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A unifying framework for marginalized random intercept models of correlated binary outcomes.

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  • 1Johns Hopkins Bloomberg School of Public Health, 615 N. Wolfe Street, Baltimore, MD 21205.

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Many marginal modeling approaches for correlated binary data are equivalent to copula models. This study clarifies copula models for marginal fixed effects estimation and interpretation in correlated binary data analysis.

Keywords:
Binary outcomesCopulasMarginal likelihoodMultivariate logitMultivariate probit

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Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Modeling

Background:

  • Marginal modeling of correlated binary outcomes is complex.
  • Existing approaches may lack clarity in their underlying mathematical structures.
  • Understanding these models is crucial for accurate data analysis.

Purpose of the Study:

  • To demonstrate the equivalence between many current marginal modeling approaches and copula-based models.
  • To elucidate the complex area of marginalized random intercept models for binary data.
  • To propose a clear nomenclature and model relationships for correlated binary data analysis.

Main Methods:

  • Utilizing copula models based on underlying latent threshold random variables.
  • Developing likelihood-based models for marginal fixed effects estimation.
  • Establishing a framework for understanding model relationships.

Main Results:

  • Many current marginal modeling approaches for correlated binary outcomes yield likelihoods equivalent to copula-based models.
  • Copula models provide a framework for marginal fixed effects estimation and interpretation.
  • A new nomenclature and set of model relationships are proposed.

Conclusions:

  • Copula-based models offer a unified approach to marginal modeling of correlated binary data.
  • The proposed framework clarifies complex relationships in marginalized random intercept models.
  • This work facilitates more precise analysis and interpretation of correlated binary data.