Using Prior Information to Aid Ecological Inference: A Bayesian Approach

Corder, J. Kevin; Wolbrecht, Christina

doi:10.1017/cbo9780511510595.008

Cited by 4 publications

(11 citation statements)

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“…Success of the homogeneous, semiparametric and non‐parametric methods suggests the value of EI for gendered voting research, an application which others (Voss, 2004; Palmquist, 2001) have suggested would be unsuccessful. EI techniques are now only beginning to be applied to political data classified by gender (Corder and Wolbrecht, 2004; Moore, 2004; Hudson et al , 2005; Hudson and Moore, 2009) and further trials such as this will inform the use of EI in this area. Also use of King's non‐parametric method to estimate men's and women's party voting at NZ elections, 1893–1919, gave plausible results (Moore, 2004).…”

Section: Discussionmentioning

confidence: 99%

“…The first is that its assumptions may not hold. In this case, the assumption that P Wg and P Mg vary only randomly across electorates about means P W and P M is equivalent to assuming that men's voting rates are much the same across electorates and that women's voting rates are much the same across electorates, which is an assumption that does not take into account electoratespecific characteristics such as rurality, social class or electoral competition and rules (Corder and Wolbrecht, 2004) which may impact on gendered voting rates. This assumption is equivalent to assuming that there is no aggregation bias.…”

Section: Goodman Ecological Regressionmentioning

confidence: 99%

“…Other EI models have also been proposed. For example, Corder and Wolbrecht (2004) used Wakefield's (2004b) hierarchical binomial normal model to estimate gendered turnout at US elections (1916)(1917)(1918)(1919)(1920)). King's method has received criticism to date.…”

Section: Neighbourhood Modelmentioning

confidence: 99%

“…One of the earliest considerations of the problem of EI considered men's and women's voting preferences at Oregon elections (Ogburn and Goltra, 1919). More recently Corder and Wolbrecht (2004) have applied a Bayesian approach using the hierarchical binomial-normal model that was described in Wakefield (2004b) to estimate the turnout of men and women at some US elections, 1920US elections, -1932. There has, however, been some discussion on the efficacy of EI for gendered voting.…”

Section: Introductionmentioning

confidence: 99%

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Ecological Inference Techniques: An Empirical Evaluation Using Data Describing Gender and Voter Turnout at New Zealand Elections, 1893–1919

Hudson

Moore

Beh

et al. 2009

Journal of the Royal Statistical Society Series A: Statistics in Society

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The difference, if any, between men's and women's voting patterns is of particular interest to historians of gender and politics. For elections that were held before the introduction of opinion surveying in the 1940s, little data are available with which to estimate such differences. We apply six methods for ecological inference to estimate men's and women's voting rates in New Zealand (NZ), 1893-1919. NZ is an interesting case-study, since it was the first selfgoverning country where women could vote. Furthermore, NZ officials recorded the voting rates of men and women at elections, making it possible to compare estimates produced by methods for ecological inference with known true values, thus testing the efficacy of different methods for ecological inference for this data set. We find that the most popular methods for ecological inference, namely Goodman's ecological regression and King's parametric method, give poor estimates, as does the much debated neighbourhood method. However, King's non-parametric method, Chambers and Steel's semiparametric method and the Steel, Beh and Chambers homogeneous approach all gave good estimates that were close to the known values, with the homogeneous approach performing best overall. The success of these methods in this example suggests that ecological inference may be a viable option when investigating gender and voting. Moreover, researchers using ecological inference in other fields may do well to consider a range of statistical methods. This work is a significant NZ contribution to historical politics and the first quantitative contribution, in the area of NZ gender and politics.

