Estimation of zero-inflated bivariate Poisson regression with missing covariates

Abstract

Zero-inflated bivariate Poisson regression (ZIBP) models are most often applied to correlated bivariate count data that contain a large proportion of zeros. These models have been applied in various fields, such as medical research, health economics, insurance, sports, etc. Because, in practice, some of the covariates involved in ZIBP regression modeling often have missing values, we propose methods for estimating the parameters of the ZIBP regression model with missing at random covariates. Assuming that the selection probability is unknown and estimated non parametrically (by a kernel estimator), we propose inverse probability weighting (IPW) and multiple imputation (MI) methods for estimating the parameters of the ZIBP regression model with missing at random covariates. Asymptotic properties of the proposed estimators are studied under certain regularity conditions. A simulation study is conducted to evaluate the performance of the proposed methods. Finally, the practical application of the proposed methodology is illustrated with data from the health-care field.