One‐inflation and unobserved heterogeneity in population size estimation

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.

Section: Representation Of the One‐inflated Zero‐truncated Negative Bmentioning

confidence: 99%

P r^{Z T N B} false(Y = y false) = P r false(Y = y false| y > 0 false) = \frac{P r (Y = y)}{P r (y > 0)} = \frac{P r (Y = y)}{1 - P r (y = 0)} y = 1, 2, … .

…”

Section: Representation Of the One‐inflated Zero‐truncated Negative Bmentioning

confidence: 99%

“…Following Godwin (), assume that

θ = \frac{λ}{α}

and this also leads to

\frac{1}{1 + θ} = \frac{α}{α + λ}

and

\frac{θ}{1 + θ} = \frac{λ}{α + λ}

. Then can be rewritten as follows:

P r^{Z T N B} false(Y = y false) = \frac{Γ false(α + y false)}{Γ (α) y!} {(\frac{1}{1 + θ})}^{α} {(\frac{θ}{1 + θ})}^{y} (\frac{1}{1 - {(\frac{1}{1 + θ})}^{α}}) y = 1, 2, …,

which is the representation given at the first page of Godwin () (no equation number). Although we are not sure about the reason why Godwin () used

θ = \frac{λ}{α} = λ ϕ

, we can easily see that θ can be interpreted as the product of mean and overdispersion parameter.…”

Section: Representation Of the One‐inflated Zero‐truncated Negative Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

İnan

2018

The one‐inflated positive Poisson mixture model for use in population size estimation

Godwin

2019

Self Cite

The one-inflated positive Poisson mixture model (OIPPMM) is presented, for use as the truncated count model in Horvitz-Thompson estimation of an unknown population size. The OIPPMM offers a way to address two important features of some capture-recapture data: one-inflation and unobserved heterogeneity. The OIPPMM provides markedly different results than some other popular estimators, and these other estimators can appear to be quite biased, or utterly fail due to the boundary problem, when the OIPPMM is the true data-generating process. In addition, the OIPPMM provides a solution to the boundary problem, by labelling any mixture components on the boundary instead as one-inflation. K E Y W O R D Scapture-recapture, count inflation, Horvitz-Thompson, mixture model, Poisson www.biometrical-journal.com

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Farcomeni

2020

We discuss Bayesian log‐linear models for incomplete contingency tables with both missing and interval censored cells, with the aim of obtaining reliable population size estimates. We also discuss use of external information on the censoring probability, which may substantially reduce uncertainty. We show in simulation that information on lower bounds and external information can each improve the mean squared error of population size estimates, even when the external information is not completely accurate. We conclude with an original example on estimation of prevalence of multiple sclerosis in the metropolitan area of Rome, where five out of six lists have interval censored counts. External information comes from mortality rates of multiple sclerosis patients.