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Section: Discussionmentioning

confidence: 99%

Section: Goodman Ecological Regressionmentioning

confidence: 99%

Section: Neighbourhood Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ecological Inference Techniques: An Empirical Evaluation Using Data Describing Gender and Voter Turnout at New Zealand Elections, 1893–1919

Hudson

Moore

Beh

et al. 2009

Journal of the Royal Statistical Society Series A: Statistics in Society

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“…This prior requires the specification of a degrees-of-freedom parameter (with a proper prior requiring this value to be 2 or greater) and a scale matrix. Corder and Wolbrecht (2004) have used the model that is described here to examine voting as a function of gender, in the period shortly after women became enfranchised in the USA in 1914. This application is difficult to answer from aggregate data alone because there is no possibility of collecting individual level data, and the proportions of women are close to 50% in all areas.…”

Section: Normal Priorsmentioning

confidence: 99%

Ecological Inference for 2 × 2 Tables

Wakefield

2004

Journal of the Royal Statistical Society Series A: Statistics in Society

122

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Summary. A fundamental problem in many disciplines, including political science, sociology and epidemiology, is the examination of the association between two binary variables across a series of 2 × 2 tables, when only the margins are observed, and one of the margins is fixed. Two unobserved fractions are of interest, with only a single response per table, and it is this non‐identifiability that is the inherent difficulty lying at the heart of ecological inference. Many methods have been suggested for ecological inference, often without a probabilistic model; we clarify the form of the sampling distribution and critique previous approaches within a formal statistical framework, thus allowing clarification and examination of the assumptions that are required under all approaches. A particularly difficult problem is choosing between models with and without contextual effects. Various Bayesian hierarchical modelling approaches are proposed to allow the formal inclusion of supplementary data, and/or prior information, without which ecological inference is unreliable. Careful choice of the prior within such models is required, however, since there may be considerable sensitivity to this choice, even when the model assumed is correct and there are no contextual effects. This sensitivity is shown to be a function of the number of areas and the distribution of the proportions in the fixed margin across areas. By explicitly providing a likelihood for each table, the combination of individual level survey data and aggregate level data is straightforward and we illustrate that survey data can be highly informative, particularly if these data are from a survey of the minority population within each area. This strategy is related to designs that are used in survey sampling and in epidemiology. An approximation to the suggested likelihood is discussed, and various computational approaches are described. Some extensions are outlined including the consideration of multiway tables, spatial dependence and area‐specific (contextual) variables. Voter registration–race data from 64 counties in the US state of Louisiana are used to illustrate the methods.

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Ecological Inference for 2 × 2 Tables (with Discussion)

Wakefield

2004

Journal of the Royal Statistical Society Series A: Statistics in Society

174

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Summary.A fundamental problem in many disciplines, including political science, sociology and epidemiology, is the examination of the association between two binary variables across a series of 2 2 tables, when only the margins are observed, and one of the margins is fixed. Two unobserved fractions are of interest, with only a single response per table, and it is this non-identifiability that is the inherent difficulty lying at the heart of ecological inference. Many methods have been suggested for ecological inference, often without a probabilistic model; we clarify the form of the sampling distribution and critique previous approaches within a formal statistical framework, thus allowing clarification and examination of the assumptions that are required under all approaches. A particularly difficult problem is choosing between models with and without contextual effects. Various Bayesian hierarchical modelling approaches are proposed to allow the formal inclusion of supplementary data, and/or prior information, without which ecological inference is unreliable. Careful choice of the prior within such models is required, however, since there may be considerable sensitivity to this choice, even when the model assumed is correct and there are no contextual effects. This sensitivity is shown to be a function of the number of areas and the distribution of the proportions in the fixed margin across areas. By explicitly providing a likelihood for each table, the combination of individual level survey data and aggregate level data is straightforward and we illustrate that survey data can be highly informative, particularly if these data are from a survey of the minority population within each area. This strategy is related to designs that are used in survey sampling and in epidemiology. An approximation to the suggested likelihood is discussed, and various computational approaches are described. Some extensions are outlined including the consideration of multiway tables, spatial dependence and area-specific (contextual) variables. Voter registration-race data from 64 counties in the US state of Louisiana are used to illustrate the methods.

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Using Prior Information to Aid Ecological Inference: A Bayesian Approach

Cited by 4 publications

References 0 publications

Ecological Inference Techniques: An Empirical Evaluation Using Data Describing Gender and Voter Turnout at New Zealand Elections, 1893–1919

Ecological Inference Techniques: An Empirical Evaluation Using Data Describing Gender and Voter Turnout at New Zealand Elections, 1893–1919

Ecological Inference for 2 × 2 Tables

Ecological Inference for 2 × 2 Tables (with Discussion)

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