Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data

Abdullah Faruk KILIÇ, (Adıyaman Üniversitesi, Eğitim Fakültesi, Eğitim Bilimleri Bölümü, Adıyaman, Türkiye)
İbrahim UYSAL, (Bolu Abant İzzet Baysal Üniversitesi, Eğitim Fakültesi, Eğitim Bilimleri Bölümü, Bolu, Türkiye)
Burcu ATAR (Hacettepe Üniversitesi, Eğitim Fakültesi, Eğitim Bilimleri Bölümü, Ankara, Türkiye)
International Journal of Assessment Tools in Education
9 2
Yıl: 2020 Cilt: 7 Sayı: 3 Sayfa Aralığı: 451 - 487 Metin Dili: İngilizce DOI: 10.21449/ijate.660353 İndeks Tarihi: 24-11-2020

Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data

Öz:
This Monte Carlo simulation study aimed to investigate confirmatoryfactor analysis (CFA) estimation methods under different conditions, such assample size, distribution of indicators, test length, average factor loading, andfactor structure. Binary data were generated to compare the performance ofmaximum likelihood (ML), mean and variance adjusted unweighted least squares(ULSMV), mean and variance adjusted weighted least squares (WLSMV), andBayesian estimators. As a result of the study, it was revealed that increased averagefactor loading and sample size had a positive effect on the performance of theestimation methods. According to the research findings, it can be said that themethods are sufficient to estimate average factor loading and interfactorcorrelations, regardless of the estimation methods, in most of the conditions wherethe average factor loading is 0.7. In small sample sizes particularly, the interfactorcorrelation was underestimated for skewed indicator conditions. According to thefindings of the study, although there is not the most accurate method in allconditions, it can be recommended to use ULSMV method because it performsadequately in more conditions.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Acar-Güvendir, M., & Özer-Özkan, Y. (2015). Türkiye’deki eğitim alanında yayımlanan bilimsel dergilerde ölçek geliştirme ve uyarlama konulu makalelerin incelenmesi [The examination of scale development and scale adaptation articles published in Turkish academic journals on education]. Electronic Journal of Social Sciences, 14(52), 23–33. https://doi.org/10.17755/esosder.54872
  • AERA, APA, & NCME. (2014). Standards for educational and psychological testing. American Educational Research Association.
  • Anıl, D., Güzeller, C. O., Çokluk, Ö., & Şekercioǧlu, G. (2010). Level determination exam (SBS-2008) the determination of the validity and reliability of 7th grade mathematics subtest. Procedia-Social and Behavioral Sciences, 2(2), 5292-5298. https://doi.org/10.1016 /j.sbspro.2010.03.863
  • Babakus, E., Ferguson, C. E., & Jöreskog, K. G. (1987). The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributional assumptions. Journal of Marketing Research, 24(2), 222-228. https://doi.org/10.2307/31 51512
  • Beauducel, A., & 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. https://doi.org/10.120 7/s15328007sem1302_2
  • Bollen, K. A. (1989). Structural equations with latent variables. John Wiley & Sons, Inc. https://doi.org/10.1002/9781118619179
  • Boomsma, A. (1985). Nonconvergence, improper solutions, and starting values in lisrel maximum likelihood estimation. Psychometrika, 50(2), 229-242. https://doi.org/10.1007 /BF02294248
  • Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). The Guilford.
  • Byrne, B. M. (2016). Structural equation modeling with AMOS: Basic concepts, applications, and programming (3rd ed.). Routledge.
  • Collins, L. M., Schafer, J. L., & Kam, C.-M. (2001). A comparison of inclusive and restrictive strategies in modern missing data procedures. Psychological Methods, 6(4), 330–351. https://doi.org/10.1037/1082-989X.6.4.330
  • Comrey, A. L., & Lee, H. B. (1992). A first course in factor analysis (2nd ed.). Lawrence Erlbaum Associates.
  • Crocker, L., & Algina, J. (2008). Introduction of classical and modern test theory. Cengage Learning.
  • Curran, P. J., West, S. G., & Finch, J. F. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1(1), 16– 29. https://doi.org/10.1037/1082-989X.1.1.16
