CONFIDENCE-INTERVALS ON VARIANCE-COMPONENTS IN REGRESSION-MODELS WITH BALANCED (Q-1)-FOLD NESTED ERROR STRUCTURE

Multi-stage cluster designs provide data that possess a nested structure. The variability of the effects associated with the levels of nesting can be described using a variance component model. Constructing confidence intervals on variance components is the problem considered in this paper. Specifically, confidence intervals are proposed for variance components in a regression model with balanced nested error structure. A method proposed by Ting, Burdick, Graybill, Jeyaratnam, and Lu (1990) is used to: construct the confidence intervals on the variance components. This method requires a set of jointly independent chi-squared random variables. A set of quadratic forms that meets this requirement for the regression model with balanced nested error structure is derived in this paper. The proposed confidence intervals are compared using computer simulation with intervals based on the restricted maximum likelihood (REML) estimators of the variance components.