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Ratio plot and ratio regression with applications to social and medical sciences

Ratio plot and ratio regression with applications to social and medical sciences
Ratio plot and ratio regression with applications to social and medical sciences
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.
0883-4237
205-218
Bohning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1
Bohning, Dankmar
1df635d4-e3dc-44d0-b61d-5fd11f6434e1

Bohning, Dankmar (2016) Ratio plot and ratio regression with applications to social and medical sciences. Statistical Science, 31 (2), 205-218. (doi:10.1214/16-STS548).

Record type: Article

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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Accepted/In Press date: 19 May 2016
e-pub ahead of print date: 24 May 2016
Organisations: Statistics, Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 398811
URI: https://eprints.soton.ac.uk/id/eprint/398811
ISSN: 0883-4237
PURE UUID: 0870626b-402d-4a8a-a2b4-f4e1f15d819a
ORCID for Dankmar Bohning: ORCID iD orcid.org/0000-0003-0638-7106

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Date deposited: 03 Aug 2016 09:36
Last modified: 06 Oct 2018 00:32

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