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Data Analysis and Decision Support pp 113–121Cite as

ANOVA Models with Generalized Inverses

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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.

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Author information

Authors and Affiliations

  1. Institute of Advanced Studies, Stumpergasse 56, A-1060, Vienna, Austria

    Wolfgang Polasek

  2. Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, ACT, 0200, Australia

    Shuangzhe Liu

Authors
  1. Wolfgang Polasek
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  2. Shuangzhe Liu
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Editor information

Editors and Affiliations

  1. Institute of Business Administration and Economics, Brandenburg University of Technology Cottbus, Konrad-Wachsmann-Allee 1, 03046, Cottbus, Germany

    Daniel Baier (Chair of Marketing and Innovation Management) (Chair of Marketing and Innovation Management)

  2. Department of Business Administration and Economics, Bielefeld University, Universitätsstr. 25, 33615, Bielefeld, Germany

    Reinhold Decker (Chair of Marketing) (Chair of Marketing)

  3. Computer Based New Media Group (CGNM), Institute for Computer Science, University of Freiburg, Georges-Köhler-Allee 51, 79110, Freiburg, Germany

    Lars Schmidt-Thieme

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© 2005 Springer-Verlag Berlin · Heidelberg

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Polasek, W., Liu, S. (2005). ANOVA Models with Generalized Inverses. In: Baier, D., Decker, R., Schmidt-Thieme, L. (eds) Data Analysis and Decision Support. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-28397-8_14

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