On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-in ated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-in ated Poisson model. We consider a frequentist analysis, a jackknife estimator and non-parametric bootstrap for parameter estimation of zero-in ated negative binomial regression models. In addition, an EM-type algorithm is developed to perform maximum likelihood estimation. Then, we derive the appropriate matrices for assessing local in uence on the parameter estimates under di erent perturbation schemes and present some ways to perform global in uence 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 relevance of the approach is illustrated with a real data set, where it is shown that, by removing the most in uential observations, the decision about which model best ts the data changes.