Behavior Research Methods

, Volume 37, Issue 1, pp 48–58 | Cite as

Exploring item and higher order factor structure with the Schmid-Leiman solution: Syntax codes for SPSS and SAS

  • Hans -Georg WolffEmail author
  • Katja Preising


To ease the interpretation of higher order factor analysis, the direct relationships between variables and higher order factors may be calculated by the Schmid-Leiman solution (SLS; Schmid & Leiman, 1957). This simple transformation of higher order factor analysis orthogonalizes first-order and higher order factors and thereby allows the interpretation of the relative impact of factor levels on variables. The Schmid-Leiman solution may also be used to facilitate theorizing and scale development. The rationale for the procedure is presented, supplemented by syntax codes for SPSS and SAS, since the transformation is not part of most statistical programs. Syntax codes may also be downloaded from


Order Factor High Order Factor General Distress High Order Construct Lower Order Factor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Bi, J. (2002). Variance of d’ for the same-different method.Behavior Research Methods, Instruments, & Computers,34, 37–45.CrossRefGoogle Scholar
  2. Carroll, J. B. (1995). On methodology in the study of cognitive abilities.Multivariate Behavioral Research,30, 429–452.CrossRefGoogle Scholar
  3. Cattell, R. B. (1978).The scientific use of factor analysis. New York: Plenum.CrossRefGoogle Scholar
  4. Chen, R. (2003). An SAS/IML procedure for maximum likelihood factor analysis.Behavior Research Methods, Instruments, & Computers,35, 310–317.CrossRefGoogle Scholar
  5. Chernyshenko, O. S., Stark, S., &Chan, K. Y. (2001). Investigating the hierarchical factor structure of the fifth edition of the 16PF: An application of the Schmid-Leiman orthogonalization procedure.Educational & Psychological Measurement,61, 290–302.CrossRefGoogle Scholar
  6. Colom, R., Contreras, M. J., Botella, J., &Santacreu, J. (2001). Vehicles of spatial ability.Personality & Individual Differences,32, 903–912.CrossRefGoogle Scholar
  7. Comrey, A. L. (1988). Factor-analytic methods of scale development in personality and clinical psychology.Journal of Consulting & Clinical Psychology,56, 754–761.CrossRefGoogle Scholar
  8. Conn, S. R., &Rieke, M. L. (1994).The 16PF fifth edition technical manual. Champaign, IL: Institute for Personality & Ability Testing.Google Scholar
  9. Gorsuch, R. L. (1983).Factor analysis (2nd ed.). Hillsdale, NJ: Erlbaum.Google Scholar
  10. Gullion, C. M., &Rush, A. J. (1998). Toward a generalizable model of symptoms in major depressive disorder.Biological Psychiatry,44, 959–972.CrossRefGoogle Scholar
  11. Hayes, A. F. (1998). SPSS procedures for approximate randomization tests.Behavior Research Methods, Instruments, & Computers,30, 536–543.CrossRefGoogle Scholar
  12. Holzinger, K. J., &Swineford, F. (1937). The bi-factor method.Psychometrika,2, 41–54.CrossRefGoogle Scholar
  13. Johnson, W. L., &Johnson, A. M. (1995). Using SAS/PC for higher order factoring.Educational & Psychological Measurement,55, 429–434.CrossRefGoogle Scholar
  14. Loehlin, J. C. (1998).Latent variable models: An introduction to factor, path, and structural analysis (3rd ed.). Mahwah, NJ: Erlbaum.Google Scholar
  15. Luo, D., Petrill, S. A., &Thompson, L. A. (1994). An exploration of genetic g: Hierarchical factor analysis of cognitive data from the Western Reserve Twin Project.Intelligence,18, 335–347.CrossRefGoogle Scholar
  16. Moser, K., Preising, K., Göritz, A. S., &Paul, K. (2002).Steigende Informationsflut am Arbeitsplatz: Belastungsgünstiger Umgang mit elektronischen Medien (E-Mail, Internet) [Increasing information load in the workplace: Strain-balanced coping with the electronic media (e-mail, Internet)]. Bremerhaven: Wirtschaftsverlag, NW.Google Scholar
  17. O’Connor, B. P. (1999). Simple and flexible SAS and SPSS programs for analyzing lag-sequential categorical data.Behavior Research Methods, Instruments, & Computers,31, 718–726.CrossRefGoogle Scholar
  18. O’Connor, B. P. (2000). SPSS and SAS programs for determining the number of components using parallel analysis and Velicer’s MAP test.Behavior Research Methods, Instruments, & Computers,32, 396–402.CrossRefGoogle Scholar
  19. O’Connor, B. P. (n.d.).SPSS, SAS, and MATLAB programs for determining the number of components and factors using parallel analysis and Velicer’s MAP test. Retrieved December 12, 2003, from http://flash.≈boconno2/nfactors.htmlGoogle Scholar
  20. Petrill, S. A., Luo, D., Thompson, L. A., &Detterman, D. K. (1996). The independent prediction of general intelligence by elementary cognitive tasks: Genetic and environmental influences.Behavior Genetics,26, 135–147.CrossRefGoogle Scholar
  21. Schmid, J. (1957). The comparability of the bi-factor and second-order factor patterns.Journal of Experimental Education,25, 249–253.CrossRefGoogle Scholar
  22. Schmid, J., &Leiman, J. N. (1957). The development of hierarchical factor solutions.Psychometrika,22, 53–61.CrossRefGoogle Scholar
  23. Schneewind, K. A., &Graf, J. (1998).Der 16-Persönlichkeits-Faktoren-Test. Revidierte Fassung (16 PF-R) [The 16-Personality-Factor Test. Rev. Ed.]. Bern: Huber.Google Scholar
  24. SPSS Inc. (2002).SPSS 11.5 Syntax Reference Guide [Computer version, available with SPSS 11 software]. Chicago: Author.Google Scholar
  25. Steer, R. A., Clark, D. A., Beck, A. T., &Ranieri, W. F. (1995). Common and specific dimensions of self-reported anxiety and depression: A replication.Journal of Abnormal Psychology,104, 542–545.CrossRefGoogle Scholar
  26. Steer, R. A., Clark, D. A., Beck, A. T., &Ranieri, W. F. (1999). Common and specific dimensions of self-reported anxiety and depression: The BDI-II versus the BDI-IA.Behavior Research & Therapy,37, 183–190.CrossRefGoogle Scholar
  27. Yung, Y.-F., Thissen, D., &McLeod, L. D. (1999). On the relationship between the higher-order factor model and the hierarchical factor model.Psychometrika,64, 113–128.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2005

Authors and Affiliations

  1. 1.Lehrstuhl für Psychologieinsb. Wirtschafts- und SozialpsychologieNürnbergGermany

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