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Two random effects models for multivariate binary data

B W McDonald1

  • 1Department of Mathematics, Royal Melbourne Institute of Technology, Australia.

Biometrics
|March 1, 1994
PubMed
Summary
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This study introduces two regression models for unequal multivariate binary data. The models differ in how random effects are applied, impacting parameter interpretation and application in dental data analysis.

Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • Multivariate binary data analysis requires careful model selection, especially when marginal success probabilities are unequal.
  • Existing regression models may not adequately capture the complexities of correlated binary outcomes with varying probabilities.

Purpose of the Study:

  • To present and compare two distinct regression models for multivariate binary data with unequal marginal success probabilities.
  • To highlight the differences in regression parameter interpretation arising from distinct random effect structures.

Main Methods:

  • The first model incorporates an additive random effect on the probability scale.
  • The second model utilizes a discrete random effect on the logit scale.
  • Both models are applied to illustrate their practical utility.

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Main Results:

  • The choice of random effect scale (probability vs. logit) significantly influences the interpretation of regression coefficients.
  • The application to dental data demonstrates the practical differences and suitability of each model.

Conclusions:

  • Two viable regression models for unequal multivariate binary data are presented.
  • The study underscores the importance of considering the random effect structure for accurate interpretation in statistical modeling.