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On the existence of maximum likelihood estimates in random effects models for clustered multivariate binary data

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Abstract

We consider a class of random effects models for clustered multivariate binary data based on the threshold crossing technique of a latent random vector. Components of this latent vector are assumed to have a Laird–Ware structure. However, in place of their Gaussian assumptions, any specified class of multivariate distribution is allowed for the random effects, and the error vector is allowed to have any strictly positive pdf. A well known member of this class of models is the multivariate probit model with random effects. We investigate sufficient and necessary conditions for the existence of maximum likelihood estimates for the location and the association parameters. Implications of our results are illustrated through some hypothetical examples.

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Authors and Affiliations

  1. Division of Biostatistics, Department of Epidemiology, Michigan State University, B601 West Fee Hall, East Lansing, MI, 48824, USA

    David Todem

  2. Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, 600 Highland Ave., Madison, WI, 53792, USA

    KyungMann Kim

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  1. David Todem
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  2. KyungMann Kim
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Correspondence to David Todem.

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Todem, D., Kim, K. On the existence of maximum likelihood estimates in random effects models for clustered multivariate binary data. Metrika 73, 23–41 (2011). https://doi.org/10.1007/s00184-009-0263-2

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  • DOI: https://doi.org/10.1007/s00184-009-0263-2

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