Comparison of Different Estimation Methods for Categorical and Ordinal Data in Confirmatory Factor Analysis

Year 2015, Volume: 6 Issue: 2, 0 - 0, 02.01.2016

Hakan Koğar , Esin Yılmaz Koğar

https://doi.org/10.21031/epod.94857

Cited By: 24

Abstract

In confirmatory factor analysis (CFA), which is used quite often for scale development and adaptation studies, the selected estimation method, affects the results obtained from the data. Because of the selected estimation method, the model parameters and their standard errors, and the model data fit values may alter the results substantially. So that, the purpose of this research is to compare the performance of different estimation methods for CFA. Maximum likelihood (ML), unweighted least squares (ULS) and diagonally weighted least squares (DWLS) are used in this research as estimation methods. These methods are applied in data sets and regression coefficients and their standard errors, t values, fit indexes and iteration numbers obtained from these estimation methods are examined. As a result, ULS method can converge with the minimum number iterations and it seems to be the more accurate method for estimating the parameters.

Key Words: Confirmatıry factor analysis, weighted least square, unweighted least square, diagonally weighted least square 

 

References

• Babakus, E. (1985). The sensitivity of maximum likelihood factor analysis given violations of interval scale and multivariate normality (Doctoral dissertation, The University of Alabama).
• Babakus, E., Ferguson, C. E., & Joreskog, K. G. (1987). The sensitivity of confirmatory maximum likelihood factor analysis to violations of measurement scale and distributional assumptions. Journal of Marketing Research, 37, 72-141.
• Bandalos, D. L. (2014). Relative performance of categorical diagonally weighted least squares and robust maximum likelihood estimation. Structural Equation Modeling: A Multidisciplinary Journal, 21, 102 – 116.
• 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, 13, 186 – 203.
• Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: John Wiley & Sons.
• Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York, N. J.: Guiford Press.
• Byrne, B. M. (1998). Structural Equation Modeling with LISREL, PRELIS, and SIMPLIS: Basic concepts, applications, and programming.
• Lawrence Erlbaum Associates, Mahwah, N. J.
• Cai, J. (2008). Structural equation modeling analysis with correlated ordered and unordered categorical data (Doctorial dissertation, The Chinese University of Hong Kong).
• Deryakulu, D. & Büyüköztürk, Ş. (2002). Epistemolojik inanç ölçeğinin geçerlik ve güvenirlik çalışması. Eğitim Araştırmaları, 8, 111– 125.
• Deryakulu, D., & Büyüköztürk, Ş. (2005). Epistemolojik inanç ölçeğinin faktör yapısının yeniden incelenmesi: cinsiyet ve öğrenim görülen program türüne göre epistemolojik inançların karşılaştırılması. Eğitim Araştırmaları, 18, 57 – 70.
• Dinler-İçöz, S. (2014). İşitme engelli çocuğa sahip olan ve olmayan annelerin umutsuzluk düzeylerinin incelenmesi (Yüksek Lisans Tezi, Ankara Üniversitesi, Fen Bilimleri Fakültesi, Ankara).
• DiStefano, C. (2002). The impact of categorization with confirmatory factor analysis. Structural Equation Modeling, 9, 327 – 346.
• 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.
• 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, 4, 108-120.
• Hoogland, J. J., & Boomsma, A. (1998). Robustness studies in covariance structure modeling: An overview and a meta-analysis. Sociological Methods & Research, 26, 329 – 367.
• Hoyle, R. H. (1995). Structural equation modeling concepts, issues, and applications. Thousand Oaksa London New Delhi: Sage Publications.
• Hu, L., Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112, 351 – 362.
• Hutchinson, S. R., & Olmos, A. (1998). Behavior of descriptive fit indexes in confirmatory factor analysis using ordered categorical data. Structural Equation Modeling, 5, 344 – 364.
• Jöreskog, K. G. (1990). New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares. Quality and Quantity, 24, 387-404.
• Jöreskog, K. G., & Sörbom, D. (1996a). LISREL 8: Structural equation modelling with the SIMPLIS command language. Hove and London: Scientific Software ınternational.
• Jöreskog, K.G., & Sörbom, D. (1996b). LISREL 8: User’s reference guide. Chicago: Scientific Software International.
• Katsikatsou, M., Moustaki, I., Yang-Wallentin, F., & Joreskog, K. (2012). Pairwise likelihood estimation for factor analysis models with ordinal data. Computational Statistics and Data Analysis, 56(12), 4243-4258.
• Kline, R. B. (2005). Principles and practice of structural equation modeling (Second Edition). New York: The Guilford Publications.
• Lee, S. Y., Poon, W. Y., & Bentler, P. M. (1995). A two-stage estimation of structural equation models with continuous and polytomous variables. British Journal of Mathematical and Statistical Psychology, 48, 339 – 358.
• Lei, P. (2009). Evaluating estimation methods for ordinal data in structural equation modeling. Quality & Quantity, 43, 495 – 507.
• Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519 –530.
• Marsh, H. W., & Grayson, D. (1995). Latent variable models of
• multitrait-multimethod data. In R. Hoyle (Ed.), Structural equation modeling: Concepts, issues and applications (pp. 177−198). Thousand Oaks, CA: Sage.
• Mîndrilă, D. (2010). Maximum likelihood (ML) and diagonally weighted least squares (DWLS) estimation procedures: A comparison of estimation bias with ordinal and multivariate nonnormal data. International Journal of Digital Society, 1(1), 60 – 66.
• Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical and continuous latent variable indicators. Psychometrika, 49, 115 – 132.
• 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.
• Muthén, B., & 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, 171–189.
• Raykov, T., & Marcoulides, G. A. (2000). A first course in structural equation modeling. London: Lawrence Erlbaum Associates, Inc.
• Rigdon, E. E., & Ferguson, C. E. (1991). The performance of the polychoric correlation coefficient and selected fitting functions in confirmatory factor analysis with ordinal data. Journal of Marketing Research, 28, 491 – 497.
• Sammel, M. D., Ryan, L. M., & Legler, J. M. (1997). Latent variable models for mixed discrete and continuous outcomes. Journal of the
• Royal Statistical Society, Series B, 59, 667 – 678.
• Savaşır, I., & Şahin, N. H. (1997). Bilişsel-davranışçı terapilerde değerlendirme: sık kullanılan ölçekler. Ankara. Türk Psikologlar Derneği Yayınları.
• Schommer, M. (1990). Effects of beliefs about the nature of knowledge on comprehension. Journal of Educational Psychology, 82(3), 498 – 504.
• Sümer, N. (2000). Yapısal eşitlik modelleri: Temel kavramlar ve örnek uygulamalar. Türk Psikoloji Yazıları, 3(6), 49-74.
• Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics (Fifth Edition). Boston: Allyn and Bacon.
• West, S. G., Finch, J. F., & Curran, P. J. (1995). Structural equation models with non-normal variables. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues and applications (pp. 56–75). Thousand Oaks, CA: Sage.
• Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling, 17, 392 – 423.