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Smoothing analysis of variance for general designs and partitioning degrees of freedom in hierarchical and other richly-parameterized models.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Smoothing analysis of variance for general designs and partitioning degrees of freedom in hierarchical and other richly-parameterized models./
Author:	Cui, Yue.
Description:	117 p.
Notes:	Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0034.
Contained By:	Dissertation Abstracts International69-01B.
標題:	Biology, Biostatistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoeng/servlet/advanced?query=3299409
ISBN:	9780549436539

Smoothing analysis of variance for general designs and partitioning degrees of freedom in hierarchical and other richly-parameterized models.
Cui, Yue.

Smoothing analysis of variance for general designs and partitioning degrees of freedom in hierarchical and other richly-parameterized models. - 117 p.

Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0034.

Thesis (Ph.D.)--University of Minnesota, 2008.

Hodges et al (2007, henceforth HCSC) developed a Bayesian method called smoothed analysis of variance (ANOVA) as an alternative to ordinary ANOVA. An extensive simulation study in HCSC (Chapter 2 of this thesis) shows advantages of smoothed ANOVA over non-smoothed ANOVA if some interations are actually absent. They used a specific notion of degree of freedom to describe the extent of smoothing in the fitted values and to specify priors on smoothing parameters. However, they considered smoothing only for balanced, single-error-term ANOVAs. To extend smoothed ANOVA to more general designs, Chapter 3 of this thesis reformulates the notion of degree of freedom used in HCSC to decompose a fit's total degrees of freedom into effect-specific degree of freedom for arbitrary normal-error linear hierarchial models, including general ANOVA designs. The new conception of degrees of freedom arises as the ratio of the modeled variance matrix to the total variance matrix. Applications show how to use this new formulation to characterize the relative complexity of different parts of a model (e.g., spatial clustering vs. heterogeneity). Chapter 4 generalizes smoothed ANOVA to general designs, possibly unbalanced or with multiple error terms. Although a Bayesian method, a smoothed ANOVA procedure produces a table like the standard ANOVA table with degrees of freedom and sums of squares. The preliminary data analysis of a large 2-arm multicenter clinical trial with many predictors shows how to use smoothed ANOVA for estimating patient-specific effects, and elaboration of subgroup analysis.

ISBN: 9780549436539Subjects--Topical Terms:

1018416
Biology, Biostatistics.

Smoothing analysis of variance for general designs and partitioning degrees of freedom in hierarchical and other richly-parameterized models.
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502 $a Thesis (Ph.D.)--University of Minnesota, 2008.
520 $a Hodges et al (2007, henceforth HCSC) developed a Bayesian method called smoothed analysis of variance (ANOVA) as an alternative to ordinary ANOVA. An extensive simulation study in HCSC (Chapter 2 of this thesis) shows advantages of smoothed ANOVA over non-smoothed ANOVA if some interations are actually absent. They used a specific notion of degree of freedom to describe the extent of smoothing in the fitted values and to specify priors on smoothing parameters. However, they considered smoothing only for balanced, single-error-term ANOVAs. To extend smoothed ANOVA to more general designs, Chapter 3 of this thesis reformulates the notion of degree of freedom used in HCSC to decompose a fit's total degrees of freedom into effect-specific degree of freedom for arbitrary normal-error linear hierarchial models, including general ANOVA designs. The new conception of degrees of freedom arises as the ratio of the modeled variance matrix to the total variance matrix. Applications show how to use this new formulation to characterize the relative complexity of different parts of a model (e.g., spatial clustering vs. heterogeneity). Chapter 4 generalizes smoothed ANOVA to general designs, possibly unbalanced or with multiple error terms. Although a Bayesian method, a smoothed ANOVA procedure produces a table like the standard ANOVA table with degrees of freedom and sums of squares. The preliminary data analysis of a large 2-arm multicenter clinical trial with many predictors shows how to use smoothed ANOVA for estimating patient-specific effects, and elaboration of subgroup analysis.
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