The rank of reduced dispersion matrices
type: Item
instance of: scholarly article
title: The rank of reduced dispersion matrices
zbMATH Open document ID: 0615.62069
DOI: 10.1007/BF02293960
author: Paul A. Bekker
author: Jan De Leeuw
published in: Psychometrika
publication date: 1987-01-01T00:00:00Z
review text: Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements. Psychometricians concentrate on cases in which low rank can be attained, preferably rank one, the Spearman case. Econometricians concentrate on cases in which the rank cannot be reduced below the number of variables minus one, the Frisch case. In this paper we give an extensive historical discussion of both fields, we prove the two key results in a more satisfactory and uniform way, we point out various small errors and misunderstandings, and we present a methodological comparison of factor analysis and regression on the basis of our results.
Mathematics Subject Classification ID: 62H25
Mathematics Subject Classification ID: 62P20
Mathematics Subject Classification ID: 62H99
zbMATH DE Number: 3996896
zbMATH Keywords: structural regression
zbMATH Keywords: errors in variables
zbMATH Keywords: Spearman model
zbMATH Keywords: Frisch model
zbMATH Keywords: Ledermann bound
zbMATH Keywords: factor analysis
zbMATH Keywords: rank of dispersion matrices
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3996896