A Note on the Eigensystem of the Covariance Matrix of Dichotomous Guttman Items

被引：2

作者：

Davis-Stober, Clintin P. ^{[1
]}

Doignon, Jean-Paul ^{[2
]}

Suck, Reinhard ^{[3
]}

机构：

[1] Univ Missouri, Dept Psychol Sci, Columbia, MO 65211 USA

[2] Univ Libre Bruxelles, Dept Math, Brussels, Belgium

[3] Univ Osnabruck, Osnabruck, Germany

来源：

FRONTIERS IN PSYCHOLOGY | 2015年 / 6卷

基金：

美国国家科学基金会;

关键词：

Guttman scale; dichotomous items; Rasch model; principal component analysis; eigenvalues; eigenvectors; TOEPLITZ MATRICES; EIGENVALUES; INVERSES;

D O I：

10.3389/fpsyg.2015.01767

中图分类号：

B84 [心理学];

学科分类号：

04 ; 0402 ;

摘要：

We consider the covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick (1987) for the correlation matrix under the same uniformity conditions. We provide an explanation for certain properties of principal components under Guttman scalability which have been first reported by Guttman (1950).

引用

页数：6

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