A Review of Higher-Order Factor Analysis Interpretation Strategies

Abstract

The purpose of the present paper was to summarize exploratory second and third-order factor analyses and explain interpretation strategies for the higher-order factors, specifically, Gorsuch’s product matrix, the Schmid and Leiman solution, and Thompson’s orthogonally rotated product matrix solution. Exploratory factor analysis is a multivariate technique to reveal information about latent constructs from the measured variables. When researchers choose an oblique rotation, they believe either that their factors are correlated or the best solution will result from an oblique rotation. Whenever primary factors are correlated, extracting higher-order factors from an inter-factor correlation matrix is vitally important to understand data from a different perspective. The SAS syntax is provided along with heuristic datasets to assist interested researchers in exploring the techniques. Advantages of each method was discussed.

Keywords

• Schmid Leiman solution, higher order factors, product matrix, triple product matrix

Yüksek Dereceden Faktör Analizi Yorumlama Tekniklerinin İncelenmesi

Abstract

Bu çalışmada, ikinci ve üçüncü dereceden faktör analizi özetlenip yorumlama teknikleri incelendi. Özellikle Gorsuch’un çarpım matrisi, Schmid ve Leiman çözümü ve Thompson’un dikey döndürülmüş çarpım matrisi incelendi. Keşif amaçlı faktör analizi çok degişkenli bir istatistiksel teknik olup, gizil durumdaki faktörleri ölçülen değişkenlerden ortaya çıkarmayı amaç edinir. Araştırmacılar eğik olarak döndürülmüş stratejiyi seçtiklerinde, faktörler arasında bir ilişki olduğuna veya en iyi çözümün eğik olarak döndürülmüş stratejiden elde edileceğini düşünürler. Birinci dereceden elde edilen faktörler birbirleriyle ilişkili olduğunda, bu foktörlerin oluşturduğu korrelasyon matrisi ikinci dereceden faktörleri elde etmede kullanılır ve bu elde edilen ikinci dereceden faktörler veriye farklı açılardan bakmakta oldukça önemli bir yer tutar. Çalısmanın anlaşılır olması için iki farklı örnek SAS kodları ile birlikte verildi. Her stratejinin avantajları tartışıldı

Keywords

• Schmid Leiman çözümü, yüksek dereceden faktörler, çarpım matris, üçlü çarpım matris

References

1. Borrello, G. M., & Thompson, B. (1990). An hierarchical analysis of the Hendrick-Hendrick measure of Lee’s typology of love. Journal of Social Behavior and Personality, 5, 327-342. Retrieved from http://search.proquest.com/docview/617883421?accountid=7082
2. Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1, 245-276. doi:10.1207/s15327906mbr0102_10
3. Cook, C., Heath, F., & Thompson, B. (2001). Users’ hierarchical perspectives on library service quality: A “LibQUAL+TM” study. College and Research Libraries, 62, 147-153. Retrieved from http://crl.acrl.org/content/62/2/147.full.pdf
4. Cook, C., & Thompson, B. (2000). Higher-order factor analytic perspectives on users’ perceptions of library service quality. Library Information Science Research, 22, 393-404. doi:10.1016/S0740-8188(00)00052-9
5. Gorsuch, R. L. (1983). Factor analysis (2nd ed.). Hillsdale, NJ: Erlbaum.
6. Henson, R., Capraro, R. M., & Capraro, M. M. (2004). Reporting practice and use of exploratory factor analysis in educational research journals: Errors and explanations. Research in the Schools, 11(2), 61-72. Retrieved from http://unt.edu/rss/class/Jon/MiscDocs/2004HensonCapraroCapraro.pdf
7. Holzinger, K. J., & Swineford, F. (1939). A study in factor analysis: The stability of a bi-factor solution. Supplementary Educational Monographs, No. 48, Chicago, IL.: The University of Chicago.
8. Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrica, 30, 179-185. doi:10.1007/BF02289447

9. Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20, 141-151. doi:10.1177/001316446002000116
10. Schmid, J., & Leiman, J. (1957). The development of hierarchical factor solutions. Psychometrica, 22, 53-61. doi:10.1007/BF02289209
11. Spearman, C. (1904). "General Intelligence," Objectively Determined and Measured. The American Journal of Psychology, 15(2), 201-292. doi:10.2307/1412107
12. Thompson, B. (1990). SECONDOR: A program that computes a second-order principal components analysis and various interpretation aids. Educational and Psychological Measurement, 50, 575-580. doi:10.1177/0013164490503011
13. Thompson, B. (1984). Canonical correlation analysis: Uses and interpretation. Newbury Park, CA: Sage.
14. Thompson, B. (2004). Exploratory and confirmatory factor analysis. Washington, DC: American Psychological Association.
15. Thompson, B., Wasserman, J. D., & Matula, K. (1996). The factor structure of the behavior rating scale of the Bayley Scales of Infant Development-II. Educational and Psychological Measurement, 56, 460-474. doi:10.1177/0013164496056003008
16. Thurstone, L. L. (1947). Multiple factor analysis. Chicago, IL: University of Chicago Press.