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

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

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.

Keywords:

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

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