Sankhya: The Indian Journal of Statistics

2007, Volume 69, Pt. 4, 648--670

Influence Diagnostics for Skew-Normal Linear Mixed Models

Heleno Bolfarine, Universidade de S\~ao Paulo, S\~ao Paulo, Brazil
Lourdes C. Montenegro, Universidade Federal de Minas Gerais, Minas Gerais, Brazil
Victor H. Lachos, Universidade Estadual de Campinas, S\~ao Paulo, Brazil

SUMMARY. 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 ({\it CJS}, 2003). Following Zhu and Lee ({\it 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.

Key words and phrases. Skew-normal distribution, EM-algorithm, skewness, local influence, case deletion.

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