J. Roy. Statist. Soc. Ser. B 63 : 111 – 126 .[Crossref] , [Google Scholar]). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.