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The Effect of Additional Variables on Factor Indeterminacy in Models with a Single Common Factor

Published online by Cambridge University Press:  01 January 2025

Stanley A. Mulaik and
Roderick P. McDonald
Stanley A. Mulaik*
Affiliation:
Georgia Institute of Technology
Roderick P. McDonald
Affiliation:
The Ontario Institute for Studies in Education
*
Requests for reprints should be sent to Dr. Stanley A. Muliak, School of Psychology, Georgia Institute of Technology, Atlanta, GA 30332.
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Abstract

“Determinate” solutions for the indeterminate common factor of p variables satisfying the single common factor model are not unique. Therefore an infinite sequence of additional variables that conform jointly with the original p variables to the original single common factor model does not determine a unique solution for the indeterminate factor of the p variables (although the solution is unique for the factor of the infinite sequence). Other infinite sequences may be found to determine different solutions for the factor of the original p variables. The paper discusses a number of theorems about the effects of additional variables on factor indeterminacy in a model with a single common factor and draws conclusions from them for factor theory in general.

Keywords

factor scoresinterpretations of factorsdomain of variables

Information

Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 2 , June 1978, pp. 177 - 192
Copyright
Copyright © 1978 The Psychometric Society

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