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Picture of all Solutions of Successive 2-Block Maxbet Problems

Published online by Cambridge University Press:  01 January 2025

Vartan Choulakian
Vartan Choulakian*
Affiliation:
Université de Moncton
*
Requests for reprints should be sent to Vartan Choulakian, Dépt. de Math./Statistique, Université de Moncton, Moncton, NB E1A 3E9, Canada. E-mail: vartan.choulakian@umoncton.ca
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Abstract

The Maxbet method is a generalized principal components analysis of a data set, where the group structure of the variables is taken into account. Similarly, 3-block[12,13] partial Maxdiff method is a generalization of covariance analysis, where only the covariances between blocks (1, 2) and (1, 3) are taken into account. The aim of this paper is to give the global maximum for the 2-block Maxbet and 3-block[12,13] partial Maxdiff problems by picking the best solution from the complete solution set for the multivariate eigenvalue problem involved. To do this, we generalize the characteristic polynomial of a matrix to a system of two characteristic polynomials, and provide the complete solution set of the latter via Sylvester resultants. Examples are provided.

Keywords

principal components analysiscentroid methodMaxbetMaxdiffmulti-block methodSylvester resultantGröbner basesalgebraic statistics
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 4 , October 2011 , pp. 550 - 563
Copyright
Copyright © 2011 The Psychometric Society

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