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Variance Components in the Two-Way Nested Model with Incomplete Nesting Information

Ruiguang Song and Stanley A. Shulman
Technometrics
Vol. 39, No. 1 (Feb., 1997), pp. 71-80
DOI: 10.2307/1270774
Stable URL: http://www.jstor.org/stable/1270774
Page Count: 10
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Variance Components in the Two-Way Nested Model with Incomplete Nesting Information
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Abstract

When part of the nesting information in a two-way nested model is missing, there has been no way to use all of the data in the analysis of variance components. Discarding the data with missing nesting information loses useful information, and in some circumstances, this approach cannot separate variance components from one another. To make use of the data with missing nesting information, computable sums of squares for the data with missing nesting information can be linearly combined with sums of squares for the data with complete nesting information. Prespecified weights are needed for the combination. Different estimates are obtained by using different weights. Because all of these estimators are unbiased, variances and covariances of these estimators are derived and used to compare these estimators. In addition, a simulation study is conducted to provide evidence for the reliability of the variances and covariances formulas. Finally, as an application, the proposed methods are applied to the analysis of a proficiency testing program.

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