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Log-mean linear models for binary data

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  • A. Roverato
  • M. Lupparelli
  • L. La Rocca

Abstract

This paper introduces a novel class of models for binary data, which we call log-mean linear models. They are specified by linear constraints on the log-mean linear parameter, defined as a log-linear expansion of the mean parameter of the multivariate Bernoulli distribution. We show that marginal independence relationships between variables can be specified by setting certain log-mean linear interactions to zero and, more specifically, that graphical models of marginal independence are log-mean linear models. Our approach overcomes some drawbacks of the existing parameterizations of graphical models of marginal independence. Copyright 2013, Oxford University Press.

Suggested Citation

  • A. Roverato & M. Lupparelli & L. La Rocca, 2013. "Log-mean linear models for binary data," Biometrika, Biometrika Trust, vol. 100(2), pages 485-494.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:2:p:485-494
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    File URL: http://hdl.handle.net/10.1093/biomet/ass080
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    Cited by:

    1. Lupparelli, Monia & Mattei, Alessandra, 2020. "Joint and marginal causal effects for binary non-independent outcomes," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    2. Kayvan Sadeghi & Alessandro Rinaldo, 2020. "Hierarchical models for independence structures of networks," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 439-457, August.
    3. Ioannis Ntzoufras & Claudia Tarantola, 2012. "Conjugate and Conditional Conjugate Bayesian Analysis of Discrete Graphical Models of Marginal Independence," Quaderni di Dipartimento 178, University of Pavia, Department of Economics and Quantitative Methods.
    4. Alberto Roverato, 2015. "Log-mean Linear Parameterization for Discrete Graphical Models of Marginal Independence and the Analysis of Dichotomizations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 627-648, June.
    5. Monia Lupparelli & Alberto Roverato, 2017. "Log-mean linear regression models for binary responses with an application to multimorbidity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 227-252, February.
    6. Ntzoufras, Ioannis & Tarantola, Claudia, 2013. "Conjugate and conditional conjugate Bayesian analysis of discrete graphical models of marginal independence," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 161-177.

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