Statistical significance in high-dimensional linear mixed models.

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• High-dimensional linear mixed effect models are crucial for analyzing complex, correlated data, such as repeated measurements from multiple subjects.
• Existing methods often struggle with large numbers of fixed effects (p) relative to the number of subjects (M), especially when random effects (q) are few.
• Inference in these models is challenging due to the interplay of fixed and random effects and high dimensionality.

Purpose of the Study:

• To develop a novel inferential framework for high-dimensional linear mixed effect models.
• To extend de-biasing techniques for penalized estimators to address the complexities of mixed effect models.
• To provide asymptotically valid confidence intervals for model parameters in high-dimensional settings.

Main Methods:

• The proposed framework adapts de-biasing strategies for penalized estimators, building upon existing work for high-dimensional linear models.
• A 'naive' ridge estimator is corrected to achieve asymptotically valid inference.
• Theoretical results are supported by numerical experiments and a practical case study.

Main Results:

• The developed method provides asymptotically valid confidence intervals for parameters in high-dimensional linear mixed effect models.
• Numerical experiments demonstrate superior performance compared to methods that ignore random effects-induced correlations.
• The framework's practical utility is shown on a riboflavin production dataset with group structure.

Conclusions:

• The proposed inferential framework offers a robust solution for high-dimensional linear mixed effect models.
• Accounting for correlations induced by random effects is critical for accurate inference.
• The method is applicable to real-world biological and industrial datasets with complex structures.