Testing multiple variance components in linear mixed-effects models.

Area of Science:

• Statistics
• Biostatistics

Background:

• Testing zero variance components in linear mixed-effects (LME) models presents significant challenges due to boundary issues with standard statistical tests.
• Existing methods for multiple or subset variance component testing in LME models are often complex and difficult to apply.

Purpose of the Study:

• To introduce a novel, simple test statistic for variance components in LME models.
• To develop a permutation procedure for approximating the finite sample distribution of the proposed test.
• To provide a flexible testing framework applicable to multiple and subset variance components in LME models.

Main Methods:

• Developed a test statistic utilizing the variance least square estimator for variance components.
• Implemented a permutation procedure to estimate the finite sample distribution of the test statistic.
• Evaluated the test's performance using simulations, assessing Type I error rates and statistical power.

Main Results:

• The proposed test effectively handles testing of multiple variance components and any subset thereof in LME models.
• The method demonstrates robustness, not relying on specific distributions of random effects or errors beyond their mean and variance.
• Simulation results indicate favorable operating characteristics regarding Type I error control and power.

Conclusions:

• The variance least square-based test offers a practical and effective solution for complex variance component testing in LME models.
• This approach provides a distribution-independent method, enhancing its applicability across various LME model scenarios.
• The test was successfully applied to real-world data, demonstrating its utility in biostatistical research, such as analyzing metabolic associations.