Cook’s distance for generalized linear mixed models

We consider an extension of Cook’s distance for generalized linear mixed models with the objective of identifying observations with high influence in the predicted conditional means of the response variable. The proposed distance can be decomposed into factors that help to distinguish between influence on the estimation of fixed effects and on the prediction of random effects. Joint and conditional influence are also considered. A first-order approximation is proposed for more efficient computation and a Monte Carlo simulation is considered to evaluate the efficacy of the proposal. An application to a dataset obtained from the literature is presented to show how such tools can be used in practice.