Linear mixed models based on skew scale mixtures of normal distributions

Abstract

Scale mixtures of normal distributions are useful for statistical procedures involving symmetric and heavy-tailed data. Ferreira, Lachos, and Bolfarine (2016) defined a multivariate skewed version of these distributions that offers much-needed flexibility by combining both skewness and heavy tails. In this work, we develop a linear mixed model based on skew scale mixtures of normal distributions, with emphasis on the skew Student-t normal, skew–slash and skew–contaminated normal distributions. Using the hierarchical structure of the model, we develop maximum likelihood estimation of the model parameters via the expectation-maximization (EM) algorithm. In addition, the standard errors are obtained via the approximate information matrix and the local influence analysis is explored under some perturbation schemes. To examine the performance and the usefulness of the proposed method, we present simulation studies and analyze a real dataset.

Keywords:

• EM algorithm
• Linear mixed models
• Local influence analysis
• Skew scale mixtures of normal distributions