A Wald Test for Homogeneity in Zero-Mixture Models for Correlated Count Data

• Activity Number: 178
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Wei-Wen Hsu*+ and David Todem and Woosung Sohn
• Companies: Michigan State University and Michigan State University and Boston University
• Keywords: Wald test ; zero-mixture ; correlated count data ; negative binomial ; Poisson ; Goodness-of-fit test

Abstract

Tests of homogeneity in zero-mixture models for discrete data have been well discussed in the literature, but the existing methodologies have relied primarily on score statistics. An often cited justification for the use of these statistics is that they do not require the model to be fitted under the alternative. But the advent of computer software with robust functions has made easy for these alternative models to be fitted routinely in practice. In this paper, we exploit this opportunity by using results generated from these analyses to develop a Wald test statistic to evaluate homogeneity in this class of models. We show how the proposed test can be performed with a minimal programming effort for the practicing statistician. To accommodate correlation in the data, we assume a pseudo-likelihood function derived from a working independent model, and the parameters' standard errors are adjusted using the sandwich estimator of the covariance matrix. The test is based on a reparameterization of the mixing weights that translates the homogeneity hypotheses into a linear combination of parameters from the marginal model. Real life applications are illustrated using dental caries data.