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The beta‐binomial convolution model for 2×2 tables with missing cell counts

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  • Rob Eisinga

Abstract

This paper considers the beta‐binomial convolution model for the analysis of 2×2 tables with missing cell counts. We discuss maximum‐likelihood (ML) parameter estimation using the expectation–maximization algorithm and study information loss relative to complete data estimators. We also examine bias of the ML estimators of the beta‐binomial convolution. The results are illustrated by two example applications.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:63:y:2009:i:1:p:24-42
    DOI: 10.1111/j.1467-9574.2008.00404.x
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    References listed on IDEAS

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    1. King, Gary, 2004. "EI: A Program for Ecological Inference," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i07).
    2. 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.
    3. Rob Eisinga, 2008. "Information loss for 2 × 2 tables with missing cell counts: binomial case," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(2), pages 239-254, May.
    4. 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.
    5. 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.
    6. K. Poortema, 1999. "On modelling overdispersion of counts," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 53(1), pages 5-20, March.
    7. 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.
    8. Imai, Kosuke & Lu, Ying & Strauss, Aaron, 2008. "Bayesian and Likelihood Inference for 2 × 2 Ecological Tables: An Incomplete-Data Approach," Political Analysis, Cambridge University Press, vol. 16(1), pages 41-69, January.
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