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Flexible Random Intercept Models for Binary Outcomes Using Mixtures of Normals.

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Computational Statistics & Data Analysis
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Random intercept models for binary data effectively handle subject differences. New flexible models using mixtures of normals maintain a "closure property," unifying various approaches and offering computational advantages.

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Random intercept models are crucial for analyzing binary data with subject-specific variations.
  • Non-linear link functions in binary models create a distinction between marginal and conditional interpretations.
  • Standard probit models with normal random intercepts possess a 'closure property,' where marginal and conditional interpretations align.

Purpose of the Study:

  • To introduce a flexible family of random intercept models for binary data.
  • To demonstrate that this closure property extends to models using mixtures of normal distributions.
  • To show the relationship between these flexible models and existing approaches in the literature.

Main Methods:

  • Extending the closure property of probit models to mixtures of normal distributions for random intercepts.
  • Developing a unified framework that synthesizes seemingly disparate modeling strategies.
  • Utilizing diverse examples to illustrate the broad applicability of the proposed models.

Main Results:

  • The closure property is achieved when using mixtures of normal distributions for random effects in binary models.
  • This approach unifies several existing statistical models for binary data.
  • The proposed family of models demonstrates significant computational benefits.

Conclusions:

  • Flexible random intercept models based on mixtures of normals offer a unified and computationally efficient approach to binary data analysis.
  • These models effectively address between-subject heterogeneity while maintaining desirable interpretational properties.
  • The framework provides a valuable tool for researchers across various scientific disciplines dealing with binary outcomes.