Department of Public Health Sciences

Identifiability of zero-inflated Poisson models

Li, C.S

Brazilian Journal of Probability and Statistics. 2012. 26(3):306-312.

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 as p(x) = exp(β0 + β1x)/[1 + exp(β0 + β1x)] and λ(x) = exp(α0+α1x) for x being a continuous covariate in a closed interval. A semiparametric ZIP regression model is shown to be identifiable in which (i) p(x) = exp(β0 + β1x)/[1 + exp(β0 + β1x)] and λ(x) = exp[s(x)], (ii) p(x) = exp[r(x)]/{1 + exp[r(x)]} and λ(x) = exp(α0 + α1x), or (iii) p(x) = exp[r(x)]/{1 + exp[r(x)]} and λ(x) = exp[s(x)] for r(x) and s(x) being unspecified smooth functions.

Keywords: Count data; semiparametric zero-inflated Poisson (ZIP) regression model

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