DOI QR코드

DOI QR Code

A Comparative Study on Factor Recovery of Principal Component Analysis and Common Factor Analysis

주성분분석과 공통요인분석에 대한 비교연구: 요인구조 복원 관점에서

  • Jung, Sunho (School of Management, Kyung Hee University) ;
  • Seo, Sangyun (School of Management, Kyung Hee University)
  • Received : 2013.08.23
  • Accepted : 2013.10.28
  • Published : 2013.12.31

Abstract

Common factor analysis and principal component analysis represent two technically distinctive approaches to exploratory factor analysis. Much of the psychometric literature recommends the use of common factor analysis instead of principal component analysis. Nonetheless, factor analysts use principal component analysis more frequently because they believe that principal component analysis could yield (relatively) less accurate estimates of factor loadings compared to common factor analysis but most often produce similar pattern of factor loadings, leading to essentially the same factor interpretations. A simulation study is conducted to evaluate the relative performance of these two approaches in terms of factor pattern recovery under different experimental conditions of sample size, overdetermination, and communality.The results show that principal component analysis performs better in factor recovery with small sample sizes (below 200). It was further shown that this tendency is more prominent when there are a small number of variables per factor. The present results are of practical use for factor analysts in the field of marketing and the social sciences.

본 연구에서는 시뮬레이션 방법을 사용해서 다양한 조건에서 주성분분석이 얼마나 잘 요인 구조를 복원할 수 있는지를 공통요인분석과 비교하여 체계적으로 평가하였다. 이 연구에서 요인 대 변수 비율, 공통성, 그리고 표본크기를 실험변수로 설정하였다. 주성분분석은 표본의 크기가 200개 이하인 경우 공통적으로 공통요인분석에 비해 더 우수한 요인구조의 복원력을 보여주었다. 특히, 요인 당 변수 수가 적은 경우, 주성분분석은 50개의 표본에서도 만족할 만한 수준의 요인복원능력을 보여주었다. 이와 더불어 공통성 수준 또한 낮은 경우 필요한 표본수는 100개로 늘어난다. 본 연구결과는 요인추출방법으로서 주성분분석의 선택의 근거를 제시하고 타당한 사용에 관한 가이드라인을 제시해 준다.

Keywords

References

  1. Acito, F. and Anderson, R. D. (1980). A monte carlo comparison of factor analytic methods, Journal of Marketing Research, 17, 228-236. https://doi.org/10.2307/3150933
  2. Bijmolt, T. H. A. and Van de V., M. (2012). Multiattribute perceptual mapping with idiosyncratic brand and attribute sets, Marketing Letters, 23, 585-601. https://doi.org/10.1007/s11002-012-9163-8
  3. Briggs, N. E. and MacCallum, R. C. (2003). Recovery of weak common factors by maximum likelihood and ordinary least squares estimation, Multivariate Behavioral Research, 38, 25-56. https://doi.org/10.1207/S15327906MBR3801_2
  4. Carroll, J. D. and Green, P. E. (1997). Psychometric methods in marketing research: Part 2, multidimensional scaling, Journal of Marketing Research, 34, 193-204. https://doi.org/10.2307/3151858
  5. Cohen, J. (1988). Statistical Power for the Behavioral Sciences, Hillsdale, Lawrence Erlbaum, NJ.
  6. Conway, J. M. and Huffcutt, A. I. (2003). A review and evaluation of exploratory factor analysis practices in organizational research, Organizational Research Methods, 6, 147-168. https://doi.org/10.1177/1094428103251541
  7. Costello, A. and Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis, Practical Assessment, Research and Evaluation, 10, 1-9.
  8. Gagne, P. and Hancock, G. R. (2006). Measurement model quality, sample size, and solution propriety in confirmatory factor models, Multivariate Behavioral Research, 41, 65-83. https://doi.org/10.1207/s15327906mbr4101_5
  9. Guilford, J. P. (1954). Psychometric Methods, McGraw Hill, New York.
  10. Hair, J. F., Black, W. C., Babin, B. J. and Anderson, R. E. (2009). Multivariate Data Analysis, Upper Saddle River, Prentice-Hall, NJ.
  11. Lorenzo-Seva, U. and ten Berge, J. M. F. (2006). Tucker's congruence coefficient as a meaningful index of factor similarity, Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 2, 57-64. https://doi.org/10.1027/1614-2241.2.2.57
  12. MacCallum, R. C., Widaman, K. F., Zhang, S. and Hong, S. (1999). Sample size in factor analysis, Psychological Methods, 4, 84-99. https://doi.org/10.1037/1082-989X.4.1.84
  13. MacCallum, R. C., Widaman, K. F., Preacher, K. and Hong, S. (2001). Sample size in factor analysis: The role of model error, Multivariate Behavioral Research, 36, 611-637. https://doi.org/10.1207/S15327906MBR3604_06
  14. 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, and Computers, 32, 396-402. https://doi.org/10.3758/BF03200807
  15. Paxton, P., Curran, P. J., Bollen, K., Kirby, J. and Chen, F. (2001). Monte Carlo Experiments: Design and implementation, Structural Equation Modeling, 8, 287-312. https://doi.org/10.1207/S15328007SEM0802_7
  16. Pennell, R. (1968). The influence of communality and N on the sampling distributions of factor loadings, Psychometrika, 33, 423-439. https://doi.org/10.1007/BF02290161
  17. Preacher, K. J. and MacCallum, R. C. (2002). Exploratory factor analysis in behavior genetics research: Factor recovery with small sample sizes, Behavior Genetics, 32, 153-161. https://doi.org/10.1023/A:1015210025234
  18. Rammstedt, B., Goldberg, L. R. and Borg, I. (2010). The measurement equivalence of big-five factor markers for persons with different levels of education, Journal of Research in Personality, 44, 53-61.
  19. Snook, S. C. and Gorsuch, R. L. (1989). Component analysis versus common factor analysis: A Monte Carlo study, Psychological Bulletin, 106, 148-154. https://doi.org/10.1037/0033-2909.106.1.148
  20. Tucker, L. R., Koopman, R. F. and Linn, R. L. (1969). Evaluation of factor analytic research procedures by means of simulated correlation matrices, Psychometrika, 34, 421-459. https://doi.org/10.1007/BF02290601
  21. Velicer, W. F. and Fava, J. L. (1998). Effects of variable and subject sampling on factor pattern recovery, Psychological Methods, 3, 231-251. https://doi.org/10.1037/1082-989X.3.2.231
  22. Velicer, W. F., Peacock, A. C. and Jackson, D. N. (1982). A comparison of component and factor patterns: A Monte Carlo approach, Multivariate Behavioral Research, 17, 371-388. https://doi.org/10.1207/s15327906mbr1703_5
  23. Velicer, W. F. and Jackson, D. N. (1990). Component analysis vs. Common factor analysis: Some issues in selecting an appropriate procedure, Multivariate Behavioral Research, 251, 1-28.
  24. Wijsman, R. A. (1959). Applications of a certain representation of the Wishart matrix, Annals of Mathematical Statistics, 30, 597-601. https://doi.org/10.1214/aoms/1177706276
  25. Witten, I. H., Frank, E. and Hall, M. A. (2011). Data Mining: Practical Machine Learning Tools and Techniques, Morgan Kaufmann, Burlington, MA.

Cited by

  1. Development and validation of the English writing strategy inventory vol.68, 2017, https://doi.org/10.1016/j.system.2017.06.014
  2. Stakeholder Management in Long-Term Complex Megaconstruction Projects: The Saemangeum Project vol.33, pp.4, 2017, https://doi.org/10.1061/(ASCE)ME.1943-5479.0000515