Estimation of the Population Size by Using the One-Inflated Positive Poisson Model

Abstract

Summary. In population size estimation, many capture-recapture-type data exhibit a preponderance of '1'-counts. This excess of 1s can arise as subjects gain information from the initial capture that provides a desire and ability to avoid subsequent captures. Existing population size estimators that purport to deal with heterogeneity can be much too large in the presence of 1-inflation, which is a specific form of heterogeneity. To deal with the phenomena of excess 1s, we propose the one-inflated positive Poisson model for use as the truncated count distribution in Horvitz-Thompson estimation of the population size.

One‐inflation and unobserved heterogeneity in population size estimation

“…An alternate form of one‐inflation that does draw from the probability of a “zero” count would lead to a different Horvitz–Thompson estimator. This idea is explored in the context of the OIPP model in Godwin and Böhning ().…”

“…In order to deal with unobserved heterogeneity, the ZTNB model has been used by Cruyff and van der Heijden (2008). In order to handle one-inflation, the OIPP model has been proposed by Godwin and Böhning (2016). The OIZTNB model addresses both unobserved heterogeneity and one-inflation.…”

“…An alternate form of one-inflation that does draw from the probability of a "zero" count would lead to a different Horvitz-Thompson estimator. This idea is explored in the context of the OIPP model in Godwin and Böhning (2016). In the ZTNB model, there is a tendency for a "boundary" (Böhning, 2015) or "identification" (Cruyff and van der Heijden, 2008) problem, wherein the estimated value of α lies very close to the boundary of zero.…”

“…The justification for a one-inflated process is presented in Godwin and Böhning (2016), and is not ad hoc, although one-inflation has been explicitly observed (Farcomeni and Scacciatelli, 2013). In a truncated count process, the subject is not observed until the observational apparatus becomes active.…”

One‐inflation and unobserved heterogeneity in population size estimation by Ryan T. Godwin

“…Tables show the model fitting results of positive Poisson (PP), one‐inflated positive Poisson (OIPP) (Godwin & Böhning, ), ZTNB, and OIZTNB regression models, respectively. The results are all consistent with the results in Godwin () except of the OIZTNB regression model for Scrapie holdings in France data.…”