Linear Mixed Models using Skew-Normal/Independent Distributions:
Estimation and Influence analysis.
The linear mixed models is discussed under skew-normal/independent
distribution. This class provides a useful generalization of normal (and
skew-normal)linear mixed models since it is assumed that the random
effects and the random error terms follow jointly a multivariate
skew-normal/independent distribution. Inspired by the EM algorithm that
is used to obtain the maximum likelihood estimates, a study
influence analysis for linear mixed models is developed, following the
approach of Zhu et al. (2001) and Zhu and Lees (2001).
The influence of observations on statistical inference is of importance in
statistical data analysis. A practical and well-established approach to
influence analysis is based on case deletion (Cook, 1977; Zhu et al.,
2001), a general approach was proposed by Cook (1986) and Zhu and
Lees (2001, that is known as the local influence method.
Finally, a real data set has been analyzed in order to illustrate the
usefulness of the proposed methodology.