Dépt. de Math./Statistique, Université de Moncton, Moncton, NB, E1A 3E9, Canada.
Psychometrika. 2011 Oct;76(4):550-63. doi: 10.1007/s11336-011-9226-4. Epub 2011 Sep 7.
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.
Maxbet 方法是对数据集的广义主成分分析，其中考虑了变量的分组结构。类似地，3 块[12,13]部分 Maxdiff 方法是协方差分析的推广，其中仅考虑块（1,2）和（1,3）之间的协方差。本文的目的是通过从涉及的多元特征值问题的完整解集选择最佳解，为 2 块 Maxbet 和 3 块[12,13]部分 Maxdiff 问题找到全局最大值。为此，我们将矩阵的特征多项式推广到两个特征多项式的系统，并通过 Sylvester 结果提供后者的完整解集。提供了示例。
