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

• Published in: Computational statistics & data analysis Vol. 55; no. 3; pp. 1304 - 1318
• Main Authors: Garay, Aldo M., Hashimoto, Elizabeth M., Ortega, Edwin M.M., Lachos, Víctor H.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2011; Elsevier
• Series: Computational Statistics & Data Analysis
• Subjects: Algorithms; Binomials; Bootstrap; Bootstrap EM algorithm Global influence Local influence Negative binomial distribution Zero-inflated models; Diagnostic systems; EM algorithm; Estimates; Exact sciences and technology; General topics; Global influence; Local influence; Mathematical models; Mathematics; Matrices; Multivariate analysis; Negative binomial distribution; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Parametric inference; Probability and statistics; Regression; Regression analysis; Sciences and techniques of general use; Statistics; Zero-inflated models; Zero-inflated models; Bootstrap; Global influence; Local influence; EM algorithm; Negative binomial distribution; Discriminant analysis; Data analysis; Error estimation; Overdispersion; Non parametric estimation; Perturbation; Multivariate analysis; Outlier; Hypothesis test; Statistical test; Statistical computation; Regression model; Jackknife method; Maximum likelihood; Resampling method
• ISSN: 0167-9473; 1872-7352
• DOI: 10.1016/j.csda.2010.09.019

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.