Zero-inflated mixture (ZIM) regression for zero-inflated population in presence of many zero value responses has been developed by Paneru and Chen [22]. The ZIM regression addresses the issue of estimation problem in generalized linear models under complex probability sampling designs via a two-component mixture model where the non-zero component follows a parametric distribution. As a technical supplement to Paneru and Chen [22], this paper presents theoretical details and complete proof of asymptotic distribution of maximum pseudo-likelihood ratio test statistic. The proposed maximum pseudo-likelihood procedure is applied to a real data set to give both point and interval estimates of expected response at different “future” covariate values. It turns out that confidence intervals under the new pseudo-likelihood procedure are shorter than those obtained from the popular maximum likelihood procedure. Nice concave curves of likelihood ratio statistics under both procedures also visualize that the pseudo-likelihood procedure gives shorter confidence intervals.

generalized linear model, mixture models, pseudo-likelihood asymptotic distribution, zero-inflated regression model.