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Binomial-Beta Hierarchical Models for Ecological Inference

Author

Listed:
  • GARY KING

    (Harvard University)

  • ORI ROSEN

    (University of Pittsburgh)

  • MARTIN A. TANNER

    (Northwestern University)

Abstract

The authors develop binomial-beta hierarchical models for ecological inference using insights from the literature on hierarchical models based on Markov chain Monte Carlo algorithms and King's ecological inference model. The new approach reveals some features of the data that King's approach does not, can be easily generalized to more complicated problems such as general R × C tables, allows the data analyst to adjust for covariates, and provides a formal evaluation of the significance of the covariates. It may also be better suited to cases in which the observed aggregate cells are estimated from very few observations or have some forms of measurement error. This article also provides an examples of a hierarchical model in which the statistical idea of “borrowing strength†is used not merely to increase the efficiency of the estimates but to enable the data analyst to obtain estimates.

Suggested Citation

  • Gary King & Ori Rosen & Martin A. Tanner, 1999. "Binomial-Beta Hierarchical Models for Ecological Inference," Sociological Methods & Research, , vol. 28(1), pages 61-90, August.
    • Handle: RePEc:sae:somere:v:28:y:1999:i:1:p:61-90
    DOI: 10.1177/0049124199028001004
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    References listed on IDEAS

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    1. A. Gupta & C. Wong, 1985. "On three and five parameter bivariate beta distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 85-91, December.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. A. Forcina & M. Gnaldi & B. Bracalente, 2012. "A revised Brown and Payne model of voting behaviour applied to the 2009 elections in Italy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(1), pages 109-119, March.
    6. 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.
    7. Bruce Western, 1999. "Bayesian Analysis for Sociologists," Sociological Methods & Research, , vol. 28(1), pages 7-34, August.
    8. William Reed, 2003. "Information and Economic Interdependence," Journal of Conflict Resolution, Peace Science Society (International), vol. 47(1), pages 54-71, February.
    9. Pelzer, B. & Eisinga, R. & Franses, Ph.H.B.F., 2002. "Ecological panel inference in repeated cross sections," Econometric Institute Research Papers EI 2002-22, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    10. Sarah Moon, 2024. "Partial Identification of Individual-Level Parameters Using Aggregate Data in a Nonparametric Binary Outcome Model," Papers 2403.07236, arXiv.org, revised Apr 2024.
    11. 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.
    12. Andrew D. Martin, 2003. "Bayesian Inference for Heterogeneous Event Counts," Sociological Methods & Research, , vol. 32(1), pages 30-63, August.

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