Doğrulayıcı Faktör Analizi için Gerekli Örneklem Büyüklüğü Kaç Kişidir? : Bayes Yaklaşımı ve Maksimum Olabilirlik Kestirimi

Yıl 2020, Cilt: 16 Sayı: 32, 5302 - 5340, 31.12.2020

Gizem Uyumaz , Gözde Sırgancı

https://doi.org/10.26466/opus.826895

Cited By: 7

Öz

Bu çalışmanın öncelikli amacı özellikle sosyal bilimler ve eğitim bilimleri alanlarında çalışmalar yapan araştırmacılara, doğrulayıcı faktör analizinde (DFA) uygun sonuçlar elde edebilmek için gerekli örneklem büyüklüğüyle ilgili kolay ulaşılabilir bir kaynak hazırlamaktır. Çalışmanın diğer amacı çeşitli koşullar altında küçük örneklemlerde, farklı faktör yükü ve faktörler arası korelasyon koşullarında, maksimum olabilirlik kestirimine ve bilgilendirici ve bilgilendirici olmayan önsellerin kullanılarak Bayes yaklaşımına dayalı olarak yapılan DFA ile elde edilen kestirimlerin kestirim yanlılığı, hata kareler ortalaması ve istatistiksel gücünün belirlenmesidir. Özellikle doğru tanımlanmış bilgilendirici önseller kullanılan Bayes DFA, tüm örneklem büyüklüklerinde en iyi performansı göstermektedir. Bilgilendirici önseller hatalı belirlendiğinde Bayes DFA daha düşük performans gösterir. Düşük faktör yüklerinde, önseller bilgilendirici olmasa bile Bayes kestirimi maksimum olabilirlik kestiriminden daha az yanlı sonuçlar verir. Zayıf faktör yükleri koşulunda tahminler, özellikle (çok) küçük örneklem büyüklüklerinde (N = 50 veya daha az) kestirimleri gerçek değerinden yüksek yapma eğilimindedir. Bayes DFA, özellikle daha küçük örneklem büyüklüklerinde, düşük faktör yüklerinde maksimum olabilirlik DFA'dan daha iyi performans gösterir. Faktör yükleriyle ilgili önseller bilgilendirici ise Bayes DFA, daha düşük örneklem büyüklüklerinde maksimum olabilirlik DFA'dan daha az yanlı sonuçlar verir. Maksimum olabilirlik kestirimlerinde, düşük örneklem büyüklüklerinde ve zayıf ile orta faktör yüklerinde sorunlarla karşılaşılırken, Bayes DFA sürekli olarak hatasız çalışır.

Anahtar Kelimeler

yapısal eşitlik modeli, bayesçi yaklaşım, küçük örneklemler, monte carlo simülasyonu

What is the Required Sample Size for Confirmatory Factor Analysis?: Bayesian Approach and Maximum Likelihood Estimation

Öz

The primary aim of this study is to prepare an easily accessible resource about the sample size necessary for researchers working in the fields of social and educational sciences to obtain appropriate results in confirmatory factor analysis (CFA). The other aim is to determine the prediction bias, mean square error and statistical power of the predictions obtained by the confirmatory factor analysis based on Bayesian approach using informative and non-informative a priori in small samples under various conditions, different factor loadings and correlation conditions between factors. determination. Especially the informative priors perform well, and this at all sample sizes and also Bayesian CFA performs less well when the informative priors are miss specified. Bayesian CFA performs better than ML-CFA when the factor loadings are weak, even with a diffuse prior. With weak factor loadings, the estimates are biased upwards, especially at (very) small sample sizes (N=50 or less). Bayesian CFA performs better than ML-CFA at low factor loadings, especially at smaller sample sizes. Bayesian CFA does better at lower sample sizes, if the priors on the factor loadings are informative. While ML-CFA runs into problems at low sample sizes and weak to moderate factor loadings, Bayesian CFA consistently runs without errors.

Anahtar Kelimeler

structural equation model, bayesian approach, small sample, monte carlo simulation

