Abstract
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.
Citation
Chin-Shang Li. "Identifiability of zero-inflated Poisson models." Braz. J. Probab. Stat. 26 (3) 306 - 312, August 2012. https://doi.org/10.1214/10-BJPS137
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