Fiducial Inference in Linear Mixed-Effects Models.

Area of Science:

• Statistics
• Statistical Modeling

Background:

• Linear mixed-effects (LME) models are widely used in various scientific fields.
• Standard methods for inference in LME models can be complex, especially for small sample sizes or when dealing with variance components.

Purpose of the Study:

• To develop a novel fiducial inference framework for LME models.
• To reformulate the standard deviation of random effects as coefficients for unified inference.
• To provide a method suitable for small sample sizes and simultaneous parameter estimation.

Main Methods:

• Developed a novel framework for fiducial inference in LME models.
• Reformulated the standard deviation of random effects as coefficients.
• Derived the exact fiducial density as the equilibrium measure of a reversible Markov chain.
• Compared confidence intervals and variance inference with Bayesian and likelihood profiling methods.

Main Results:

• The fiducial density is equivalent in form to a Bayesian LME with a noninformative prior.
• The framework unifies the inference of random effects and other parameters simultaneously.
• The proposed method requires no additional tests for zero variance and is suitable for small sample sizes.
• Fiducial confidence intervals are comparable to Bayesian and likelihood profiling methods.
• Inference for the variance of random effects shows competitive power with the likelihood ratio test.

Conclusions:

• The novel fiducial inference framework provides a unified and efficient approach for LME models.
• This method is particularly advantageous for small sample sizes and complex variance structures.
• The fiducial approach offers a robust alternative to existing inference methods in LME modeling.