A Wald test for zero inflation and deflation for correlated count data from dental caries research

Tests of homogeneity in zero-inflated models for count 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 and procedures has made it easy for these alternative models to be fitted routinely in practice. In this article, we exploit this opportunity by using results generated from these analyses to develop a Wald test statistic to evaluate homogeneity in the class of zero-inflated models. We show how the proposed test can be performed with minimal programming effort for the practicing statistician. Technically, the test is based on a reparameterization of the mixing weights that naturally incorporates covariates under heterogeneity, a characteristic often ignored by existing testing procedures. A quasi-likelihood function derived from a working independence model coupled with the so-called sandwich estimator of the covariance matrix of the parameter estimates is used to accommodate correlation in the data. A simulation study is conducted to evaluate the empirical performance of the proposed Wald test and its real life applications are illustrated using correlated dental caries counts in young children.