Farklı Örneklem Büyüklüğü ve Dağılımı Koşullarında WLS ve Robust WLS Yöntemlerinin Karşılaştırılması
Öz
Yapısal eşitlik modellemesinde kullanılan parametre kestirim
yöntemleri verinin sürekli, sıralı olup olmamasına ve dağılımın normalliğine
göre farklılık göstermektedir. Sıralı verilerle çalışıldığında en sık
kullanılan parametre kestirim yöntemi WLS (weighted least squares-
ağırlıklandırılmış en küçük kareler) olup, dağılıma ilişkin herhangi bir
varsayım gerektirmemesi avantajı iken, büyük örneklemler gerektirmesi
dezavantajı olarak karşımıza çıkmaktadır. Son yıllarda Robust WLS kestirim
yöntemleri WLSM (weighted least squares mean-ortalamaya göre düzeltilmiş
ağırlıklandırılmış en küçük kareler) ve WLSMV (weighted least squares mean and
variance-ortalama ve varyansa göre düzeltilmiş ağırlıklandırılmış en küçük
kareler) sıklıkla kullanılmakla beraber, küçük örneklemlerde ve farklı dağılım
koşullarında WLS kestirim yöntemine alternatif olup olamayacağı önemli
görülmektedir. Bu çalışmada PISA 2012’de yer alan matematiğe yönelik tutum
maddelerinden oluşan 5 faktörlü model temel alınarak 3 farklı dağılım (ÇK=0,00;
1,00 ve 1,50) ve 4 farklı örneklem büyüklüğü (N=200, 500 ve 1000) koşullarında
WLS, WLSM ve WLSMV yöntemleri karşılaştırılmıştır. Farklı örneklem büyüklüğü
koşulu altında WLSMV yönteminin WLSM ve WLS yöntemlerinden daha iyi uyum
indeksleri ürettiği belirlenirken, özellikle küçük örneklem koşullarında WLS
yöntemine bir alternatif olabileceği belirlenmiştir. Dağılımın çarpıklığına
göre ise WLS, WLSM ve WLSMV kestirim yöntemleri incelendiğinde, dağılımın
çarpıklığına karşı en dayanıklı kestirim yönteminin WLSMV olduğu görülmüştür.
Anahtar Kelimeler
Yapısal Eşitlik modellemesi ağırlıklandırılmış en küçük kareler (wls) ortalamaya göre düzeltilmiş ağırlıklandırılmış en küçük kareler (wlsm) ortalama ve varyansa göre düzeltilmiş ağırlıklandırılmış en küçük kareler (wlsmv) parametre kestirim yöntemleri dağılım ve örneklem büyüklüğü simülasyon
Kaynakça
- Arslan, M. S. T. (2011). Ordinal Değişkenli Yapısal Eşitlik Modellerinde Kullanılan Parametre Tahmin Yöntemlerinin Karşılaştırılması, Yüksek Lisans Tezi, Eskişehir Osmangazi Üniversitesi Fen Bilimleri Enstitüsü, Eskişehir. Austin, .J. T .& Calde1·6n, R. F. (1 996). Theoretical and technical contributions to structural equation modeling: An updated annotated bibliography. Structural Equation Modeling: A Multi-disciplinary journal, 3, I 05-175. Babakus, E., Ferguson Jr, 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, 222-228. Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley. Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: The Guilford Press. 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. Finney, S. J., & DiStefano, C. (2006). Non-normal and categorical data in structural equation modeling. In Hancock, G.R. & Mueller R. O. (Eds.), Structural equation modeling: A second course, (pp. 269-314). Information Age Publishing, U.S.A. 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, 466–491. 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, 16, 625–641. Hox, J. J., Maas, C. J., & Brinkhuis, M. J. (2010). The effect of estimation method and sample size in multilevel structural equation modeling. Statistica Neerlandica, 64:2, 157-170. Kline, P. (2005). Principal and practice of structural equation modeling. NY: Guilford Muthén, B. O. (1993). Goodness of fit with categorical and other non normal variables. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 205–243). Newbury Park, CA: Sage. Patton, M.Q. (1990). Qualitative evaluation and research methods. London: Sage. Schermelleh-Engel, Karin; Helfried Moosbrugger; Hans Müler .(2003).Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness-of-Fit Measures, Methods of Psychological Research Online, Vol.8, No.2, pp. 23-74. Schumacker, R. E., & Lomax, R. G. (2004). A beginner's guide to structural equation modeling. Psychology Press. Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling, 17(3), 392-423. Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Tests of significance and descriptive goodness-of-fit measures. Methods of psychological research online, 8(2), 23-74. Yu, C.-Y., & Muthén, B. (2002, April). Evaluation of model fit indices for latent variable models with categorical and continuous outcomes. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
