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R×C ecological inference: bounds, correlations, flexibility and transparency of assumptions

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  • D. James Greiner
  • Kevin M. Quinn

Abstract

Summary. Despite its potential pitfalls, ecological inference is an unavoidable part of some quantitative settings, including US voting rights litigation. In such applications, the analyst will typically encounter two‐way tables with more than two rows and columns. Although several ecological inference methods are currently available for 2×2 tables, there are fewer options for analysing general R×C tables, and virtually none that model counts as opposed to fractions. We propose a count R×C method that respects the bounds deterministically, that allows for complex relationships between internal cell quantities, that is easily extensible and that results from transparent assumptions. We study the method via simulation, and then apply it to an example that is drawn from the state of Texas relevant to recent redistricting litigation there.

Suggested Citation

  • D. James Greiner & Kevin M. Quinn, 2009. "R×C ecological inference: bounds, correlations, flexibility and transparency of assumptions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 172(1), pages 67-81, January.
    • Handle: RePEc:bla:jorssa:v:172:y:2009:i:1:p:67-81
    DOI: 10.1111/j.1467-985X.2008.00551.x
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    References listed on IDEAS

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    1. Jon Wakefield, 2004. "Ecological inference for 2 × 2 tables (with discussion)," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(3), pages 385-445, July.
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    3. Ferree, Karen E., 2004. "Iterative Approaches to R × C Ecological Inference Problems: Where They Can Go Wrong and One Quick Fix," Political Analysis, Cambridge University Press, vol. 12(2), pages 143-159, April.
    4. Andrew Gelman & David K. Park & Stephen Ansolabehere & Phillip N. Price & Lorraine C. Minnite, 2001. "Models, assumptions and model checking in ecological regressions," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(1), pages 101-118.
    5. Jon Wakefield, 2004. "Ecological inference for 2 × 2 tables," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 167(3), pages 385-425, July.
    6. Ori Rosen & Wenxin Jiang & Gary King & Martin A. Tanner, 2001. "Bayesian and Frequentist Inference for Ecological Inference: The R×C Case," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 55(2), pages 134-156, July.
    7. David A. Freedman & Stephen P. Klein & Jerome Sacks & Charles A. Smyth & Charles G. Everett, 1991. "Ecological Regression and Voting Rights," Evaluation Review, , vol. 15(6), pages 673-711, December.
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    Cited by:

    1. Carolina Plescia & Lorenzo De Sio, 2018. "An evaluation of the performance and suitability of R × C methods for ecological inference with known true values," Quality & Quantity: International Journal of Methodology, Springer, vol. 52(2), pages 669-683, March.
    2. Puig, Xavier & Ginebra, Josep, 2014. "A cluster analysis of vote transitions," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 328-344.
    3. Zax Jeffrey S., 2012. "Single Regression Estimates of Voting Choices When Turnout is Unknown," Statistics, Politics and Policy, De Gruyter, vol. 4(1), pages 1-22, October.
    4. Roberto Colombi & Antonio Forcina, 2016. "Latent class models for ecological inference on voters transitions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 25(4), pages 501-517, November.
    5. Antonio Forcina & Davide Pellegrino, 2019. "Estimation of voter transitions and the ecological fallacy," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1859-1874, July.

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