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May 2016 Ratio Plot and Ratio Regression with Applications to Social and Medical Sciences
Dankmar Böhning
Statist. Sci. 31(2): 205-218 (May 2016). DOI: 10.1214/16-STS548

Abstract

We consider count data modeling, in particular, the zero-truncated case as it arises naturally in capture–recapture modeling as the marginal distribution of the count of identifications of the members of a target population. Whereas in wildlife ecology these distributions are often of a well-defined type, this is less the case for social and medical science applications since study types are often entirely observational. Hence, in these applications, violations of the assumptions underlying closed capture–recapture are more likely to occur than in carefully designed capture–recapture experiments. As a consequence, the marginal count distribution might be rather complex. The purpose of this note is to sketch some of the major ideas in the recent developments in ratio plotting and ratio regression designed to explore the pattern of the distribution underlying the capture process. Ratio plotting and ratio regression are based upon considering the ratios of neighboring probabilities which can be estimated by ratios of observed frequencies. Frequently, these ratios show patterns which can be easily modeled by a regression model. The fitted regression model is then used to predict the frequency of hidden zero counts. Particular attention is given to regression models corresponding to the negative binomial, multiplicative binomial and the Conway–Maxwell–Poisson distribution.

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Dankmar Böhning. "Ratio Plot and Ratio Regression with Applications to Social and Medical Sciences." Statist. Sci. 31 (2) 205 - 218, May 2016. https://doi.org/10.1214/16-STS548

Information

Published: May 2016
First available in Project Euclid: 24 May 2016

zbMATH: 06946222
MathSciNet: MR3506100
Digital Object Identifier: 10.1214/16-STS548

Keywords: Closed capture–recapture , Conway–Maxwell–Poisson , mixtures , multiplicative binomial , negative binomial , zero-truncated count distributions

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.31 • No. 2 • May 2016
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