  • DiStefano, C., & Morgan, G. B. (2014). A comparison of diagonal weighted least squares robust estimation techniques for ordinal data. Structural Equation Modeling: A Multidisciplinary Journal, 21(3), 425-438. https://doi.org/10.1080/10705511.2014.9153 73
  • Dolan, C. V. (1994). Factor analysis of variables with 2, 3, 5 and 7 response categories: A comparison of categorical variable estimators using simulated data. British Journal of Mathematical and Statistical Psychology, 47(2), 309-326. https://doi.org/10.1111/j.2044 -8317.1994.tb01039.x
  • Flora, D. B., & 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. https://doi.org/10.1037/1082-989X.9.4.466
  • Floyd, F. J., & Widaman, K. F. (1995). Factor analysis in the development and refinement of clinical assessment instruments. Psychological Assessment, 7(3), 286–299. https://doi.org/10.1037/1040-3590.7.3.286
  • Forero, C. G., Maydeu-Olivares, A., & 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. https://doi.org/10.108 0/10705510903203573
  • Gilbert, N. (1999). Simulation: A new way of doing social science. American Behavioral Scientist, 42(10), 1485–1487. https://doi.org/10.1177/0002764299042010002
  • Gorsuch, R. L. (1974). Factor analysis. W. B. Saunders.
  • Green, S. B., Akey, T. M., Fleming, K. K., Hershberger, S. L., & Marquis, J. G. (1997). Effect of the number of scale points on chi‐square fit indices in confirmatory factor analysis. Structural Equation Modeling: A Multidisciplinary Journal, 4(2), 108-120. https://doi.o rg/10.1080/10705519709540064
  • Guadagnoli, E., & Velicer, W. F. (1988). Relation of sample size to the stability of component patterns. Psychological Bulletin, 103(2), 265-275. https://doi.org/10.1037/0033-2909.10 3.2.265
  • Hallquist, M., & Wiley, J. (2017). MplusAutomation: Automating Mplus Model Estimation and Interpretation [Computer software]. https://cran.r-project.org/web/packages/MplusAuto mation/
  • Harrison, R. L. (2010). Introduction to Monte Carlo Simulation. AIP Conference Proceedings, 1204, 17–21. https://doi.org/10.1063/1.3295638
  • Holtmann, J., Koch, T., Lochner, K., & Eid, M. (2016). A Comparison of ML, WLSMV, and Bayesian methods for multilevel structural equation models in small samples: A simulation study. Multivariate Behavioral Research, 51(5), 661-680. https://doi.org/10. 1080/00273171.2016.1208074
  • Jin, S., Luo, H., & Yang-Wallentin, F. (2016). A simulation study of polychoric instrumental variable estimation in structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 23(5), 680-694. https://doi.org/10.1080/10705511.2016.1189 334
  • Kılıç, A. F., & Kelecioğlu, H. (2016). TEOG ortak ve mazeret sınavındaki Türkçe ve matematik alt testlerinin psikometrik özelliklerinin karşılaştırılması [The comparison of psychometric properties of standardised and make up maths and Turkish subtest questions in TEOG]. Journal of Measurement and Evaluation in Education and Psychology, 7(1), 33–58. https://doi.org/10.21031/epod.14532
  • Kline, R. B. (2016). Principle and practice of structural equation modeling (4th ed.). The Guilford.
  • Koğar, H., & Yılmaz Koğar, E. (2015). Comparison of different estimation methods for categorical and ordinal data in confirmatory factor analysis. Journal of Measurement and Evaluation in Education and Psychology, 6(2), 351-364. https://doi.org/10.21031/epod. 94857
  • Lei, P. (2009). Evaluating estimation methods for ordinal data in structural equation modeling. Quality and Quantity, 43(3), 495–507. https://doi.org/10.1007/s11135-007-9133-z
  • Li, C.-H. (2016a). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48(3), 936–949. https://doi.org/10.3758/s13428-015-0619-7
  • Li, C.-H. (2016b). The performance of ML, DWLS, and ULS estimation with robust corrections in structural equation models with ordinal variables. Psychological Methods, 21(3), 369– 387. https://doi.org/10.1037/met0000093
