PLACE:  319 Snedecor

SPEAKER:
Kok-Leong Chiang
Iowa State University

TITLE:
A Simple General Method of Constructing Confidence Inervals For
Functions of Variance Components

ABSTRACT:

A variety of methods for constructing approximate confidence intervals for particular functions of variance components in balanced data random effects models have been proposed by various authors. These range from the popular Satterthwaite (1946) method to the latest Modified Large-Sample (MLS) method suggested by Gui, Graybill, Burdick, and Ting (1995). The monograph of Burdick and Graybill (1992) gives recommendations on the best existing methods. Some examples are the MLS methods of Graybill and Wang (1979, 1980), Wang and Graybill (1981), Arteaga, Jeyaratnam, and Graybill (1982), Leiva and Graybill
(1986), Ting, Burdick, Graybill, Jeyaratnam, and Lu (1990), and Ting, Burdick, and Graybill (1991). The methods in these provide intervals for particular functions of variance components in selected models, and usually involve complicated formulas.

We propose a simple general method for constructing confidence intervals for arbitrary functions of variance components in balanced data normal theory random effects models. The concept of "surrogate variables" is introduced as part of the description of the proposed method. The proposed method produces the commonly known exact (Chi Square and F distribution based) confidence intervals for expected mean squares and ratios of them. Moreover, it is extremely easy to implement and delivers both "equal-tail" and "shortest-length" confidence intervals for any parametric function of interest. (In contrast, only a small number of MLS methods have prescriptions for computing a sort of "shortest-length" interval.)

We demonstrate the effectiveness of the proposed method for estimating several commonly studied functions of variance components in various standard models, including the two-way random effects model (with and without interaction), the two-fold nested random effects model and the three-factor cross-classification random effects model. We show that the proposed intervals easily maintain the nominal confidence level and have average interval lengths that are comparable to or better than those of the best existing methods. Moreover, we show that in a particular application, the standard MLS method of Gui et al. (1995) can be
extremely liberal, while the proposed method easily maintains the nominal confidence level.
 

COFFEE: 3:45 p.m., 104 Snedecor