Inference in skew generalized t-link models for clustered binary outcome via a parameter-expanded EM algorithm

Area of Science:

• Statistics
• Biostatistics
• Social Sciences

Background:

• Binary generalized linear mixed models (GLMMs) are widely used for clustered binary data.
• Traditional GLMMs can produce biased estimates due to rigid distribution assumptions (logistic, normal).
• This bias can lead to incorrect conclusions in biological and social science research.

Purpose of the Study:

• To propose a novel approach using skew generalized t-distributions for analyzing clustered binary data.
• To develop a flexible skew generalized t-link model (SGTLM) framework.
• To evaluate the performance of the SGTLM against traditional GLMMs.

Main Methods:

• Utilized skew generalized t-distributions, which accommodate skewed and heavy-tailed data.
• Implemented the Expectation-Maximization algorithm accelerated by parameter-expansion for model fitting.
• Conducted simulation experiments varying sample size and data distribution to assess performance.
• Applied the SGTLM to respiratory infection data.

Main Results:

• The proposed SGTLM demonstrated superior performance in estimating population parameters and predicting random effects compared to traditional methods when assumptions were violated.
• Empirical standard errors and information criteria were effective in identifying spurious skewness and simplifying model selection.
• The SGTLM proved to be the most adequate model for the respiratory infection data analysis.

Conclusions:

• The SGTLM offers a robust and flexible alternative to traditional GLMMs, particularly for data violating standard distributional assumptions.
• The methodology enhances the reliability of statistical inference in biological and social sciences.
• Future research should explore integrating this flexible approach into other generalized linear mixed models for robust statistical modeling.