  • Liang, X., & Yang, Y. (2014). An evaluation of WLSMV and Bayesian methods for confirmatory factor analysis with categorical indicators. International Journal of Quantitative Research in Education, 2(1), 17-38. https://doi.org/10.1504/IJQRE.2014.0 60972
  • Lissitz, R. W., Hou, X., & Slater, S. C. (2012). The contribution of constructed response items to large scale assessment: Measuring and understanding their impact. Journal of Applied Testing Technology, 13(3), 1-50. http://www.jattjournal.com/index.php/atp/article/view/ 48366/39234
  • Morata-Ramirez, M. de los A., & Holgado-Tello, F. P. (2013). Construct validity of likert scales through confirmatory factor analysis: A simulation study comparing different methods of estimation based on Pearson and polychoric correlations. International Journal of Social Science Studies, 1(1), 54-61. https://doi.org/10.11114/ijsss.v1i1.27
  • Moshagen, M., & Musch, J. (2014). Sample size requirements of the robust weighted least squares estimator. Methodology, 10(2), 60-70. https://doi.org/10.1027/1614-2241/a0000 68
  • Mulaik, S. A. (2009). Linear causal modeling with structural equations. Chapman & Hall.
  • Muthén, B. O., & Asparouhov, T. (2002). Latent variable analysis with categorical outcomes: Multiple-group and growth modeling in Mplus. https://www.statmodel.com/download/ webnotes/CatMGLong.pdf
  • Muthén, B. O., & Asparouhov, T. (2012). Bayesian structural equation modeling: A more flexible representation of substantive theory. Psychological Methods, 17(3), 313–335. https://doi.org/10.1037/a0026802
  • Muthén, B. O., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of non-normal Likert variables. British Journal of Mathematical and Statistical Psychology, 38(2), 171–189. https://doi.org/10.1111/j.2044-8317.1985.tb00832.x
  • Muthén, L. K., & Muthén, B. O. (2012). Mplus statistical modeling software: Release 7.0 [Computer software]. Muthén & Muthén.
  • Muthén, L. K., & Muthén, B. O. (2015). Mplus user’s guide (7th ed.). Muthén & Muthén.
  • Nalbantoğlu Yılmaz, F. (2019). Comparison of different estimation methods used in confirmatory factor analyses in non-normal data: A monte carlo study. International Online Journal of Educational Sciences, 11(4), 131-140. https://doi.org/10.15345/iojes. 2019.04.010
  • Nestler, S. (2013). A monte carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis. British Journal of Mathematical and Statistical Psychology, 66(1), 127-143. https://doi.org/10.1111/j.2044-8317.2012.02044. x
  • Önen, E. (2019). A comparison of frequentist and Bayesian approaches: The power to detect model misspecifications in confirmatory factor analytic models. Universal Journal of Educational Research, 7(2), 494–514. https://doi.org/10.13189/ujer.2019.070223
  • Potthast, M. J. (1993). Confirmatory factor analysis of ordered categorical variables with large models. British Journal of Mathematical and Statistical Psychology, 46(2), 273–286. https://doi.org/10.1111/j.2044-8317.1993.tb01016.x
  • R Core Team. (2018). R: A language and environment for statistical computing [Computer software]. R Foundation for Statistical Computing. https://www.r-project.org/
  • Raykov, T., & Marcoulides, G. A. (2006). A first course in structural equation modeling (2nd ed.). Lawrence Erlbaum Associates.
  • Rhemtulla, M., Brosseau-Liard, P. É., & 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. https://doi.org/10.1037/a0029315
  • Rosseel, Y. (2012). lavaan: An R Package for Structural Equation Modeling. Journal of Statistical Software, 48(2), 1–36. https://doi.org/10.18637/jss.v048.i02
  • Şahin, M. G., & Boztunç Öztürk, N. (2018). Eğitim alanında ölçek geliştirme süreci: Bir içerik analizi çalışması [Scale development process in educational field: A content analysis research]. Kastamonu Education Journal, 26(1), 191-199. https://doi.org/10.24106/kefd ergi.375863
  • Shi, D., DiStefano, C., McDaniel, H. L., & Jiang, Z. (2018). Examining chi-square test statistics under conditions of large model size and ordinal Data. Structural Equation Modeling: A Multidisciplinary Journal, 25(6), 924-945. https://doi.org/10.1080/10705511.2018.1449 653
