Zero-inflated Poisson (ZIP) models, which are mixture models, have been popularly used for count data that often contain large numbers of zeros, but their identifiability has not yet been thoroughly explored. In this work, we systematically investigate the identifiability of the ZIP models under a number of different assumptions. More specifically, we show the identifiability of a parametric ZIP model in which the incidence probability p(x) and Poisson mean λ(x) are modeled parametrically for x being a continuous covariate in a closed interval. A semiparametric ZIP regression model is shown to be identifiable in which for r(x) and s(x) being unspecified smooth functions.
- Count data
- Semiparametric zero-inflated Poisson (ZIP) regression model
ASJC Scopus subject areas
- Statistics and Probability