Fiducial Inference in Linear Mixed-Effects Models

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We develop a novel framework for fiducial inference in linear mixed-effects (LME) models, with the standard deviation of random effects reformulated as coefficients. The exact fiducial density is derived as the equilibrium measure of a reversible Markov chain over the parameter space. The density is equivalent in form to a Bayesian LME with noninformative prior, while the underlying fiducial structure adds new benefits to unify the inference of random effects and all other parameters in a neat and simultaneous way. Our fiducial LME needs no additional tests or statistics for zero variance and is more suitable for small sample sizes. In simulation and empirical analysis, our confidence intervals (CIs) are comparable to those based on Bayesian and likelihood profiling methods. And our inference for the variance of random effects has competitive power with the likelihood ratio test.