Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models

Yixuan Zou,Derek S Young,Jan Hannig

doi:10.1186/s40488-021-00117-0

Abstract

Zero-inflated and hurdle models are widely applied to count data possessing excess zeros, where they can simultaneously model the process from how the zeros were generated and potentially help mitigate the effects of overdispersion relative to the assumed count distribution. Which model to use depends on how the zeros are generated: zero-inflated models add an additional probability mass on zero, while hurdle models are two-part models comprised of a degenerate distribution for the zeros and a zero-truncated distribution. Developing confidence intervals for such models is challenging since no closed-form function is available to calculate the mean. In this study, generalized fiducial inference is used to construct confidence intervals for the means of zero-inflated Poisson and Poisson hurdle models. The proposed methods are assessed by an intensive simulation study. An illustrative example demonstrates the inference methods.

Highlights

The Poisson distribution is arguably one of the most commonly used models for count data
One of the earliest papers to address the problem of excess zeros was (Mullahy 1986), who proposed a two-part model that permits a more flexible data-generating process: zeros are from a binomial distribution while positive values are from a truncated distribution
If treatment plans are benchmarked against the 95% bootstrap confidence intervals, smaller and larger values beyond the respective limits of that interval will be omitted from such plans, whereas those values will be reflected via the 95% Generalized confidence interval (GCI)

Summary

Introduction

The Poisson distribution is arguably one of the most commonly used models for count data. One of the earliest papers to address the problem of excess zeros was (Mullahy 1986), who proposed a two-part model that permits a more flexible data-generating process: zeros are from a binomial distribution while positive values are from a truncated distribution. Such a model can accommodate under- and over-dispersion. 2.1 Generalized fiducial inference on discrete data Let Y be a discrete random variable with the distribution function F(·|θ). According to the philosophy of generalized fiducial inference, we need to solve the data generating equation to get the parameter as a function of the data and a known random distribution. We can obtain the fiducial distribution of ξ2 followed by the fiducial distribution of ξ1 given that ξ2 is known

Fiducial distributions for poisson data with excess zeros

Conclusion