Ranking group-level outcomes with multilevel models: An information-theoretic measure of statistical separation

Area of Science:

• Social Epidemiology
• Biostatistics
• Information Theory

Background:

• Social epidemiologists use multilevel models to assess how contexts influence individual outcomes.
• Quantifying uncertainty in group-level outcome rankings from these models is challenging.
• Existing methods often qualitatively assess ranking stability.

Purpose of the Study:

• To introduce a novel, entropy-based metric, the separation statistic (S), for quantifying the stability of predicted group-level rankings.
• To provide a principled way to integrate group-level differences and statistical uncertainty.
• To enhance the interpretation of multilevel model predictions in social epidemiology.

Main Methods:

• Developed an entropy-based coefficient, the separation statistic (S), grounded in information theory.
• Applied the separation statistic to group-level predictions from Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA) models.
• Demonstrated compatibility with both Bayesian and frequentist estimation approaches.

Main Results:

• The separation statistic (S) quantifies the stability of predicted group-level rankings by integrating difference magnitude and uncertainty.
• The metric can be computed globally or locally, offering flexible application.
• Applied examples from intersectional MAIHDA illustrate the utility of the separation statistic.

Conclusions:

• The separation statistic (S) is a broadly applicable tool for describing certainty in relative group outcome ordering from multilevel models.
• It offers a quantitative measure for ranking uncertainty, complementing traditional analyses.
• The metric should be used descriptively, with careful consideration of its limitations in applied settings.