Öz
In structural equation modeling parameter estimation
methods vary according to whether data is continuous or ordinal and the
normality of distribution. When working with ordinal data, the most commonly
used parameter estimation method is WLS (weighted least square), the advantage
of which is not requiring any assumption, as the disadvantage of it is
requiring large samples. Recently, while Robust estimation methods, WLSM and
WLSMV, are commonly used, it is important to see whether they are alternative
to WLS in different distribution and sample size conditions. In this study, it
is based on the model with five factor model about students’ attitudes towards
mathematics in PISA 2012. The performance of parameter estimation methods
including WLS, WLSM, and WLSMV were compared in four different sample sizes
(N=200, 500, and 1000) and 3 different distribution types (Sk=0,00; 1,00, and
1,50). As a result, it was seen that WLSMV method has better fit indices than
WLSM and WLS methods in different sample size conditions, especially in small
sample size condition it is an alternative to WLS method. When it was examined
WLS, WLSM, and WLSMV estimation methods according to skewness of distribution,
it was seen that the most robust method to skewness of distribution is WLSMV.
Anahtar Kelimeler
WLS wlsm wlsmv parameter estimation methods distribution and sample size conditions simulation
Kaynakça
- Arslan, M. S. T. (2011). Ordinal Değişkenli Yapısal Eşitlik Modellerinde Kullanılan Parametre Tahmin Yöntemlerinin Karşılaştırılması, Yüksek Lisans Tezi, Eskişehir Osmangazi Üniversitesi Fen Bilimleri Enstitüsü, Eskişehir. Austin, .J. T .& Calde1·6n, R. F. (1 996). Theoretical and technical contributions to structural equation modeling: An updated annotated bibliography. Structural Equation Modeling: A Multi-disciplinary journal, 3, I 05-175. Babakus, E., Ferguson Jr, 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, 222-228. Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley. Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: The Guilford Press. 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. Finney, S. J., & DiStefano, C. (2006). Non-normal and categorical data in structural equation modeling. In Hancock, G.R. & Mueller R. O. (Eds.), Structural equation modeling: A second course, (pp. 269-314). Information Age Publishing, U.S.A. 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, 466–491. 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, 16, 625–641. Hox, J. J., Maas, C. J., & Brinkhuis, M. J. (2010). The effect of estimation method and sample size in multilevel structural equation modeling. Statistica Neerlandica, 64:2, 157-170. Kline, P. (2005). Principal and practice of structural equation modeling. NY: Guilford Muthén, B. O. (1993). Goodness of fit with categorical and other non normal variables. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 205–243). Newbury Park, CA: Sage. Patton, M.Q. (1990). Qualitative evaluation and research methods. London: Sage. Schermelleh-Engel, Karin; Helfried Moosbrugger; Hans Müler .(2003).Evaluating the Fit of Structural Equation Models: Tests of Significance and Descriptive Goodness-of-Fit Measures, Methods of Psychological Research Online, Vol.8, No.2, pp. 23-74. Schumacker, R. E., & Lomax, R. G. (2004). A beginner's guide to structural equation modeling. Psychology Press. Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling, 17(3), 392-423. Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Tests of significance and descriptive goodness-of-fit measures. Methods of psychological research online, 8(2), 23-74. Yu, C.-Y., & Muthén, B. (2002, April). Evaluation of model fit indices for latent variable models with categorical and continuous outcomes. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Araştırma Makaleleri |
| Yazarlar | |
| Yayımlanma Tarihi | 15 Mart 2018 |
| Yayımlandığı Sayı | Yıl 2018 Cilt: 17 Sayı: 1 |