Exploring Applicability of Target Rotation in Factor Analysis

목표회전은 사전에 설계된 요인부하행렬을 요인 회전에 적용시키는 요인분석 방법으로, 전통적인 탐색적 요인분석과는 다르게 연구자의 사전 가설을 요인 모형에 반영할 수 있다는 특징을 갖는다. 본 연구는 목표회전 요인분석을 소개하고, 이론에 따른 구조를 가질 것으로 기대되는 척도의 개발 및 타당화 연구에서 실질적으로 목표회전의 적용 가능성을 탐색하는 것을 목적으로 한다. 이에 따라 요인분석에서의 전통적인 요인 회전과 목표회전 방법의 역사적 발전 과정과 수리적 원리를 체계적으로 정리하고, 실제 자료를 이용한 분석 결과를 비교하여 목표회전의 유용성을 확인하고자 하였다. 가천대학교의 창의성 검사 개발 프로젝트에서 사용된 총 211명의 1차 예비검사 자료가 두 요인분석 방법에 의해 산출된 요인부하행렬을 비교하는 데 이용되었다. 분석 결과, 목표회전 방법은 전통적 방법에 비해 더 간명하고 해석가능성이 높은 요인구조를 확보할 수 있도록 해 주었으며, 사회과학 영역의 척도개발 및 타당화 상황에서도 유용성이 높음이 확인되었다.

keywords: 요인분석, 목표회전, 부분적으로 설정된 회전, 척도개발, 타당화, factor analysis, target rotation, partially specified target, scale development, validation

Abstract

Target rotation is one of the rotation criteria of factor analysis, which is designed to rotate the pattern matrix to a partially targeted matrix in advance. The factor analysis with targe rotation is different from the traditional exploratory factor analysis in that a priori substantive theory can be reflected to the factor analytic model. The purpose of the present study is to introduce the factor analysis with target rotation and to explore applicability of target rotation in practical situations, especially in the scale development. To achieve this goal, we explore the historical development and the mathematical principles of the two factor analysis methods, traditional exploratory factor analysis vs. factor analysis with target rotation, and compare the performances of the two methods. 211 participants from a pilot study of developing a creativity scale were used for comparing the pattern matrix solutions of each method. The results showed that the solution of the pattern matrix from the target rotation had a simpler structure and better construability than the traditional factor rotation method when data had complex underlying structure and large inter-construct correlations.

keywords: 요인분석, 목표회전, 부분적으로 설정된 회전, 척도개발, 타당화, factor analysis, target rotation, partially specified target, scale development, validation

참고문헌

김수영 (2016). 구조방정식 모형의 기본과 확장. 서울: 학지사.

이순묵, 윤창영, 이민형, 정선호 (2016). 탐색적요인분석: 어떻게 달라지나?. 한국심리학회지: 일반, 35(1), 217-255.

Abad, F. J., Garcia-Garzon, E., Garrido, L. E., & Barrada J. R. (2017). Iteration of partially specified target matrices: application to bi-factor case. Multivariate Behavioral Research, 52(4), 416-429.

Armstrong, J. S. (1967). Derivation of theory by means of factor analysis of Tom Swift and his electric factor analysis machine. The American Statistician, 21, 17-21.

Asparouhov, T., & Muthén, B. O. (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16, 397-438.

Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238-246.

Browne, M. W. (1972a). Oblique rotation to a partially specified target. British Journal of Mathematical and Statistical Psychology, 25, 207-212.

Browne, M. W. (1972b). Orthogonal rotation to a partially specified target. British Journal of Mathematical and Statistical Psychology, 25, 115-120.

Browne, M. W. (2001). An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research, 36, 111-150.

10.

Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In Bollen, K.A., & Long, J. S. (Eds.), Testing structural equation models(pp. 136-162). Newbury Park, CA: Sage.

11.

Comrey, A. L. (1978). Common methodological problems in factor analytic studies. Journal of Consulting and Clinical Psychology, 46, 648-659.

12.

Comrey, A. L., & Lee, H. B. (1992). A First Course in Factor Analysis(2nd edition). Hillsdale, NJ: Lawrence Erlbaum.

13.

Crawford, C. B., & Ferguson, G. A. (1970). A general rotation criterion and its use inorthogonal rotation. Psychometrika, 35, 321-332.

14.

Cudeck, R., & MacCallum, R. C. (2007). Factor analysis at 100: Historical depelopments and future directions. Mahwah, NJ: Erlbaum.

15.

DiStefano, C., & Motl, R. W. (2006). Further investigating method effects associated with negatively worded items on self-report surveys. Structural Equation Modeling: A Multidisciplinary Journal, 13(3), 440-464.

16.

Ford, J. K., MacCallum, R. C., & Tail, M. (1986). The applications of exploratory factor analysis in applied psychology: a critical review and analysis. Personnel Psychology, 39, 291-314.

17.

Gibson, W. A. (1959). Three multivariate models:factor analysis, latent structure analysis, and laten profile analysis. Psychometrika, 41, 385-404.

18.

Gorsuch, R. L. (1997). Exploratory factor analysis:Its role in item analysis. Journal of Personality Assessment, 68, 532-560.

19.

Gorsuch, R. L. (2015). Factor Analysis(classic edition). NY: Routledge.

20.