Kaynakça

• Anderson, J. C., ve Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49(2), 155-173.
• Asparouhov, T., ve Muthén, B. (2010). Bayesian analysis using Mplus: Technical implementation. Los Angeles, CA: Muthén & Muthén.
• Bandalos, D. L. (2006). The use of Monte Carlo studies in structural equation modeling research. In R. C. Serlin (Series Ed.), G. R. Hancock, ve R. O. Mueller (Vol. Eds.), Structural equation modeling: A second course (s. 385–462). Greenwich, CT: Information Age.
• Bentler, P. M., ve Chou, C. P. (1987). Practical issues in structural modeling. Sociological methods & research, 16(1), 78-117.
• Bollen, K. A. (1989). A new incremental fit index for general structural equation models. Sociological methods & research, 17(3), 303-316.
• Boomsma, A. (1985). Nonconvergence, improper solutions, and starting values in LISREL maximum likelihood estimation. Psychometrika, 50(2), 229-242.
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, N J: Erlbaum.
• Cohen, J., & Cohen, P. (1983). Applied multiple regression/correlation analysis for the behavioral sciences. Hillsdale, NJ: L. NJ Eribaum.
• Comrey, A. L., ve Lee, H. B. (1992). A first course in factor analysis, (2nd Edition). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
• De Winter, J. C. F, Dodou, D., and P. A. Wieringa (2009). Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research, 44, 147-181.
• Goodwin, L. D. (1999). The role of factor analysis in the estimation of construct validity. Measurement in Physical Education and Exercise Science, 3(2), 85-100.
• Hair, J. F. Jr. , Anderson, R. E., Tatham, R. L., ve Black, W. C. (1998). Multivariate data analysis, (5th Edition). Upper Saddle River, NJ: Prentice Hall.
• Hancock, G. R., ve French, B. F. (2013). Power analysis in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Quantitative methods in education and the behavioral sciences: Issues, research, and teaching. Structural equation modeling: A second course (s. 117–159). IAP Information Age Publishing.
• Heerwegh, D. (2014). Small sample Bayesian factor analysis. Phuse. Retrieved from http://www. lexjansen.com/phuse/2014/sp/SP03. Pdf adresinden erişilmiştir.
• Helm, J. L., Castro-Schilo, L., ve Oravecz, Z. (2017). Bayesian versus maximum likelihood estimation of multitrait–multimethod confirmatory factor models. Structural Equation Modeling: A Multidisciplinary Journal, 24(1), 17-30.
• Hu, L. T., ve Bentler, P. M. (1999). Cut-off criteria for fit indexes in covariance structure analysis: convenfional criteria versus new alternafives. Structural equafion modelling. Ref. Bibliográfica, 6(1), 1-55..
• Jackson, D. L. (2001). Sample size and number of parameter estimates in maximum likelihood confirmatory factor analysis: A Monte Carlo investigation. Structural Equation Modeling, 8, 205-223.
• Jöreskog, K. G., ve Sörbom, D. (1996). LISREL 8 user’s reference guide. Uppsala, Sweden: Scientific Software International.
• Kelley, K., ve Maxwell, S. E. (2003). Sample size for multiple regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8, 305-321.
• MacCallum, R. C., Widaman, K. F., Zhang, S., ve Hong, S. (1999). Sample size in factor analysis. Psychological methods, 4(1), 84.
• Maxwell, S. E., Kelley, K., ve Rausch, J. R. (2008). Sample size planning for statistical power and accuracy in parameter estimation. Annual review of psychology, 59.
• Muthén, B., ve Asparouhov, T. (2012). Bayesian structural equation modeling: a more flexible representation of substantive theory. Psychological methods, 17(3), 313.
• Muthén, L. K., ve Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural equation modeling, 9(4), 599-620.
• Nevitt, J., ve Hancock, G. R. (2004). Evaluating small sample approaches for model test statistics in structural equation modeling. Multivariate Behavioral Research, 39(3), 439-478.
• Satorra, A., ve Saris, W. E. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50(1), 83-90.
• Song, X. Y., ve Lee, S. Y. (2012). Basic and advanced Bayesian structural equation modeling: With applications in the medical and behavioral sciences. Chichester, England: Wiley.
• Stevens, J. (2002). Applied multivariate statistics for the social sciences. Mahwah, NJ: Lawrence Erlbaurn Associates.
• Tanaka, J. S. (1987). How big is big enough?": Sample size and goodness of fit in structural equation models with latent variables. Child development, 134-146.
• Van de Schoot, R., Kaplan, D., Denissen, J., Asendorpf, J. B., Neyer, F. J., ve Van Aken, M. A. (2014). A gentle introduction to Bayesian analysis: Applications to developmental research. Child development, 85(3), 842- 860.
• Wolf, E. J., Harrington, K. M., Clark, S. L., ve Miller, M. W. (2013). Sample size requirements for structural equation models: An evaluation of power, bias, and solution propriety. Educational and psychological measurement, 73(6), 913-934.
• Yu, C. Y., ve Muthén, B. O. (2002). Evaluation of model fit indices for latent variable models with categorical and continuous outcomes. Los Angeles: University of California, Los Angeles, Graduate School of Education and Information Studies. Graduate School of Education and Information Studies.