Influence Diagnostics for Correlated Binomial Regression Models: An Application to a Data Set on High-Cost Health Services Occurrence

Abstract

This paper considers a frequentist perspective to deal with the class of correlated binomial regression models (Pires & Diniz, 2012), thus providing a new approach to analyze correlated binary response variables. Model parameters are estimated by direct maximization of the log-likelihood function. We also consider a diagnostic analysis under the correlated binomial regression model setup, which is performed considering residuals based on predictive values and deviance residuals (Cook & Weisberg, 1982) to check for model assumptions, and global in˛uence measure based on case-deletion (Cook, 1977) to detect in˛uential observations. Moreover, a sensitivity analysis is carried out to detect possible in˛uential observations that could a˙ect the inferential results. This is done using local in˛uence metrics (Cook, 1986) with case-weight, response, and covariate perturbation schemes. A simulation study is conducted to assess the frequentist properties of model parameter estimates and check the performance of the considered diagnostic metrics under the correlated binomial regression model. A data set on high-cost claims made to a private health care provider in Brazil is analyzed to illustrate the proposed methodology.