A class of generalized linear mixed models adjusted for marginal interpretability.

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Generalized estimating equations (GEE) provide marginal parameter estimates for correlated non-Gaussian data but lack formal models for prediction and fit assessment.
• Generalized linear mixed models (GLMMs) offer formal models but yield conditional parameter estimates, requiring approximations for marginal interpretation.
• Standard GLMMs present interpretational challenges and undesirable implications for marginal inference.

Purpose of the Study:

• To develop a class of marginally interpretable GLMMs that bridge the gap between marginal and conditional modeling approaches.
• To provide parameter estimates with direct marginal interpretation while retaining the desirable properties of mixed-effects models.
• To address computational challenges, particularly the evaluation of intractable integrals in logistic-normal mixed models.

Main Methods:

• Introduced a novel class of marginally interpretable GLMMs.
• Established the mathematical form of these models for common link functions.
• Developed an accurate and efficient method for evaluating the logistic-normal integral in logistic mixed-effects models.

Main Results:

• The proposed marginally interpretable GLMMs yield parameter estimates with a marginal interpretation.
• These models maintain the statistical advantages of conditionally specified models.
• The developed computational method enhances the practical application of these models, especially for logistic regression.

Conclusions:

• Marginally interpretable GLMMs offer a superior framework for analyzing correlated non-Gaussian data, providing both estimability and interpretability.
• The new approach resolves limitations of traditional GEE and standard GLMMs for prediction and model assessment.
• The efficient integral evaluation method facilitates the use of these advanced models in statistical practice.