Abstract

Zero-inflated models are widely used to analyze count data with excess zero counts. They provide additional flexibility in model fitting and can estimate the underlying proportion of susceptibility (that is, potential event counts) in the population. The proportion of susceptibility is often the critical parameter of interest in various applications, such as biosciences and ecology. In this study, we focus on the effects of parameter estimation when heterogeneity is present in both the event count intensity and the susceptibility probability. We show that the susceptibility probability will lead to underestimation if heterogeneity in the event count intensity is ignored.
On the other hand, the behavior is different if heterogeneity in the susceptibility probability is ignored; notably, an estimate of the average susceptibility probability may be unbiased or over- or under-estimated depending on the relationship between count intensities and susceptibility probabilities. In addition, when heterogeneity in the event count intensity is related to covariates, we propose a conditional likelihood approach to estimate the intensity parameters. This alternative method shares an optimal estimating function property and ensures robustness against model specification on the susceptibility probability. We then propose a consistent estimator for the average susceptibility probability, provided that the count intensity component model is correctly specified. We illustrate the bias effects and estimator performance in simulation studies and real data analysis.