Faktör Sayısının Belirlenmesinde MAP Testi, Paralel Analiz, K1 ve Yamaç Birikinti Grafiği Yöntemlerinin Karşılaştırılması

Abstract

Bu araştırmada faktör sayısına karar vermede kullanılan; K1, Yamaç Birikinti grafiği, Paralel Analiz ve MAP testi yöntemleri ile elde edilen faktör sayılarının, yine faktör sayısı belirlemedeki etkililiklerinden dolayı, farklı örneklem büyüklüğü ve madde sayısı koşulları altında karşılaştırılması amaçlanmıştır. Analiz için kullanılacak veriler, simülasyon çalışması ile elde edilmiştir. K1 yöntemi ve Yamaç Birikinti grafiğine ilişkin analizler SPSS yardımıyla yapılmıştır. MAP testi ve Paralel Analiz ise R yazılımındaki {psych} paketindeki mevcut komutlardan faydalanılarak yapılmıştır. Bu çalışma kapsamında yapılan incelemeler; Paralel Analiz ve MAP testi yöntemlerinin faktör sayısını belirlemede birbiri ile tutarlı sonuçlar ürettiğini göstermiştir. Ancak, K1 ve Yamaç Birikinti grafiği yöntemlerinin ise diğer yöntemlere göre daha fazla sayıda faktör belirleme eğiliminde olduğu ortaya çıkmıştır. Araştırmacılara, açımlayıcı faktör analizinde faktör sayısını belirleme noktasında, K1 ve Yamaç Birikinti grafiği sonuçlarına ek olarak Paralel Analiz ve MAP testi yöntemlerini de uygulamaları ve sonuçları birlikte değerlendirmeleri önerilebilir. Bu yolla, psikometrik ölçüm sürecinin daha rasyonel olabileceği kanaatine varılmıştır

Keywords

• K1
• MAP Testi
• Paralel Analiz
• Yamaç Birikinti Grafiği
• Yapı Geçerliği

The Comparison of MAP Test, Parallel Analysis, K1 and Scree-Plot Methods in Terms of Assigning Factor Numbers

Abstract

This research investigated K1, Scree-Plot, Parallel Analysis and MAP tests, comparatively. To make a robust decision, these methods were compared with each other at different sample size and item numbers. The data which will be used for this research was derived from a simulation study. K1 methods and Scree-plot graphic were produced via SPSS. MAP test and Parallel Analysis were done by using R software {psych}. According to the findings of this research, Parallel Analysis and MAP test have consistent results in terms of assigning factor numbers. In other words, the findings of Parallel Analysis are similiar to MAP test in terms of assigning factor numbers. On the other hand, K1 and Scree-Plot graphic methods produced more factor numbers than Parallel Analysis and MAP test had. It is suggested to researchers that Parallel Analysis and MAP test should be used to confirm the findings of the K1 and the Scree-Plot methods. By this way, the robustness of a psychometric study can be reinforced

Keywords

• K1
• Map Test
• Parallel Analysis
• Scree-Plot Graphic
• Construct Validity

References

1. Anastasi, A. (1968). Psychological testin .London: The Macmillian Company, New York CollierMacmillan Limited.
2. Atılgan, H., Kan, A. ve Doğan N. (2006). Eğitimde ölçme ve değerlendirme. Ankara: Anı Yayıncılık.
3. Baykul, Y. (2000). Eğitimde ve psikolojide ölçme. Ankara: ÖSYM Yayınları. Beauducel A. (2001). Problems with paralel analysis in data sets with oblique simple structure. Methods of Psychological Research Online, 6(2), 141-157. , Cattell, R. B. (1978). The scientific use of factor analysis in behavioral and life sciences. New York: Plenum.
4. Cliff, N. (1988). The eigenvalues-greater-than-one rule and the reliability of components. Psychological Bulletin, 103(2), 276-279.
5. Crawford, A. V.,Green, B. S., Levy, R., Lo, W. J., Scott, L.,… Svetina, D. (2010). Evaluation of paralel analysis methods for determining the number of factors. Educational and Psychological Measurements, 70(6), 885-901.
6. Crawford, C. B. & Koopman, P. (1979). Inter-rater reliability of scree test and mean square ratio test of number of factors. Perceptual & Motor Skills, 49, 223-226
7. Crocker, L., & Algina, J. (1986) Introduction to classical and modern test theory. Harcourt Brace Jovanovich College Publishers: Philadelphia.
8. Cronbach, LJ. (I 990). Essentials of psychological testing. New York: HarperCoIIins.

9. Comrey, A. L. & Lee, H. B. (1992). A firstcourse in factor analysis. Hillsdale, NJ: Lawrence Erlbaum. Comrey, A. L., & Lee, H. B.(1973). A first course in factor analysis. New York: Academic Press.
10. Çokluk, Ö., Şekercioğlu, G. ve Büyüköztürk, Ş. (2010). Sosyal bilimler için çok değişkenli istatistik SPSS ve Lisrel uygulamaları. Ankara: Pegem Akademi.
11. Dancey C. & Reidy J. (2004). Statistics without maths for psychology: Using SPSS for Windows. London: Prentice Hall.
12. Dinno, A. (2009). Exploring the sensitivity of Horn’s paralel analysis to the distributional form of random data. Multivariate Behavioral Research, 44, 362-388.
13. Dinno, A. (2010). Gently clarifying the application of Horn’s paralel analysis to principal component analysis versus factor analysis. http://doyenne.com/Software/files/PA_for_PCA_vs_FA.pdf
14. Erkuş A. (2003). Psikometri üzerine yazılar. Ankara: Türk Psikologlar Derneği Yayınları.
15. Fabrigar, L. R.,Wegener, D. T., MacCallum, R. C. & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272-299.
16. Fava, J. L. & Velicer, W. F. (1992). The effects of over extraction on factor and component analysis. Multivariate Behavioral Research, 27, 387-415.
17. Floyd, F. J. & Widaman, K. F. (1995). Factor analysis in the development and refinement of clinical assessment in struments. Psychological Assessment, 7(3), 286-299.
18. Ford, J. K., MacCallum, R. C. & Tait, M. (1986). The applications of exploratory factor analysis in applied psychology: A critical review and analysis. Personnel Psychology, 39, 291-314.
19. Garrido, L. E.,Abad, F. J. & Ponsoda, V. (2011). Performance of Velicer‟s minimum average partial factor retention method with categorical variables. Educationaland Psychological Measurements, 71(6), 551-570.
20. Gorsuch, R. L. (1983). Factor Analysis. Philadelphia: Saunders. Gorsuch, R. L. (1997). Exploratory factor analysis: Its role in item analysis. Journal of Personality Assessment, 68(3), 532-560.
21. Harman, H.H. (1967). Modern Factor Analysis. Chicago. The University of Chicago Press.
22. Hayton, J. C.,Allen, D. G & Scarpello, V. (2004). Factor retention decisions in exploratory factor analysis: A tutorial on paralel analysis. Organizational Research Methods, 7(2), 191-205.
23. 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(3), 393-416.
24. Humphreys, L. G & Montanelli, R. G. Jr. (1975). An investigation of the paralel analysis criterion for determining the number of common factors. Multivariate Behavioral Research, 10, 193- 205.
25. Humphreys, L. G. & Ilgen, D. (1969). Note on a criterion for the number of common factors. Educationaland Psychological Measurement, 29, 571-578
26. Hogarty, K. Y.,Hines, C. V., Kromrey, J. D., Ferron, J. M. & Mumford, K. R. (2005). The quality of factor solutions in exploratory factor analysis: The influence of sample size, communality and over determination. Educationaland Psychological Measurement, 65(2), 202-226.
27. Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrica, 30(2), 179-185.
28. Kaiser, H. F. (1960). The applications of electronic computer to factor analysis. Educationaland Psychological Measurement, 20, 141-151.
29. Kline, P. (1994). An easy guide to factor analysis. New York: Routledge. Ledesma, D. R. & Mora, P. V. (2007). Determining the number of factors to retain in EFA: An easy-to-use computer program for carrying out paralel analysis. Practica Assessment, Research and Evaluation, 12 (2).
30. Lee, H. B. & Comrey, A. L. (1979). Distortions in a commonly used factor analytic procedure. Multivariate Behavioral Research, 14(3),301-321
31. Linn, R. L. (1968). A Monte Carlo approach to the number of factor problem. Psychometrica, 33, 37-71.
32. Liu, Y.,Zumbo, B. D. & Wu, A. D. (2011). A demonstration of impact of outliers on the decisions about the number of factors in exploratory factor analysis. Educational and Psychological Measurement.
33. MacCallum, R.C.,Widaman, K. F., Zhang,S. & Hong, S. (1999). Sample size in factor analysis. Psychological Methods, 4(1), 84-99.
34. MacCallum, R. C., Widaman, K. F., Preacher, K. J. & Hong, S. (2001). Sample size in factor analysis: The role of model error. Multivariate Behavioral Research, 36(4), 611-637.
35. Murphy, K. R. & Davidshofer, C. O. (2001). Psychological testing. New Jersey: Prentice Hall.
36. Nunnally, J. C. & Bernstein, I. H. (1994) Psychometrictheory. New York, NY: McGraw-Hill, Inc.
37. O’Connor, B. P. (2000). SPSS and SAS programs for determining the number of components using paralel analysis and Velicer’s) MAP test. Behavior Research Methods, Instrumentsand Computers, 32(3), 396-402.
38. Osborne, J. W. & Anna B. C. (2004). Sample size and subject to item ratio in principal components analysis. Practical Assessment, Research & Evaluation, 9(11).
39. Osborne, J. W. & Anna B. C. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research & Evaluation, 10(7).
40. Pedhazur, E. & Schmelkin, L. P. (1991). Measurement, design and analysis: An in the grated approach.
41. Revelle, W. & Rocklin, T. (1979). Very simple structure: An alternative procedure for estimating the optimal number of interpretable factors. Multivariate Behavioral Research, 14(3), 403- 414
42. Revelle, W. (2007). Determining the number of factors: the example of the NEO-PI-R. http://personality-project.org/r/book/numberoffactors.pdf.
43. Stapleton, C.D. (1997). Basic concepts and procedures of confirmatory factor analysis. Paper Presented at the Annual Meeting of the South west Educational Research Association. Austin, January.
44. Stewens, J. (1996). Applied multivariate statistics for the social science. New Jersey: Lawrence Erlbaum Associates.
45. Silverstein, A. B. (1977). Comparison of two criteria for determining the number of factors. Psychological Reports, 41, 387-390.
46. Silverstein, A. B. (1987). Note on the paralel analysis criterion for determining the number of common factor or principal components. Psychological Reports, 61, 351-354.
47. Şencan, H. (2005). Sosyal ve Davranışsal Ölçümlerde Güvenilirlik ve Geçerlilik. Ankara: Seçkin Yayıncılık.
48. Tabachnick, B.G. & Fidel, L.S. (2007). Using multivariate statistics. MA: Allyn& Bacon, Inc.
49. Tavşancıl, E. (2005). Tutumların ölçülmesi ve SPSS ile veri analizi. (2. Baskı). Ankara; Nobel Yayınları.
50. Tucker, L.R., Koopman, R. F. & Linn, R. L. (1969). Evaluation of factor analytic research procedures by means of simulated correlationmatrices. Psychometrica, 34(4),421-459.
51. Urbina S. (2004). Essentials of psychological testing. John Wiley and Sons.
52. Uyar, S. (2012). Açımlayıcı Faktör Analizinde Boyut Sayısını Belirlemede Kullanılan Yöntemlerin Karşılaştırılması (Yayınlanmamış yüksek lisans tezi.) Hacettepe Üniversitesi Sosyal Bilimler Enstitüsü. Ankara.
53. Velicer, W. F., Eaton, C. A. & Fava, J. L. (2000). Construct explication through factor or component analysis: A review and evaluation of alternative procedures for determining the number of factors or components. Problems and solutions in human assessment, 41-71.
54. Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrica, 41(3), 321-327 Watkins, M. W. (2006). Determining paralel analysis criteria. Journal of Applied Statistical Methods, 5(2), 344-346
55. Weng, L.J. & Cheng, C.P. (2005). Parallel analysis with unidimensional binary data. Educational and Psychological Measurements, 75(5), 697-716.
56. Winter, J.C.F., Dodou, D. & Wieringa, P. A. (2009). Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research, 25, 147-181.
57. Wood, J M., Tataryn, D. J. & Gorsuch, R.L. (1996). Effects of under- and over extraction on principal axis factor analysis with varimax rotation. Psyhological Methods, 1(4), 354-365.
58. Zwick, W. R. & Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99(3), 432-442.