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Year 2020, , 193 - 211, 22.03.2020

Cengiz Gazeloglu , Zerrin Aşan Greenacre

https://doi.org/10.17776/csj.648054
Cited By: 4

Abstract

Supporting Institution

Anadolu Üniversitesi

Project Number

1506F501

Thanks

Anadolu Üniversitesi BAP birimine teşekkürler.

References

  • [1] Agresti A., Categorical Data Analysis, Second edition, John Wiley Sons, 2003.
  • [2] Edward C., Wirht R.J., Houts C.R. and Xi N., Categorical Data in The Structural Equation Modeling Framework. Hoyle RH. (Ed.) Handbook of Structural Equation Modeling. Guilford Press, 2012;. 195-208.
  • [3] Arıcıgil Ç., Sosyal Bilimlerde Kategorik Verilerle İlişki Analizi, (Second Edition), Ankara, Pegem Akademi, 2013.
  • [4] Kateri M., Contingency Table Analysis Methods and Implementation Using R, New York, Springer, 2014.
  • [5] Agresti A., Booth J.G., Hobert J.P. and Caffo B., Random-Effects modeling of Categorical Response Data. Sociological Methodology., 30 (2000) 27-80.
  • [6] Akıncı E.D., Yapısal eşitlik modellerinde bilgi kriterleri, Doctoral Thesis, Fen Bilimleri Enstitüsü, İstanbul, Mimar Sinan Güzel Sanatlar Üniversitesi, 2007.
  • [7] Schumacker R.E. and Lomax R.G., A beginner's guide to structural equation modeling, Third edition, Routledge, Taylor and Francis Group, LLC 2010.
  • [8] Likert R., A Technique for the Measurement of Attitudes, New York University 1932.
  • [9] Lee S.Y., Structural Equation Modeling A Bayesian Approach, England, John Wiley Sons, 2007.
  • [10] Arslan M.S.T., Ordinal değişkenli yapısal eşitlik modellerinde kullanılan parametre tahmin yöntemlerinin karşılaştırılması, Master Thesis, Fen Bilimleri Enstitüsü, Eskişehir, Eskişehir Osmangazi Üniversitesi, 2011.
  • [11] Jörekog K.G. and Sörbom D., LISREL 8: Structural Equation Modelling with the Simples Command Language, Scientific Sofware International, 1993.
  • [12] Kline R.B., Principles and Practice of Structural Equation Modelling, London, Guilford Press, 2011.
  • [13] Kline R.B., Principles and Practice of Structural Equation Modelling, London, Guilford Press, 2005.
  • [14] Schumacker R.E. and Lomax R.G., A beginner's guide to structural equation modeling, Second edition, Mahwah, Lawrence Erlbaum Associates, 2004.
  • [15] Çelik H.E., Yapısal eşitlik modellemesi ve bir uygulama: genişletilmiş online alışveriş kabul modeli, Doctoral Thesis, Fen Bilimleri Enstitüsü, Eskişehir Osman Gazi Üniversitesi, Eskişehir, 2009.
  • [16] Agresti A. , Analysis of Ordinal Categorical Data, John Wiley Sons, 2010.
  • [17] Bollen K.A., Structural Equation with Latent Variables, New York, John Wiley Sons, 1989.
  • [18] Çelik H.E., Yılmaz V., LISREL 9.1 ile Yapısal Eşitlik Modellemesi, Ankara, Anı Yayıncılık, 2013.
  • [19] Muthén B. O., A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika., 49 (1984) 115–132.
  • [20] Doğan İ., Farklı veri yapısı ve örneklem büyüklüklerinde yapısal eşitlik modellerinin geçerliliği ve güveniliğinin değerlendirilmesi. Doktora Tezi. Sağlık Bilimleri Enstitüsü. Eskişehir: Eskişehir Osmangazi Üniversitesi, 2015.
  • [21] Akaike H., A new look at the statistical model identification, IEEE Transactions on Automatic Control., 19(6) (1974), 716–723.
  • [22] Akaike H., Information theory as an extension of the maximum likelihood principle. In. B.N. Petrov and F. Csaki (Eds.), Proceedings of the Second International Symposium on Information Theory, Akademiai Kiado, Budapest, 1973; pp 267–28.
  • [23] Akaike H., Likelihood of a model and information criteria, Journal of Econometrics., 16 (1981) 3-14.
  • [24] Bozdogan H., Model selection and Akaike’s information criterion (AIC): the general theory and its analytical extensions. Psychometrika., 52(3) (1987), 345-370.
