OPTIMIZED CONFIDENCE INTERVALS ON THE VARIANCE COMPONENTS IN A TWO-FACTOR MODEL WITH A COVARIATE

A two-factor model with a covariate is useful for reducing large error variances that a two-factor model might have. In applications using the two-factor model with a covariate, interest often focuses on inferences concerning variability of the effects in the model. This article proposes confidence intervals on total variance and the ratio of random effects variance to total variance in the model. In order to construct the confidence intervals we use a modified large sample method and generalized inference concept. Computer simulation is performed to compare the proposed confidence intervals. A numerical example is provided to demonstrate the proposed intervals.