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. A frequentist analysis, a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered. In addition, an EM-type algorithm is developed for performing maximum likelihood estimation. Then, the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived. In order to study departures from the error assumption as well as the presence of outliers, residual analysis based on the standardized Pearson residuals is discussed. The relevance of the approach is illustrated with a real data set, where it is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart.