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On some models for multivariate binary variables parallel in complexity with the multivariate Gaussian distribution


  • D. R. Cox


It is shown that both the simple form of the Rasch model for binary data and a generalisation are essentially equivalent to special dichotomised Gaussian models. In these the underlying Gaussian structure is of single factor form; that is, the correlations between the binary variables arise via a single underlying variable, called in psychometrics a latent trait. The implications for scoring of the binary variables are discussed, in particular regarding the scoring system as in effect estimating the latent trait. In particular, the role of the simple sum score, in effect the total number of 'successes', is examined. Relations with the principal component analysis of binary data are outlined and some connections with the quadratic exponential binary model are sketched. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • D. R. Cox, 2002. "On some models for multivariate binary variables parallel in complexity with the multivariate Gaussian distribution," Biometrika, Biometrika Trust, vol. 89(2), pages 462-469, June.
  • Handle: RePEc:oup:biomet:v:89:y:2002:i:2:p:462-469

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    References listed on IDEAS

    1. Gareth O. Roberts & Jeffrey S. Rosenthal, 1999. "Convergence of Slice Sampler Markov Chains," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 643-660.
    2. Francesco Bartolucci & Luisa Scaccia & Antonietta Mira, 2006. "Efficient Bayes factor estimation from the reversible jump output," Biometrika, Biometrika Trust, vol. 93(1), pages 41-52, March.
    3. Sylvia Fruhwirth-Schnatter, 2004. "Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 143-167, June.
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    Cited by:

    1. Forcina, A. & Dardanoni, V., 2008. "Regression models for multivariate ordered responses via the Plackett distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2472-2478, November.
    2. Montangie, Lisandro & Montani, Fernando, 2017. "Higher-order correlations in common input shapes the output spiking activity of a neural population," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 845-861.
    3. Eshima, Nobuoki, 2004. "Canonical exponential models for analysis of association between two sets of variables," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 135-144, January.

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