Linear mixed models with flexible distributions of random effects for longitudinal data

Area of Science:

• Statistics
• Econometrics
• Biostatistics

Background:

• Linear mixed models commonly assume normally distributed random effects.
• This assumption can be unrealistic and mask crucial variations among individuals.
• Departures from normality can significantly impact model interpretation and findings.

Purpose of the Study:

• To relax the normality assumption in linear mixed models.
• To introduce a flexible method for capturing nonnormal random effects.
• To provide tools for selecting model complexity and detecting deviations from normality.

Main Methods:

• Utilized the seminonparametric (SNP) representation to approximate random effects density.
• The SNP approach offers flexibility, including normality as a special case.
• Inference is facilitated by a closed-form marginal likelihood, enabling standard optimization.

Main Results:

• Demonstrated that standard information criteria can effectively select the tuning parameter for the SNP model.
• Showcased the ability of the method to detect departures from normality.
• Successfully applied the approach to simulated data and real-world longitudinal data from the Framingham study.

Conclusions:

• The proposed seminonparametric approach offers a flexible alternative to standard normality assumptions in mixed models.
• This method allows for a more nuanced understanding of among-individual variation.
• The approach is practical for analyzing complex longitudinal data and identifying deviations from normality.