On Estimation and Influence Diagnostics for Zero-Inflated Negative Binomial Regression Models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-inflated Poisson model. We consider a frequentist analysis, a jackknife estimator and non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models. In addition, an EM-type algorithm is developed to perform maximumlikelihood estimation. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform globalinfluence analysis. In order to study departures from the error assumption as well as the presence of outliers, we perform residual analysis based on the standardized Pearson residuals. The relevanceof the approach is illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data changes.