Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-02-04T11:11:10.556Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aptech Systems (1992). GAUSS: System and graphics manual. Maple Valley, WA: Author.Google Scholar
Bartholomew, D.J. (1981). Posterior analysis of the factor model. British Journal of Mathematical and Statistical Psychology, 34, 93–99.CrossRefGoogle Scholar
Bartlett, M.S. (1937). The statistical conception of mental factors. British Journal of Psychology, 28, 97–104.Google Scholar
Bartlett, M.S. (1938). Methods of estimating mental factors. Nature, 141, 609–610.Google Scholar
Bollen, K.A. (1989). Structural equations with latent variables. New York, NY: Wiley.CrossRefGoogle Scholar
Bollen, K.A., & Lennox, R. (1991). Conventional wisdom on measurement: A structural equation perspective. Psychological Bulletin, 110, 305–314.CrossRefGoogle Scholar
Dwyer, P.S. (1937). The determination of the factor loadings of a given test from the known factor loadings of other tests. Psychometrika, 2, 173–178.CrossRefGoogle Scholar
Furnam, A. (1994). Explaining health and illness: Lay beliefs on the nature of health. Personality and Individual Differences, 17, 455–466.CrossRefGoogle Scholar
Gorsuch, R.L. (1983). Factor analysis. Hillsdale, NJ: Erlbaum.Google Scholar
Hauser, R.M., & Goldberger, A.S. (1971). The treatment of unobservable variables in path analysis. In Costner, H.L. (Eds.), Sociological methodology 1971 (pp. 81–117). San Francisco, CA: Jossey-Bass.Google Scholar
Holzinger, K.J., & Swineford, F. (1939). A study in factor analysis: The stability of a bifactor solution. Chicago, IL: University of Chicago Press.Google Scholar
Iwata, S. (1992). Errors-in-variables regression using estimated latent variables. Econometric Reviews, 11, 195–200.CrossRefGoogle Scholar
Jöreskog, K.G. (1973). A general method for estimating a linear structural equation system. In Goldberger, A.S., & Duncan, O.D. (Eds.), Structural equation models in the social sciences (pp. 85–112). New York, NY: Seminar Press.Google Scholar
Jöreskog, K.G. (1977). Structural equation models in the social sciences: Specification, estimation and testing. In Krishnaiah, P.R. (Eds.), Applications of Statistics (pp. 265–286). Amsterdam: North-Holland.Google Scholar
Jöreskog, K.G., & Sörbom, D. (1989). LISREL7: A guide to the program and applications. Chicago, IL: SPSS.Google Scholar
Kim, J.-O., Mueller, C.W. (1978). Factor analysis: Statistical methods and practical issues. Beverly Hills, CA: Sage.CrossRefGoogle Scholar
Krijnen, W.P., Wansbeek, T.J., & ten Berge, J.M.F. (2001). Best linear predictors for factor scores. Communications in Statistics—Theory and Methods, 25, 3013–3025.CrossRefGoogle Scholar
Lastovicka, J.L., & Thamodaran, K. (1991). Common factor score estimates in multiple regression problems. Journal of Marketing Research, 28, 105–112.CrossRefGoogle Scholar
Lavik, N.J., Hauff, E., Skrondal, A., & Solberg, O. (2001). Mental disorder among refugees and the impact of persecution and exile: Some findings from an outpatient population. British Journal of Psychiatry, 169, 726–732.CrossRefGoogle Scholar
Lawley, D.N., & Maxwell, A.E. (1971). Factor analysis as a statistical method. London: Butterworths.Google Scholar
Mardia, K.V., Kent, J.T., & Bibby, J.M. (1979). Multivariate analysis. New York, NY: Academic.Google Scholar
McDonald, R.P., & Burr, E.J. (1967). A comparison of four methods of constructing factor scores. Psychometrika, 32, 381–401.CrossRefGoogle Scholar
Mira, M., Abraham, S., McNeil, D., Vizzard, J., Macaskill, P., Fraser, I., & Llewellyn-Jones, D. (1995). The interrelationship of premenstrual symptoms. Psychological Medicine, 25, 947–955.CrossRefGoogle ScholarPubMed
Rosen, L.N., Durand, D., Westhuis, D.J., & Teitelbaum, J.M. (1995). Marital adjustment of army spouses one year after Operation Desert Storm. Journal of Applied Social Psychology, 25, 677–692.CrossRefGoogle Scholar
Schoenberg, R., & Arminger, G. (1990). LINCS2.0. Kent, WA: RJS Software.Google Scholar
Skrondal, A. (2000). Design and analysis of Monte Carlo experiments: Attacking the conventional wisdom. Multivariate Behavioral Research, 35, 137–167.CrossRefGoogle ScholarPubMed
ten Berge, J.M.F. (1983). On Green's best linear composites with a specified structure, and oblique estimates of factor scores. Psychometrika, 48, 371–375.CrossRefGoogle Scholar
ten Berge, J.M.F., Krijnen, W.P., Wansbeek, T.J., & Shapiro, A. (1999). Some new results on correlation-preserving factor scores prediction methods. Linear Algebra and its Applications, 289, 311–318.CrossRefGoogle Scholar
Thomson, G.H. (1934). The meaning of i in the estimate of g. British Journal of Psychology, 25, 92–99.Google Scholar
Thurstone, L.L. (1935). The vectors of mind. Chicago, IL: University of Chicago Press.Google Scholar
Tucker, L.R. (1971). Relations of factor score estimates to their use. Psychometrika, 36, 427–436.CrossRefGoogle Scholar
Zellner, A. (1970). Estimation of regression relationships containing unobservable variables. International Economic Review, 11, 441–454.CrossRefGoogle Scholar