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Regression Among Factor Scores

Published online by Cambridge University Press:  01 January 2025

Anders Skrondal  and
Petter Laake
Anders Skrondal*
Affiliation:
Department of Epidemiology, National Institute of Public Health, Oslo
Petter Laake
Affiliation:
Section of Medical Statistics, University of Oslo
*
Requests for reprints should be sent to Anders Skrondal, Department of Epidemiology, National Institute of Public Health, P.O.Box 4404 Nydalen, N-0403 Oslo, NORWAY. E-Mail: anders.skrondal@folkehelsa.no
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Abstract

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.

Keywords

regressionfactor scoresstructural equation modelslatent variablesfactor score regression

Information

Type
Articles
Information
Psychometrika , Volume 66 , Issue 4 , December 2001 , pp. 563 - 575
Copyright
Copyright © 2001 The Psychometric Society

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