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

Abstract

In this study, we would like to show that the one-inflated zero-truncated negative binomial (OIZTNB) regression model can be easily implemented in R via built-in functions when we use mean-parameterization feature of negative binomial distribution to build OIZTNB regression model. From the practitioners' point of view, we believe that this approach presents a computationally convenient way for implementation of the OIZTNB regression model.

Semiparametric empirical likelihood inference for abundance from one‐inflated capture–recapture data

“…Together with the conclusions in Section 5.3, it also implies that one‐inflation, observed covariates, and unobserved heterogeneity are three key factors for the variation of capture probabilities of the prinia data. The one‐inflated Poisson mixture model, one‐inflated negative binomial regression model, and one‐inflated geometric regression model were investigated by Godwin (2017), Inan (2018), Godwin (2019), and Böhning and Friedl (2021), can account for all these three factors. Our semiparametric EL estimation procedure and the accompanying EM algorithm can be straightforwardly extended to such models.…”

“…To account for the excess 1s, Godwin and Böhning (2017) proposed using a one-inflated zero-truncated Poisson distribution (see model (24) in Section 3) and a zero-truncated one-inflated Poisson distribution (see model (2) in Section 2.1) to model the probability mass function of the number of captures, and they suggested a score test for the one-inflation parameter. More complicated count models have been investigated in the literature, such as the one-inflated zero-truncated negative binomial model (Godwin, 2017;Inan, 2018), the one-inflated zero-truncated Poisson mixture model (Godwin, 2019), and the oneinflated zero-truncated geometric model (Böhning & van der Heijden, 2019;Böhning & Friedl, 2021). The zero-truncated one-inflated geometric model was also investigated in Chapter 14 of Böhning et al (2018).…”

“…Under the one‐inflated zero‐truncated negative binomial regression model, Godwin (2017) also proposed a Horvitz–Thompson‐type estimator and CL‐based likelihood ratio tests for the one‐inflation and unobserved heterogeneity. Inan (2018) further investigated the computation problem in terms of a mean‐parameterized negative binomial distribution. However, the aforementioned methods have at least two limitations.…”