AUTHOR=Davis-Stober Clintin P. , Doignon Jean-Paul , Suck Reinhard 

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

JOURNAL=Frontiers in Psychology

VOLUME=6

YEAR=2015

URL=https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2015.01767

DOI=10.3389/fpsyg.2015.01767

ISSN=1664-1078

ABSTRACT=<p>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 (<xref ref-type="bibr" rid="B12">1987</xref>) 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 (<xref ref-type="bibr" rid="B6">1950</xref>).</p>