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Variance components in the two-way nested model with incomplete nesting information.
Song R; Shulman SA
Technometrics 1997 Feb; 39(1):71-80
Estimation methods that used all of the data in a two way nested model, including data with missing nesting information, were examined. Nesting information was needed in the two way nesting model to separate the variance components from one another. In the two way nested model used, each observation was associated with a main group and a subgroup. Data completely missing subgroup nesting information were considered. In one simple analytical method, the data with missing nesting information was discarded and only the data with complete nesting information was used. However, such a technique reduced the two way nested model to a one way nested model. Thus, it was important to try to use the data with missing nesting information. Using an analysis of variance (ANOVA) procedure, the computable sums of squares from the data with missing nesting information were combined with the sums of squares from the data with complete nesting information. The sums of squares were combined using equal weights, weights that minimized the variances of the combined sums of squares, or weights that minimized the variances of resulting estimators. The unbiased estimators derived with different weights were compared by comparing their variances and covariances. The most stable estimates were determined using weights that minimized the variances of the resulting estimators. The above method was applied to data with missing nesting information obtained in the American Industrial Hygiene Association Asbestos Analyst Registry Program. The authors conclude that data with missing nesting information can be used in a two way nested model by computing sums of squares via the ANOVA method.
Mathematical-models; Quantitative-analysis; Statistical-analysis; Analytical-models; Analytical-methods; Information-systems; Laboratory-testing
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