Identifying one-inflation in regression models for ratio estimators in single-source capture-recapture problems

Abstract

Regression modelling of ratio estimators, in short ratio regression, has been developed as a flexible instrument to allow for a wide class of count data distributions. In particular, it turns out to be useful in zero-truncated count distributions as they typically arise in capture-recapture settings. One-inflation describes the occurrence of extra-ones relative to a base count distribution and is a phenomenon frequently occurring in capture-recapture studies caused, for example, by behavioural change. The work presented here shows how one-inflation can be incorporated into ratio regression modelling and how one-inflation can be assessed in ratio regression modelling. Population size estimation on the basis of ratio regression is discussed and applied to a case study on heroin users in Chiang Mai, Thailand. For all model-based estimators, computational inference is developed by means of the bootstrap. As several versions of the bootstrap are possible, a simulation study is included comparing the different approaches. One of the main results shows that integrating the model selection into the population size inference leads to favourable properties, such as good coverage probabilities.

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ORCID for Dankmar Böhning: orcid.org/0000-0003-0638-7106

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