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Deciding The Number Of Dimensions In Explanatory Factor Analysis: A Brief Overview Of The Methods

Year 2022, Issue: 51, 305 - 318, 09.08.2022

Abdullah Faruk Kılıç

https://doi.org/10.30794/pausbed.1095936
Cited By: 2

Abstract

Exploratory factor analysis (EFA) finds its place in many scientific fields (e.g. education, health science or economics). With this analysis, information about the nature and structure of the measured feature can be obtained. It is possible to have information about the nature of the measured feature by fulfilling the requirements of this analysis. Correctly deciding on the number of dimensions in EFA can also be challenging for researchers. For this reason, this study presents information on the theoretical background of the factor retention methods used when deciding on the number of dimensions in EFA. In addition, it has been given information about which software is available for these methods. Moreover, there is information about which method gives more accurate results in the simulation studies. As a result, the number of dimensions can be decided by using traditional methods such as optimal parallel analysis, comparative data, or minimum average partial, as well as making use of machine learning methods (random forest or extreme gradient augmentation), which have found new uses in the literature, to researchers who will perform EFA.

Keywords

parallel analysis minimum average partial exploratory graph analysis random forest xgboost

References

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  • Golino, H. F., & Epskamp, S. (2017). Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research. PLOS ONE, 12(6), 1–26. https://doi.org/10.1371/journal.pone.0174035
  • Golino, H. F., Moulder, R., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Nesselroade, J., Sadana, R., Thiyagarajan, J. A., & Boker, S. M. (2020). Entropy fit indices: New fit measures for assessing the structure and dimensionality of multiple latent variables. Multivariate Behavioral Research, 1–29. https://doi.org/10.1080/00273171.2020.1779642
  • Golino, H. F., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Sadana, R., Thiyagarajan, J. A., & Martinez-Molina, A. (2020). Investigating the performance of exploratory graph analysis and traditional techniques to identify the number of latent factors: A simulation and tutorial. Psychological Methods, 25(3), 292–320. https://doi.org/10.1037/met0000255
  • Goretzko, D., & Bühner, M. (2020). One model to rule them all? Using machine learning algorithms to determine the number of factors in exploratory factor analysis. Psychological Methods, 25(6), 776–786. https://doi.org/10.1037/met0000262
  • Green, S. B., Levy, R., Thompson, M. S., Lu, M., & Lo, W.-J. (2012). A proposed solution to the problem with using completely random data to assess the number of factors with parallel analysis. Educational and Psychological Measurement, 72(3), 357–374. https://doi.org/10.1177/0013164411422252
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  • Kılıç, A. E., & Yılmaz, R. (2021). YouTube’un eğitsel amaçlı kabul durumunun incelenmesi. Ahmet Keleşoğlu Eğitim Fakültesi Dergisi, 3(1), 69–89. https://doi.org/10.38151/akef.2021.10
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AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ

Year 2022, Issue: 51, 305 - 318, 09.08.2022

Abdullah Faruk Kılıç

https://doi.org/10.30794/pausbed.1095936
Cited By: 2

Abstract

Açımlayıcı faktör analizi (AFA), bilimsel çalışma alanlarının birçoğunda (eğitim, sağlık, iktisat gibi) kendine yer bulmaktadır. Bu analizle ölçülen özelliğin doğası ve yapısı hakkında bilgi sahibi olunabilmektedir. Ölçülen özelliğin doğası hakkında bilgi sahibi olmak ise bu analizin gerekliliklerini yerine getirerek mümkündür. Açımlayıcı faktör analizinde boyut sayısına doğru bir şekilde karar verilmesi de araştırmacılar için zorlayıcı olabilmektedir. Bu nedenle bu çalışmada, açımlayıcı faktör analizinde boyut sayısına karar verirken kullanılabilecek yöntemlerin hem teorik alt yapısına hem de bu yöntemlerin hangi yazılımlarda bulunduğuna yönelik bilgiler sunulmuştur. Dahası gerçekleştirilen çalışmalarda hangi yöntemin daha uygun sonuçlar verdiği ve hangi yöntemlerin güncel çalışmalarda kullanılabileceğine yer verilmiştir. Sonuç olarak geleneksel yöntemlerden optimal paralel analiz, karşılaştırmalı veriler ya da kısmi korelasyonların ortalaması yöntemleriyle boyut sayısına karar verilebileceği gibi literatürde kendine daha yeni kullanım alanı bulmuş makine öğrenmesi yöntemlerinden de (rastgele orman ya da aşırı gradyan arttırma) yararlanılması AFA gerçekleştirecek araştırmacılara önerilebilir.

