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One-inflated zero-truncated count regression models

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  • Ryan T. Godwin

Abstract

We find that in zero-truncated count data (y=1,2,...), individuals often gain information at first observation (y=1), leading to a common but unaddressed phenomenon of "one-inflation". The current standard, the zero-truncated negative binomial (ZTNB) model, is misspecified under one-inflation, causing bias and inconsistency. To address this, we introduce the one-inflated zero-truncated negative binomial (OIZTNB) regression model. The importance of our model is highlighted through simulation studies, and through the discovery of one-inflation in four datasets that have traditionally championed ZTNB. We recommended OIZTNB over ZTNB for most data, and provide estimation, marginal effects, and testing in the accompanying R package oneinfl.

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  • Ryan T. Godwin, 2024. "One-inflated zero-truncated count regression models," Papers 2402.02272, arXiv.org.
    • Handle: RePEc:arx:papers:2402.02272
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    1. Ryan T. Godwin & Dankmar Böhning, 2017. "Estimation of the population size by using the one-inflated positive Poisson model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 425-448, February.
    2. James W. Hardin & Joseph M. Hilbe, 2015. "Regression models for count data from truncated distributions," Stata Journal, StataCorp LP, vol. 15(1), pages 226-246, March.
    3. Grogger, J T & Carson, Richard T, 1991. "Models for Truncated Counts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(3), pages 225-238, July-Sept.
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