Modeling Zero-Inflated Continuous Data with Varying Dispersion

Abstract

Zero-inflated data are often observed in empirical studies of different scientific fields. Data are considered as zero-inflated if the observed values of a random vector contain significantly more zeros than expected. Excessive occurred zeros to the dependent variable in a regression model discourage straightforward modelling by classical regression techniques. In the past, zero-inflation is considered as a count data problem and Zero-Inflated Poisson regression (ZIP) has been established to be the standard tool for zero-inflation modelling. The approach is based on a joint probability density function in which the probability for non-zero observations and response mean are both parameters and interlinked by two pseudo-simultaneously estimated linear models. However, constant dispersion is often assumed even when overdispersion is a common feature in almost every empirical data set. In our paper, the dispersion is formulated as a gamma generalized submodel interlinked with a mean and a zero-inflation probability submodel. We propose a modified triple, nested iterative approach to model response mean, dispersion and zero-inflation probability simultaneously.