  • Stevens, J. P. (2009). Applied multivariate statistics for the social science (5th ed.). Taylor & Francis.
  • Streiner, D. L. (1994). Figuring out factors: The use and misuse of factor analysis. Canadian Journal of Psychiatry, 39(3), 135-140. https://doi.org/10.1177%2F07067437940390030 3
  • Tabachnik, B. G., & Fidell, L. S. (2012). Using multivariate statistics (6th ed.). Pearson.
  • Thissen, D., Wainer, H., & Wang, X.-B. (1994). Are tests comprising both multiple-choice and free-response items necessarily less unidimensional than multiple-choice tests? An analysis of two tests. Journal of Educational Measurement, 31(2), 113–123. https://doi.org/10.1111/j.1745-3984.1994.tb00437.x
  • Wolf, E. J., Harrington, K. M., Clark, S. L., & Miller, M. W. (2013). Sample size requirements for structural equation models: An evaluation of power, bias, and solution propriety. National Institutes of Health, 76(6), 913-934. https://doi.org/10.1177/001316441349523 7
  • Xu, M. (2019). A comparison of frequentist and Bayesian approaches for confirmatory factor analysis (Publication No. 27534819) [Doctoral dissertation, The Ohio State University]. ProQuest Dissertations and Theses Global.
  • Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling: A Multidisciplinary Journal, 17(3), 392–423. https://doi.org/10.1080/10705511.2010.489003
APA Kilic A, UYSAL I, Atar B (2020). Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. , 451 - 487. 10.21449/ijate.660353
Chicago Kilic Abdullah Faruk,UYSAL IBRAHIM,Atar Burcu Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. (2020): 451 - 487. 10.21449/ijate.660353
MLA Kilic Abdullah Faruk,UYSAL IBRAHIM,Atar Burcu Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. , 2020, ss.451 - 487. 10.21449/ijate.660353
AMA Kilic A,UYSAL I,Atar B Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. . 2020; 451 - 487. 10.21449/ijate.660353
Vancouver Kilic A,UYSAL I,Atar B Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. . 2020; 451 - 487. 10.21449/ijate.660353
IEEE Kilic A,UYSAL I,Atar B "Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data." , ss.451 - 487, 2020. 10.21449/ijate.660353
ISNAD Kilic, Abdullah Faruk vd. "Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data". (2020), 451-487. https://doi.org/10.21449/ijate.660353
APA Kilic A, UYSAL I, Atar B (2020). Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. International Journal of Assessment Tools in Education, 7(3), 451 - 487. 10.21449/ijate.660353
Chicago Kilic Abdullah Faruk,UYSAL IBRAHIM,Atar Burcu Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. International Journal of Assessment Tools in Education 7, no.3 (2020): 451 - 487. 10.21449/ijate.660353
MLA Kilic Abdullah Faruk,UYSAL IBRAHIM,Atar Burcu Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. International Journal of Assessment Tools in Education, vol.7, no.3, 2020, ss.451 - 487. 10.21449/ijate.660353
AMA Kilic A,UYSAL I,Atar B Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. International Journal of Assessment Tools in Education. 2020; 7(3): 451 - 487. 10.21449/ijate.660353
Vancouver Kilic A,UYSAL I,Atar B Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data. International Journal of Assessment Tools in Education. 2020; 7(3): 451 - 487. 10.21449/ijate.660353
IEEE Kilic A,UYSAL I,Atar B "Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data." International Journal of Assessment Tools in Education, 7, ss.451 - 487, 2020. 10.21449/ijate.660353
ISNAD Kilic, Abdullah Faruk vd. "Comparison of Confirmatory Factor Analysis Estimation Methods on Binary Data". International Journal of Assessment Tools in Education 7/3 (2020), 451-487. https://doi.org/10.21449/ijate.660353
Sayfa Oluşturulma Tarihi
17-04-2024 17:20

İLETİŞİM

TÜBİTAK ULAKBİM TR Dizin

Yüzüncüyıl, İşçi Blokları Mahallesi

Muhsin Yazıcıoğlu Caddesi No:51/C

06530 Çankaya / ANKARA +90 (312) 298 92 00

trdizin@tubitak.gov.tr

TÜBİTAK ULAKBİM Ulusal Akademik Ağ ve Bilgi Merkezi Cahit Arf Bilgi Merkezi © Tüm Hakları Saklıdır. Gizlilik Politikası Kullanım Şartları