Measuring the source and magnitude of components of variation has important
applications in industrial, environmental and biological studies. This thesis considers
the problem of constructing confidence intervals for variance components in Gaussian
mixed linear models. A number of methods based on the usual ANOVA mean squares
have been proposed for constructing confidence intervals for variance components in
balanced mixed models. Some authors have suggested extending balanced model
procedures to unbalanced models by replacing the ANOVA mean squares with mean
squares from an unweighted means ANOVA. However, the unweighted means
ANOVA is only defined for a few specific mixed models. In Chapter 2 we define a
generalization of the unweighted means ANOVA for the three variance component
mixed linear model and illustrate how the mean squares from this ANOVA may be used
to construct confidence intervals for variance components. Computer simulations
indicate that the proposed procedure gives intervals that are generally consistent with the
stated confidence level, except in the case of extremely unbalanced designs. A set of
statistics that can be used as an alternative to the generalized unweighted mean squares
is developed in Chapter 3. The intervals constructed with these statistics have better
coverage probability and are often narrower than the intervals constructed with the
generalized unweighted mean squares. / Graduation date: 1998
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/33883 |
| Date | 08 May 1998 |
| Creators | Purdy, Kathleen G. |
| Contributors | Seely, Justus F. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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