Validation likelihood estimation method for a zero-inflated Bernoulli regression model with missing covariates

Abstract

A zero-inflated Bernoulli (ZIBer) regression model is an alternative model in order to improve fitting the binary outcome data that have many more zeros than expected under a regular logistic regression model. Because some covariates often have missing values, we propose the validation likelihood (VL) method to estimate the parameters of the ZIBer regression model with covariates missing at random. We consider the true selection probability (SP) model, a parametric SP model and a nonparametric SP model to compare the efficiency of the true SP, parametric SP, and semiparametric SP VL estimators. The asymptotic results of these three estimators are studied under some regularity conditions. Both the theoretical and simulation results reveal that the parametric and semiparametric SP VL estimation methods outperform the true SP VL estimation method if the parametric SP model is correct. The simulation results also indicate that the semiparametric SP VL estimation method is preferred to the inverse probability weighting and multiple imputation estimation methods. The practical application of the proposed methodology is adorned with a survey data set of violations of traffic rules of motorcyclist respondents in Taiwan.