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A random-effects ordinal regression model for multilevel analysis

D Hedeker1, R D Gibbons

  • 1Prevention Research Center, School of Public Health, University of Illinois at Chicago, Illinois 60607.

Biometrics
|December 1, 1994
PubMed
Summary
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This study introduces a random-effects ordinal regression model for analyzing clustered and longitudinal ordinal data. The novel approach uses a threshold concept and maximum marginal likelihood estimation for robust statistical insights.

Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Ordinal response data, common in various fields, often exhibits clustering or longitudinal dependencies.
  • Existing statistical models may not adequately capture the complexities of such data structures.
  • A need exists for flexible regression models that accommodate both ordinal outcomes and correlated observations.

Purpose of the Study:

  • To propose a novel random-effects ordinal regression model.
  • To extend the model for both probit and logistic response functions.
  • To provide a robust statistical framework for analyzing clustered and longitudinal ordinal data.

Main Methods:

  • Development of a random-effects ordinal regression model based on the threshold concept.

Related Experiment Videos

  • Incorporation of a latent continuous response following a linear mixed-effects model.
  • Application of maximum marginal likelihood (MML) estimation with Gauss-Hermite quadrature for numerical integration.

    • Main Results:

    • The proposed model effectively analyzes ordinal data with clustered structures, as demonstrated with student performance data.
    • The model's utility for longitudinal ordinal data is illustrated using repeated severity ratings from psychiatric patients.
    • The random-effects framework provides a comprehensive approach to handling complex dependencies in ordinal outcomes.

    Conclusions:

    • The random-effects ordinal regression model offers a powerful tool for analyzing complex ordinal data.
    • The methodology is applicable to both clustered and longitudinal study designs.
    • This approach enhances the statistical rigor and interpretability of findings in fields utilizing ordinal outcomes.