Keywords

paralel analiz kısmi korelasyonların ortalaması açımlayıcı grafik analizi rastgele orman aşırı gradyan artırma

References

  • Auerswald, M., & Moshagen, M. (2019). How to determine the number of factors to retain in exploratory factor analysis: A comparison of extraction methods under realistic conditions. Psychological Methods, 24(4), 468–491. https://doi.org/10.1037/met0000200
  • Bandalos, D. L., & Finney, S. J. (2019). Factor analysis: Exploratory and confirmatory. In G. R. Hancock & R. O. Mueller (Eds.), The reviewers guide to quantitative methods in the social sciences (2nd. ed.). Routledge.
  • Beavers, A. S., Lounsbury, J. W., Richards, J. K., Huck, S. W., Skolits, G. J., & Esquivel, S. L. (2013). Practical considerations for using exploratory factor analysis in educational research. Practical Assessment, Research & Evaluation, 18(6), 1–13. https://pareonline.net/pdf/v18n6.pdf
  • Braeken, J., & van Assen, M. A. L. M. (2017). An empirical Kaiser criterion. Psychological Methods, 22(3), 450–466. https://doi.org/10.1037/met0000074
  • Breiman, L. (2001). Random forests. Machine Learning, 45, 5–32. https://doi.org/10.1023/A:1010933404324
  • Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). The Guilford.
  • Büyüköztürk, Ş. (2020). Sosyal bilimler için veri analizi el kitabı: İstatistik, araştırma deseni, SPSS uygulamaları ve yorum (28. Baskı). Pegem Akademi.
  • Cattell, R. B. (1966). The scree test for the number of factors. Multivariate Behavioral Research, 1(2), 245–276. https://doi.org/10.1207/s15327906mbr0102_10
  • Chen, T., He, T., Benesty, M., Khotilovich, V., Tang, Y., Cho, H., Chen, K., Mitchell, R., Cano, I., Zhou, T., Li, M., Xie, J., Lin, M., Geng, Y., Li, Y., & Yuan, J. (2022). xgboost: Extreme Gradient Boosting (1.5.2.1). https://cran.r-project.org/package=xgboost
  • Cosemans, T., Rosseel, Y., & Gelper, S. (2021). Exploratory graph analysis for factor retention: Simulation results for continuous and binary data. Educational and Psychological Measurement. https://doi.org/10.1177/00131644211059089
  • Crawford, A. V., Green, S. B., Levy, R., Lo, W.-J., Scott, L., Svetina, D., & Thompson, M. S. (2010). Evaluation of parallel analysis methods for determining the number of factors. Educational and Psychological Measurement, 70(6), 885–901. https://doi.org/10.1177/0013164410379332
  • Cronbach, L. J., & Meehl, P. E. (1955). Construct validity in psychological tests. Psychological Bulletin, 52(4), 281–302. https://doi.org/10.1037/h0040957
  • 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. https://doi.org/10.1080/00273170902938969
  • Erkuş, A. (2019). Psikolojide ölçme ve ölçek geliştirme-I: Temel kavramlar ve işlemler (4nd ed.). Pegem Akademi.
  • Fabrigar, L. R., & Wegener, D. T. (2012). Exploratory factor analysis. Oxford University.
  • 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. https://doi.org/10.1037/1082-989X.4.3.272
  • Friedman, J., Hastie, T., & Tibshirani, R. (2000). Additive logistic regression: a statistical view of boosting. The Annals of Statistics, 28(2). https://doi.org/10.1214/aos/1016218223
  • Garrido, L. E., Abad, F. J., & Ponsoda, V. (2011). Performance of Velicer’s minimum average partial factor retention method with categorical variables. Educational and Psychological Measurement, 71(3), 551–570. https://doi.org/10.1177/0013164410389489
  • 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. https://doi.org/10.1177/0013164495055003002
  • Golino, H. F., & Christensen, A. P. (2020). EGAnet: Exploratory Graph Analysis -- A framework for estimating the number of dimensions in multivariate data using network psychometrics.
  • Golino, H. F., & Epskamp, S. (2017). Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research. PLOS ONE, 12(6), 1–26. https://doi.org/10.1371/journal.pone.0174035
  • Golino, H. F., Moulder, R., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Nesselroade, J., Sadana, R., Thiyagarajan, J. A., & Boker, S. M. (2020). Entropy fit indices: New fit measures for assessing the structure and dimensionality of multiple latent variables. Multivariate Behavioral Research, 1–29. https://doi.org/10.1080/00273171.2020.1779642
  • Golino, H. F., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Sadana, R., Thiyagarajan, J. A., & Martinez-Molina, A. (2020). Investigating the performance of exploratory graph analysis and traditional techniques to identify the number of latent factors: A simulation and tutorial. Psychological Methods, 25(3), 292–320. https://doi.org/10.1037/met0000255
  • Goretzko, D., & Bühner, M. (2020). One model to rule them all? Using machine learning algorithms to determine the number of factors in exploratory factor analysis. Psychological Methods, 25(6), 776–786. https://doi.org/10.1037/met0000262
  • Green, S. B., Levy, R., Thompson, M. S., Lu, M., & Lo, W.-J. (2012). A proposed solution to the problem with using completely random data to assess the number of factors with parallel analysis. Educational and Psychological Measurement, 72(3), 357–374. https://doi.org/10.1177/0013164411422252
  • Guilford, J. P. (1946). New standards for test evaluation. Educational and Psychological Measurement, 6(4), 427–438. https://doi.org/10.1177/001316444600600401
  • Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2009). Multivariate data analysis (7th ed.). Pearson.
  • Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179–185. https://doi.org/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. https://doi.org/10.1080/10447318.2015.1087664
  • Humphreys, L. G., & Ilgen, D. R. (1969). Note on a criterion for the number of common factors. Educational and Psychological Measurement, 29(3), 571–578. https://doi.org/10.1177/001316446902900303
  • Kahn, J. H. (2006). Factor analysis in counseling psychology research, training, practice: Principles, advances, and applications. The Counseling Psychologist, 34(5), 684–718. https://doi.org/10.1177/0011000006286347
  • Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and Psychological Measurement, 20(1), 141–151. https://doi.org/10.1177/001316446002000116
  • Kılıç, A. E., & Yılmaz, R. (2021). YouTube’un eğitsel amaçlı kabul durumunun incelenmesi. Ahmet Keleşoğlu Eğitim Fakültesi Dergisi, 3(1), 69–89. https://doi.org/10.38151/akef.2021.10
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Details

