Deletion measures for generalized linear mixed effects models

Generalized linear mixed models (GLMMs) have wide applications in practice. Similar to other data analyses, the identification of influential observations that may be potential outliers is an important step beyond estimation in GLMMs. Since the pioneering work of Cook in 1977, deletion measures have been applied to many statistical models for identifying influential observations. However, as this well-known approach is based on the observed-data likelihood, it is very difficult to apply it to developing diagnostic measures for GLMMs due to the complexity of the observed-data likelihood that involves multidimensional integrals. The objective of this article is to develop diagnostic measures for identifying influential observations. Deletion measures are developed on the basis of the conditional expectation of the complete-data log-likelihood at the E-step of a stochastic approximation Markov chain Monte Carlo algorithm. Making use of by-products of the estimation to compute building blocks of the proposed diagnostic measures and activating appropriate approximations, the proposed methods require little additional computation. The performance of the methods is illustrated by an artificial example, a real example, and some simulation studies.

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