Addressing outliers in mixed-effects logistic regression: a more robust modeling approach

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Hierarchically structured bounded count data analysis presents challenges, particularly with outliers.
• Existing models like beta-binomial and binomial-logit-normal may lack robustness against data anomalies.
• Handling overdispersion and outliers is crucial for accurate statistical inference in such data.

Purpose of the Study:

• To introduce an outlier-robust Bayesian model for hierarchically structured bounded count data.
• To develop a model that incorporates a t-distributed latent variable for enhanced robustness.
• To provide a reliable measure of central tendency using a pseudo-median.

Main Methods:

• Bayesian framework utilizing logistic regression implemented in JAGS.
• Incorporation of a t-distributed latent variable to model overdispersion and outliers.
• Comparison with conventional models including beta-binomial, binomial-logit-normal, and standard binomial models.

Main Results:

• The proposed binomial-logit-t model demonstrates superior performance and robustness against outliers in simulations.
• Comparison statistics favored the new model over conventional approaches.
• The model effectively handles outliers, leading to more accurate parameter estimates.

Conclusions:

• The developed outlier-robust model provides a reliable and interpretable approach for analyzing complex count data.
• This methodology enhances data integrity and statistical accuracy in the presence of outliers.
• The model is practically demonstrated on a longitudinal medication adherence dataset.