  • [25] Browne M.W. and Cudeck R., Alternative ways of assessing model fit. In: K. A. Bollen & J. S. Long (Eds.), Testing structural equation models, Beverly Hills, CA: Sage Publication, 1993; pp136-162.
  • [26] Bozdogan H., Akaike's Information Criterion and Recent Developments in Information Complexity. Journal of Mathematical Psychology., 44 (2000) 62-91.
  • [27] Bozdogan H., Choosing the number of component clusters in the mixture-model using a new informational complexity criterion of the inverse-fisher information matrix. Information and Classification, Concepts, Methods and Applications Proceedings of the 16th Annual Conference of the “Gesellschaft für Klassifikation e.V.” University of Dortmund, April 1–3, 1992.
  • [28] Scharwz G., Estimating the dimension of a model, The Annals of Statistics, 6 (1978) 461-464.
  • [29] Mallows C.L., Some commet on Cp, Technometrics., 8 (1973) 661-675.
  • [30] Cheung G.W. and Rensvold R.B., Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance, Structural Equation Modeling., 9(2) (2002), 233-255.
  • [31] Anderson D.R., Burnham K.P. and White G.C., Comparison of akaike information criterion and consistent Akaike information criterion for model selection and statistical inference from capture-recapture studies. Journal of Applied Statistics,. 25(2) (1998), 263-282.
  • [32] Muthén B.O., Latent variable structural equation modeling with categorical data. Journal of Econometrics., 22 (1983) 48-65.
  • [33] Muthén B.O. and Kaplan D., A comparison of some methodologies for the factor analysis of non- normal Likert variables. British Journal of Mathematical and Statistical Psychology., 38 (1985) 171-189.
  • [34] Jöreskog K.G., Latent variable modeling with ordinal variables. Paper presented at the international Workshop on statistical Modeling and Latent Variables in Trento, Italy, 1991.
  • [35] Muthén B.O. and Satorra A., Technical aspects of Muthen’s LISCOMP approach to estimation of latent variable relations with a comprehensive measurement model. Psychometrika, 60 (1995) 489-503.
  • [36] J.R. Hipp J.R. and Bollen K.A., Model fit in structural equation models with censored, ordinal, and dichotomous variables: Testing vanishing tetrads, Sociological Methodology., 33(1) (2003), 267-305.
  • [37] Flora D.B. and Curran P.J., An emprical evaluation of Alternative methods of estimation for confirmatory factor analysis with ordinal data. Psyco Methods., 9(4) (2004), 466-491.
  • [38] Forero C. G., Maydeu-Olivares M. and Gallardo-Pujol D., Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling., 16 (2009) 625–641.
  • [39] Beauducel A., and Herzberg P: Y., On the performance of maxi- mum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling., 13 (2006) 186– 203.
  • [40] DiStefano C., The impact of categorization with confirmatory factor analysis. Structural Equation Modeling., 9 (2002) 327–346.
  • [41] Yang-Wallentin F., Jöreskog K.G. and H. Luo H., Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling., 17 (2010) 392–423.
  • [42] Savalei V. and Rhemtull M., The performance of robust test statistics with categorical data, British Journal of Mathematical and Statistical Psychology., 66 (2013) 201-223.
  • [43] Rhemtulla M., Brosseau-Liard P.E. and Savalei V., 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) (2012) 354-373.
  • [44] DiStefano C. and Morgan B.G., A comparison of diagonal weighted least squares robust estimation techniques for ordinal data, Structural Equation Modeling: A Multidisciplinary Journal., 21(3) (2014) 425-438.
  • [45] Li C.H., Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavioral Research., 48 (2016) 936–949.
  • [46] Byrne M.B., Equation modeling Computer Software Snapshots of LISREL, EQS, Amos, and Mplus. