Research Article
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FAKTÖR ÇIKARMA YÖNTEMLERİNİN PARALEL ANALİZ SONUÇLARINA ETKİSİ

Year 2021, Volume 11, Issue 2, 926 - 942, 11.05.2021
https://doi.org/10.24315/tred.747075

Abstract

Açımlayıcı faktör analizinden en önemli kararlardan biri faktör sayısını belirlemektir. Bunun için birçok yöntem geliştirilmiş olsa da paralel analiz, hala en çok önerilen ve kullanılan yöntemler arasında yer almaktadır. Sıklıkla kullanılması birçok modifikasyonun yapılmasına ve analizle ilgili araştırmaların yoğunlaşmasına neden olmuştur. Bu araştırmada açımlayıcı faktör analizinde kullanılan faktör çıkarma yöntemlerinin paralel analiz sonuçlarına etkisinin incelenmesi amaçlanmış ve Monte Carlo simülasyon çalışması gerçekleştirilmiştir. İki kategorili veri setleriyle gerçekleştirilen simülasyon çalışmasında ortalama faktör yükü, madde sayısı, ölçme modeli, örneklem büyüklüğü ve kullanılan korelasyon matrisi koşulları manipüle edilmiştir. Paralel analizde uygulanan en küçük kalıntı, temel bileşenler, temel eksenler, en çok olabilirlik, ağırlıklandırılmamış en küçük kareler, en küçük ki-kare ve optimal paralel analizde uygulanan en küçük rank faktör çıkarma yöntemleri karşılaştırılmıştır. Araştırma sonucunda tetrakorik korelasyon matrisiyle gerçekleştirilen optimal paralel analiz yönteminin uygulandığı en küçük rank yönteminin en iyi sonucu verdiği gözlenmiştir. Bununla birlikte ortalama faktör yükü .70 olan koşullarda Pearson korelasyon matrisiyle gerçekleştirilen analizlerde tüm yöntemler yeterli performans gösterirken tetrakorik korelasyon matrisinin kullanılmasıyla paralel analiz uygulanan temel bileşenler ve optimal paralel analiz uygulanan en küçük rank yöntemleri hariç diğer yöntemlerin aşırı faktör çıkardığı söylenebilir. Araştırma bulgularına göre tetrakorik (polikorik) korelasyon matrisiyle en küçük rank yöntemiyle optimal paralel analizin kullanılması önerilmektedir

References

  • Bandalos, D. L. ve Leite, W. (2013). Use of Monte Carlo studies in structural equation modeling research. G. R. Hancock ve R. O. Mueller (Ed.), Structural equation modeling: A second course içinde (2nd ed.). Charlotte, NC: Information Age.
  • Beauducel, A. ve Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling: A Multidisciplinary Journal, 13(2), 186–203. doi:10.1207/s15328007sem1302_2
  • Buja, A. ve Eyuboglu, N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27(4), 509–540. doi:10.1207/s15327906mbr2704_2
  • Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. doi:10.1207/s15327906mbr0102_10
  • Cho, S.-J., Li, F. ve Bandalos, D. L. (2009). Accuracy of the parallel analysis procedure with polychoric correlations. Educational and Psychological Measurement, 69(5), 748–759. doi:10.1177/0013164409332229
  • Çokluk, Ö. ve Koçak, D. (2016). Using Horn’s parallel analysis method in exploratory factor analysis for determining the number of factors. Educational Sciences: Theory & Practice, 16(2), 537–552. doi:10.12738/estp.2016.2.0328
  • Crawford, A. V., Green, S. B., Levy, R., Lo, W.-J., Scott, L., Svetina, D. ve Thompson, M. S. (2010). Evaluation of parallel analysis methods for determining the number of factors. Educational and Psychological Measurement, 70(6), 885–901. doi:10.1177/0013164410379332
  • Curran, P. J., West, S. G. ve Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1(1), 16–29. doi:10.1037/1082-989X.1.1.16
  • Dinno, A. (2009). Exploring the sensitivity of Horn’s parallel analysis to the distributional form of random data. Multivariate Behavioral Research, 44(3), 362–388. doi:10.1080/00273170902938969
  • Fabrigar, L. R., Wegener, D. T., MacCallum, R. C. ve Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272–299. doi:10.1037/1082-989X.4.3.272
  • Flora, D. B. ve Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9(4), 466–491. doi:10.1037/1082-989X.9.4.466
  • Forero, C. G., Maydeu-Olivares, A. ve Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A monte carlo study comparing DWLS and ULS estimation. Structural Equation Modeling: A Multidisciplinary Journal, 16(4), 625–641. doi:10.1080/10705510903203573
  • Glorfeld, L. W. (1995). An improvement on Horn’s parallel analysis methodology for selecting the correct number of factors to retain. Educational and Psychological Measurement, 55(3), 377–393. doi:10.1177/0013164495055003002
  • Goretzko, D., Pham, T. T. H. ve Bühner, M. (2019). Exploratory factor analysis: Current use, methodological developments and recommendations for good practice. Current Psychology, 1-12. doi:10.1007/s12144-019-00300-2
  • Gorsuch, R. L. (1974). Factor analysis. Toronto: W. B. Saunders.
  • Green, S., Xu, Y. ve Thompson, M. S. (2018). Relative accuracy of two modified parallel analysis methods that use the proper reference distribution. Educational and Psychological Measurement, 78(4), 589–604. doi:10.1177/0013164417718610
  • Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179–185. doi:10.1007/BF02289447
  • Howard, M. C. (2016). A review of exploratory factor analysis decisions and overview of current practices: What we are doing and how can we improve? International Journal of Human-Computer Interaction, 32(1), 51–62. doi:10.1080/10447318.2015.1087664
  • Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20(1), 141–151. doi:10.1177/001316446002000116
  • Keith, T. Z., Caemmerer, J. M. ve Reynolds, M. R. (2016). Comparison of methods for factor extraction for cognitive test-like data: Which overfactor, which underfactor? Intelligence, 54, 37–54. doi:10.1016/j.intell.2015.11.003
  • Koçak, D., Çokluk, Ö. ve Kayri, M. (2016). Faktör sayısının belirlenmesinde MAP testi, paralel analiz, K1 ve yamaç birikinti grafiği yöntemlerinin karşılaştırılması. YYÜ Eğitim Fakültesi Dergisi, 13(1), 330–359.
  • Li, C.-H. (2016a). The performance of ML, DWLS, and ULS estimation with robust corrections in structural equation models with ordinal variables. Psychological Methods, 21(3), 369–387. doi:10.1037/met0000093
  • Li, C.-H. (2016b). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48(3), 936–949. doi:10.3758/s13428-015-0619-7
  • Liu, O. L. ve Rijmen, F. (2008). A modified procedure for parallel analysis of ordered categorical data. Behavior Research Methods, 40(2), 556–562. doi:10.3758/BRM.40.2.556
  • Lorenzo-Seva, U. ve Ferrando, P. J. (2019). Factor (Version 10.10.01) [Computer software]. Tarragona: Universitat Rovira i Virgili. MEB. (2020). Merkezî sınav başvuru ve uygulama klavuzu. http://www.meb.gov.tr/meb_iys_dosyalar/2020_05/06105923_BasYvuru_ve_Uygulama_KYlavuzu_2020_GuYncel.pdf adresinden erişildi.
  • Moshagen, M. ve Musch, J. (2014). Sample size requirements of the robust weighted least squares estimator. Methodology, 10(2), 60–70. doi:10.1027/1614-2241/a000068
  • Navarro-Gonzalez, D. ve Lorenzo-Seva, U. (2020). EFA.MRFA: Dimensionality assessment using minimum rank factor analysis. https://cran.r-project.org/package=EFA.MRFA adresinden erişildi.
  • 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(3), 396–402. doi:10.3758/BF03200807
  • Preacher, K. J., Zhang, G., Kim, C. ve Mels, G. (2013). Choosing the optimal number of factors in exploratory factor analysis: A model selection perspective. Multivariate Behavioral Research, 48(1), 28–56. doi:10.1080/00273171.2012.710386
  • R Core Team. (2018). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.r-project.org/. adresinden erişildi.
  • Revelle, W. (2009). An introduction to psychometric theory with applications in R. Springer. http://www.personality-project.org/r/book/ adresinden erişildi.
  • Revelle, W. (2018). psych: Procedures for psychological, psychometric, and personality research. Evanston, Illinois. https://cran.r-project.org/package=psych adresinden erişildi.
  • Rhemtulla, M., Brosseau-Liard, P. É. ve Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373. doi:10.1037/a0029315
  • Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1–36.
  • Ruscio, J. ve Roche, B. (2012). Determining the number of factors to retain in an exploratory factor analysis using comparison data of known factorial structure. Psychological Assessment, 24(2), 282–292. doi:10.1037/a0025697
  • Sočan, G. ve ten Berge, J. M. F. (2003). The determinants of the bias in minimum rank factor analysis (MRFA). H. Yanai, A. Okada, K. Shigemasu, Y. Kano ve J. J. Meulman (Ed.), New Developments in Psychometrics içinde (ss. 95–102). Tokyo: Springer Japan.
  • Steger, M. F. (2006). An illustration of issues in factor extraction and identification of dimensionality in psychological assessment data. Journal of Personality Assessment, 86(3), 263–272. doi:10.1207/s15327752jpa8603_03
  • Tabachnik, B. G. ve Fidell, L. S. (2012). Using multivariate statistics (6th ed.). Boston: Pearson. ten Berge, J. M. F. ve Kiers, H. A. L. (1991). A numerical approach to the approximate and the exact minimum rank of a covariance matrix. Psychometrika, 56(2), 309–315. doi:10.1007/BF02294464
  • Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding consepts and applications. Washington DC: APA.
  • Timmerman, M. E. ve Lorenzo-Seva, U. (2011). Dimensionality assessment of ordered polytomous items with parallel analysis. Psychological Methods, 16(2), 209–220. doi:10.1037/a0023353
  • Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3), 321–327.
  • Weng, L.-J. ve Cheng, C.-P. (2005). Parallel analysis with unidimensional binary data. Educational and Psychological Measurement, 65(5), 697–716. doi:10.1177/0013164404273941
  • West, S. G., Finch, J. F. ve Curran, P. J. (1995). Structural equation models with non-normal variables: Problems and remedies. R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications içinde. Thousand Oaks, CA: Sage.
  • Xia, Y., Green, S. B., Xu, Y. ve Thompson, M. S. (2019). Proportion of indicator common variance due to a factor as an effect size statistic in revised parallel analysis. Educational and Psychological Measurement. 79(1), 85-107. doi:10.1177/0013164418754611
  • Zwick, W. R. ve Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99(3), 432–442. doi:10.1037/0033-2909.99.3.432

Year 2021, Volume 11, Issue 2, 926 - 942, 11.05.2021
https://doi.org/10.24315/tred.747075

Abstract

References

  • Bandalos, D. L. ve Leite, W. (2013). Use of Monte Carlo studies in structural equation modeling research. G. R. Hancock ve R. O. Mueller (Ed.), Structural equation modeling: A second course içinde (2nd ed.). Charlotte, NC: Information Age.
  • Beauducel, A. ve Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling: A Multidisciplinary Journal, 13(2), 186–203. doi:10.1207/s15328007sem1302_2
  • Buja, A. ve Eyuboglu, N. (1992). Remarks on parallel analysis. Multivariate Behavioral Research, 27(4), 509–540. doi:10.1207/s15327906mbr2704_2
  • Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. doi:10.1207/s15327906mbr0102_10
  • Cho, S.-J., Li, F. ve Bandalos, D. L. (2009). Accuracy of the parallel analysis procedure with polychoric correlations. Educational and Psychological Measurement, 69(5), 748–759. doi:10.1177/0013164409332229
  • Çokluk, Ö. ve Koçak, D. (2016). Using Horn’s parallel analysis method in exploratory factor analysis for determining the number of factors. Educational Sciences: Theory & Practice, 16(2), 537–552. doi:10.12738/estp.2016.2.0328
  • Crawford, A. V., Green, S. B., Levy, R., Lo, W.-J., Scott, L., Svetina, D. ve Thompson, M. S. (2010). Evaluation of parallel analysis methods for determining the number of factors. Educational and Psychological Measurement, 70(6), 885–901. doi:10.1177/0013164410379332
  • Curran, P. J., West, S. G. ve Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1(1), 16–29. doi:10.1037/1082-989X.1.1.16
  • Dinno, A. (2009). Exploring the sensitivity of Horn’s parallel analysis to the distributional form of random data. Multivariate Behavioral Research, 44(3), 362–388. doi:10.1080/00273170902938969
  • Fabrigar, L. R., Wegener, D. T., MacCallum, R. C. ve Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272–299. doi:10.1037/1082-989X.4.3.272
  • Flora, D. B. ve Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9(4), 466–491. doi:10.1037/1082-989X.9.4.466
  • Forero, C. G., Maydeu-Olivares, A. ve Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A monte carlo study comparing DWLS and ULS estimation. Structural Equation Modeling: A Multidisciplinary Journal, 16(4), 625–641. doi:10.1080/10705510903203573
  • Glorfeld, L. W. (1995). An improvement on Horn’s parallel analysis methodology for selecting the correct number of factors to retain. Educational and Psychological Measurement, 55(3), 377–393. doi:10.1177/0013164495055003002
  • Goretzko, D., Pham, T. T. H. ve Bühner, M. (2019). Exploratory factor analysis: Current use, methodological developments and recommendations for good practice. Current Psychology, 1-12. doi:10.1007/s12144-019-00300-2
  • Gorsuch, R. L. (1974). Factor analysis. Toronto: W. B. Saunders.
  • Green, S., Xu, Y. ve Thompson, M. S. (2018). Relative accuracy of two modified parallel analysis methods that use the proper reference distribution. Educational and Psychological Measurement, 78(4), 589–604. doi:10.1177/0013164417718610
  • Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179–185. doi:10.1007/BF02289447
  • Howard, M. C. (2016). A review of exploratory factor analysis decisions and overview of current practices: What we are doing and how can we improve? International Journal of Human-Computer Interaction, 32(1), 51–62. doi:10.1080/10447318.2015.1087664
  • Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20(1), 141–151. doi:10.1177/001316446002000116
  • Keith, T. Z., Caemmerer, J. M. ve Reynolds, M. R. (2016). Comparison of methods for factor extraction for cognitive test-like data: Which overfactor, which underfactor? Intelligence, 54, 37–54. doi:10.1016/j.intell.2015.11.003
  • Koçak, D., Çokluk, Ö. ve Kayri, M. (2016). Faktör sayısının belirlenmesinde MAP testi, paralel analiz, K1 ve yamaç birikinti grafiği yöntemlerinin karşılaştırılması. YYÜ Eğitim Fakültesi Dergisi, 13(1), 330–359.
  • Li, C.-H. (2016a). The performance of ML, DWLS, and ULS estimation with robust corrections in structural equation models with ordinal variables. Psychological Methods, 21(3), 369–387. doi:10.1037/met0000093
  • Li, C.-H. (2016b). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48(3), 936–949. doi:10.3758/s13428-015-0619-7
  • Liu, O. L. ve Rijmen, F. (2008). A modified procedure for parallel analysis of ordered categorical data. Behavior Research Methods, 40(2), 556–562. doi:10.3758/BRM.40.2.556
  • Lorenzo-Seva, U. ve Ferrando, P. J. (2019). Factor (Version 10.10.01) [Computer software]. Tarragona: Universitat Rovira i Virgili. MEB. (2020). Merkezî sınav başvuru ve uygulama klavuzu. http://www.meb.gov.tr/meb_iys_dosyalar/2020_05/06105923_BasYvuru_ve_Uygulama_KYlavuzu_2020_GuYncel.pdf adresinden erişildi.
  • Moshagen, M. ve Musch, J. (2014). Sample size requirements of the robust weighted least squares estimator. Methodology, 10(2), 60–70. doi:10.1027/1614-2241/a000068
  • Navarro-Gonzalez, D. ve Lorenzo-Seva, U. (2020). EFA.MRFA: Dimensionality assessment using minimum rank factor analysis. https://cran.r-project.org/package=EFA.MRFA adresinden erişildi.
  • 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(3), 396–402. doi:10.3758/BF03200807
  • Preacher, K. J., Zhang, G., Kim, C. ve Mels, G. (2013). Choosing the optimal number of factors in exploratory factor analysis: A model selection perspective. Multivariate Behavioral Research, 48(1), 28–56. doi:10.1080/00273171.2012.710386
  • R Core Team. (2018). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.r-project.org/. adresinden erişildi.
  • Revelle, W. (2009). An introduction to psychometric theory with applications in R. Springer. http://www.personality-project.org/r/book/ adresinden erişildi.
  • Revelle, W. (2018). psych: Procedures for psychological, psychometric, and personality research. Evanston, Illinois. https://cran.r-project.org/package=psych adresinden erişildi.
  • Rhemtulla, M., Brosseau-Liard, P. É. ve Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354–373. doi:10.1037/a0029315
  • Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1–36.
  • Ruscio, J. ve Roche, B. (2012). Determining the number of factors to retain in an exploratory factor analysis using comparison data of known factorial structure. Psychological Assessment, 24(2), 282–292. doi:10.1037/a0025697
  • Sočan, G. ve ten Berge, J. M. F. (2003). The determinants of the bias in minimum rank factor analysis (MRFA). H. Yanai, A. Okada, K. Shigemasu, Y. Kano ve J. J. Meulman (Ed.), New Developments in Psychometrics içinde (ss. 95–102). Tokyo: Springer Japan.
  • Steger, M. F. (2006). An illustration of issues in factor extraction and identification of dimensionality in psychological assessment data. Journal of Personality Assessment, 86(3), 263–272. doi:10.1207/s15327752jpa8603_03
  • Tabachnik, B. G. ve Fidell, L. S. (2012). Using multivariate statistics (6th ed.). Boston: Pearson. ten Berge, J. M. F. ve Kiers, H. A. L. (1991). A numerical approach to the approximate and the exact minimum rank of a covariance matrix. Psychometrika, 56(2), 309–315. doi:10.1007/BF02294464
  • Thompson, B. (2004). Exploratory and confirmatory factor analysis: Understanding consepts and applications. Washington DC: APA.
  • Timmerman, M. E. ve Lorenzo-Seva, U. (2011). Dimensionality assessment of ordered polytomous items with parallel analysis. Psychological Methods, 16(2), 209–220. doi:10.1037/a0023353
  • Velicer, W. F. (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3), 321–327.
  • Weng, L.-J. ve Cheng, C.-P. (2005). Parallel analysis with unidimensional binary data. Educational and Psychological Measurement, 65(5), 697–716. doi:10.1177/0013164404273941
  • West, S. G., Finch, J. F. ve Curran, P. J. (1995). Structural equation models with non-normal variables: Problems and remedies. R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications içinde. Thousand Oaks, CA: Sage.
  • Xia, Y., Green, S. B., Xu, Y. ve Thompson, M. S. (2019). Proportion of indicator common variance due to a factor as an effect size statistic in revised parallel analysis. Educational and Psychological Measurement. 79(1), 85-107. doi:10.1177/0013164418754611
  • Zwick, W. R. ve Velicer, W. F. (1986). Comparison of five rules for determining the number of components to retain. Psychological Bulletin, 99(3), 432–442. doi:10.1037/0033-2909.99.3.432

Details

Primary Language Turkish
Subjects Education, Scientific Disciplines
Journal Section Articles
Authors

Abdullah Faruk KILIÇ (Primary Author)
Adıyaman Üniversitesi
0000-0003-3129-1763
Türkiye


İbrahim UYSAL
ABANT İZZET BAYSAL ÜNİVERSİTESİ
0000-0002-6767-0362
Türkiye

Publication Date May 11, 2021
Published in Issue Year 2021, Volume 11, Issue 2

Cite

APA Kılıç, A. F. & Uysal, İ. (2021). FAKTÖR ÇIKARMA YÖNTEMLERİNİN PARALEL ANALİZ SONUÇLARINA ETKİSİ . Trakya Eğitim Dergisi , 11 (2) , 926-942 . DOI: 10.24315/tred.747075