Grimm, K. J., Steele, J. S., Ram, N., & Nesselroade, J. R. (2013). Exploratory latent growth models in the structural equation modeling framework. Structural Equation Modeling: A Multidisciplinary Journal, 20(4), 568-591.

21.

Gruvaeus, G. T. (1970). A general approach to procrustes pattern rotation. Psychometrika, 34, 493-505.

22.

Guilford, J. P. (1956). The Structure of Intellect. Psychological Bulletin, 53, 267-293.

23.

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate Data Analysis(7th edition). NJ: Prentice Hall.

24.

Harman, H. H. (1967). Modern Factor Analysis. Chicago: The University of Chicago Press.

25.

Henson, R. K., & Roberts, J. K. (2006). Use of exploratory factor analysis in published research: Common errors and some comment on improved practice. Educational and Psychological Measurement, 66, 393-416.

26.

Horst, A. P. (1941). A non-graphical method for transforming an arbitrary factor matrix into a simple structure factor matrix. Psychometrika, 6, 79-99.

27.

Howe, W. G. (1955). Some contributions to factor analysis. Report No. ORNL-1919, Oak Ridge National Laboratory, Tennessee: Oak Ridge.

28.

Hu, L., & Bentler, P. (1999). Cutoff criteria for fit indices in covariance structure analysis:conventional criteria versus new alternatives. Structural Equation Modeling, 6, 1-55.

29.

Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183-202.

30.

Jöreskog, K. G., Sörbom, D., & Magidson, J. (1979). Advances in factor analysis and structural equation models. Cambridge, MA: Abt Books.

31.

Lawley, D. N., & Maxwell, A. E. (1964). Factor transformation methods. British Journal of Statistical Psychology, 17, 97-103.

32.

Marsh, H. W., Morin, A. J. S., Parker, P. D., & Kaur, G. (2014). Exploratory structural equation modeling: an integration of the best features of exploratory and confirmatory factor analysis. Annual Review of Clinical Psychology, 10, 95-110.

33.

McDonald, R. P. (1981). The dimensionality of tests and items. British Journal of Mathmatical and Statistical Psychology, 34, 100-117.

34.

McKeon, J. J. (1968). Rotation for maximum association between factors and tests. Unpublished manuscript, Biometric Laboratory, George Washington University.

35.

Moore, T. M., Reise, S. P., Depaoli, S., & Haviland, M. G. (2015). Iteration of partially specified target matrices: application in exploratory and bayesian confirmatory factor analysis. Multivariate Behavioral Research, 50(2), 149-161.

36.

Mulaik, S. A., & Millsap, R. E. (2000). Doing the four-step right. Structural Equation Modeling, 7, 36-73.

37.

Muthén, L., & Muthén, B. (1998-2019). Mplus (Version 7). Los Angeles, CA: Muthén &Muthén.

38.

Myers, N. D., Ahn, S., & Jin, Y. (2013). Rotation to a partially specified target matrix in exploratory factor analysis: How many targets?. Structural Equation Modeling, 20, 131-147.

39.

Myers, N. D., Jin, Y., Ahn, S., Celimli, S., & Zopluoglu, C. (2015). Rotation to a partially specified target matrix in exploratory factor analysis in practice. Behavior Research Methods, 47(2), 494-505.

40.

Nunnally, J. C. (1978). Psychometric theory(2nd Edition). New York: McGraw-Hil

41.

O’Leary-Kelly, S. W., & Vokurka, R. J. (1998). The empirical assessment of construct validity. Journal of Operations Management, 16(4), 387-405.

42.

Pett, M., Lackey, N., & Sullivan, J. (2003). Making sense of factor analysis. Thousand Oaks: Sage Publications, Inc.

43.

Reise, S. P., Moore, T., & Maydeu-Olivares, A. (2011). Target rotations and assessing the impact of model violations on the parameters of unidimensional item response theory models. Educational and Psychological Measurement, 71(4), 684-711.

44.

Spearman, C. (1904). “General intelligence,”objectively determined and measured. American Journal of Psychology, 15, 201-292.

45.

Tabachnick, B. G., & Fidell, L. S. (2007). Using Multivariate Statistics(5th edition). New York:Allyn and Bacon.

46.

Thurstone, L. L. (1947). Multiple Factor Analysis. Chicago: University of Chicago Press.

47.

Tucker, L. R. (1944). A semi-analytical method of factorial rotation to simple structure. Psychometrika, 9, 43-68.

48.

Waller, N. G., Tellegen, A., McDonald, R. P., & Lykken, D. T. (1996). Exploring nonlinear models in personality assessment: Development and preliminary validation of a negative emotionality scale. Journal of Personality, 64, 545-576.

49.

Yates, A. (1987). Multivariate Exploratory Data Analysis: A Perspective on Exploratory Factor Analysis. Albany: State University of New York Press.

50.

Zhang, X., Noor, R., & Savalei, V. (2016). Examining the effect of reverse worded items on the factor structure of the Need for Cognition scale. PloS ONE 11(6): e0157795.

바로가기메뉴

논문 상세

Vol.38 No.3

요인분석에서 목표회전의 적용 가능성 탐색

Exploring Applicability of Target Rotation in Factor Analysis

초록

Abstract

참고문헌

한국심리학회지: 일반