Outlier detection to hierarchical and mixed effects models

Hierarchical and mixed effects models are models where a varying number of coefficients may be random at different levels of the hierarchy. The purpose of outlier analysis for these models is to determine whether an outlying unit at higher level is entirely outlying, or outlying due to effect of one or a few aberrant lower level units. Most works on diagnostics for these complex models have focused on the mixed model rather than on the hierarchical models, obscuring some relevant aspects of the hierarchical model. In this paper we will present an approach to influence analysis and outlier detection for mixed and hierarchical model, focusing on the special structure of nested data that these models describe.