Alternative Confidence Intervals on Variance Components in a Simple Regression Model with a Balanced Two-Fold Nested Error Structure

In applications using a linear regression model with a balanced two-fold nested error structure, interest focuses on inferences concerning variability of the effects associated with the levels of nesting. This article proposes confidence intervals on the variance components associated with the primary and secondary levels in the model. In order to construct the confidence intervals we use a modified large sample method, generalized inference method, and Satterthwaite approximation. Computer simulation is performed to compare the proposed confidence intervals. A numerical example is provided to demonstrate the intervals.