Fiducial Intervals for Variance Components in an Unbalanced Two-Component Normal Mixed Linear Model

Abstract

In this article we propose a new method for constructing confidence intervals for σα2,σϵ2, and the intraclass correlation ρ==σα2(σα2++σε2) in a two-component mixed-effects linear model. This method is based on an extension of R. A. Fisher's fiducial argument. We conducted a simulation study to compare the resulting interval estimates with other competing confidence interval procedures from the literature. Our results demonstrate that the proposed fiducial intervals have satisfactory performance in terms of coverage probability, as well as shorter average confidence interval lengths overall. We also prove that these fiducial intervals have asymptotically exact frequentist coverage probability. The computations for the proposed procedures are illustrated using real data examples.