ANOVA Models with Generalized Inverses

Wolfgang Polasek; Shuangzhe Liu

doi:10.1007/3-540-28397-8_14

ANOVA Models with Generalized Inverses

Wolfgang Polasek, Shuangzhe Liu

Information Systems

Research output: A Conference proceeding or a Chapter in Book › Chapter › peer-review

Abstract

The 2-way ANOVA model is analyzed with generalized matrix or ginverses. We derive the co-called OLS− and OLS+ estimators of the rank deficient ANOVA model. The new g-inverses lead to two simple effects in a two-way ANOVA model: column means and adjusted row means or vice versa: row means and adjusted column means. For the F- Test this parameterizations is invariant.

Original language	English
Title of host publication	Data Analysis and Decision Support
Editors	Daniel Baier, Reinhold Decker, Lars Schmidt-Thieme
Place of Publication	Germany
Publisher	Springer
Pages	113-121
Number of pages	9
Edition	1
ISBN (Electronic)	9783540283973
ISBN (Print)	9783540260073
DOIs	https://doi.org/10.1007/3-540-28397-8_14
Publication status	Published - 2006

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AB - The 2-way ANOVA model is analyzed with generalized matrix or ginverses. We derive the co-called OLS− and OLS+ estimators of the rank deficient ANOVA model. The new g-inverses lead to two simple effects in a two-way ANOVA model: column means and adjusted row means or vice versa: row means and adjusted column means. For the F- Test this parameterizations is invariant.

U2 - 10.1007/3-540-28397-8_14

DO - 10.1007/3-540-28397-8_14

M3 - Chapter

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A2 - Baier, Daniel

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A2 - Schmidt-Thieme, Lars

PB - Springer

CY - Germany

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ANOVA Models with Generalized Inverses

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