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Bayesian and Frequentist Inference for Ecological Inference: The R×C Case

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  • Ori Rosen
  • Wenxin Jiang
  • Gary King
  • Martin A. Tanner

Abstract

In this paper we propose Bayesian and frequentist approaches to ecological inference, based on R×C contingency tables, including a covariate. The proposed Bayesian model extends the binomial‐beta hierarchical model developed by King, Rosen and Tanner (1999) from the 2×2 case to the R×C case. As in the 2×2 case, the inferential procedure employs Markov chain Monte Carlo (MCMC) methods. As such, the resulting MCMC analysis is rich but computationally intensive. The frequentist approach, based on first moments rather than on the entire likelihood, provides quick inference via nonlinear least‐squares, while retaining good frequentist properties. The two approaches are illustrated with simulated data, as well as with real data on voting patterns in Weimar Germany. In the final section of the paper we provide an overview of a range of alternative inferential approaches which trade‐off computational intensity for statistical efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:55:y:2001:i:2:p:134-156
    DOI: 10.1111/1467-9574.00162
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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. de Bromhead, Alan & Fernihough, Alan & Hargaden, Enda, 2020. "Representation of the People: Franchise Extension and the “Sinn Féin Election” in Ireland, 1918," The Journal of Economic History, Cambridge University Press, vol. 80(3), pages 886-925, September.
    3. Lehmann, Sibylle H., 2010. "The German Elections in the 1870s: Why Germany Turned from Liberalism to Protectionism," The Journal of Economic History, Cambridge University Press, vol. 70(1), pages 146-178, March.
    4. Puig, Xavier & Ginebra, Josep, 2014. "A cluster analysis of vote transitions," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 328-344.
    5. Irene L. Hudson & Linda Moore & Eric J. Beh & David G. Steel, 2010. "Ecological inference techniques: an empirical evaluation using data describing gender and voter turnout at New Zealand elections, 1893–1919," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(1), pages 185-213, January.
    6. 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.
    7. Olga Orlanski & Günther G. Schulze, 2017. "The Determinants of Islamophobia - An Empirical Analysis of the Swiss Minaret Referendum," CESifo Working Paper Series 6741, CESifo.
    8. Rob Eisinga, 2009. "The beta‐binomial convolution model for 2×2 tables with missing cell counts," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(1), pages 24-42, February.
    9. Ludo Peeters & Coro Chasco-Yrigoyen, 2005. "Ecological Inference And Spatial Heterogeneity - A New Approach Based On Entropy Econometrics," ERSA conference papers ersa05p705, European Regional Science Association.
    10. 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.
    11. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    12. 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.
    13. Sarah Moon, 2024. "Partial Identification of Individual-Level Parameters Using Aggregate Data in a Nonparametric Model," Papers 2403.07236, arXiv.org, revised May 2024.
    14. 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.
    15. Pablo Sandoval & Silvia Ojeda, 2023. "Estimation of electoral volatility parameters employing ecological inference methods," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(1), pages 405-426, February.
    16. Joan G. Staniswalis, 2008. "Incorporating Marginal Covariate Information in a Nonparametric Regression Model for a Sample of R×C Tables," Biometrics, The International Biometric Society, vol. 64(4), pages 1054-1061, December.
    17. 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.
    18. Matt Barreto & Loren Collingwood & Sergio Garcia-Rios & Kassra AR Oskooii, 2022. "Estimating Candidate Support in Voting Rights Act Cases: Comparing Iterative EI and EI-R×C Methods," Sociological Methods & Research, , vol. 51(1), pages 271-304, February.

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