Primary Language Turkish
Subjects Economics
Journal Section Articles
Authors

Abdullah Faruk Kılıç 0000-0003-3129-1763

Early Pub Date August 26, 2022
Publication Date August 9, 2022
Acceptance Date April 11, 2022
Published in Issue Year 2022 Issue: 51

Cite

APA Kılıç, A. F. (2022). AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ. Pamukkale Üniversitesi Sosyal Bilimler Enstitüsü Dergisi(51), 305-318. https://doi.org/10.30794/pausbed.1095936
AMA Kılıç AF. AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ. PAUSBED. August 2022;(51):305-318. doi:10.30794/pausbed.1095936
Chicago Kılıç, Abdullah Faruk. “AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ”. Pamukkale Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, no. 51 (August 2022): 305-18. https://doi.org/10.30794/pausbed.1095936.
EndNote Kılıç AF (August 1, 2022) AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ. Pamukkale Üniversitesi Sosyal Bilimler Enstitüsü Dergisi 51 305–318.
IEEE A. F. Kılıç, “AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ”, PAUSBED, no. 51, pp. 305–318, August 2022, doi: 10.30794/pausbed.1095936.
ISNAD Kılıç, Abdullah Faruk. “AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ”. Pamukkale Üniversitesi Sosyal Bilimler Enstitüsü Dergisi 51 (August 2022), 305-318. https://doi.org/10.30794/pausbed.1095936.
JAMA Kılıç AF. AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ. PAUSBED. 2022;:305–318.
MLA Kılıç, Abdullah Faruk. “AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ”. Pamukkale Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, no. 51, 2022, pp. 305-18, doi:10.30794/pausbed.1095936.
Vancouver Kılıç AF. AÇIMLAYICI FAKTÖR ANALİZİNDE BOYUT SAYISINA KARAR VERME: YÖNTEMLERE KISA BİR BAKIŞ. PAUSBED. 2022(51):305-18.

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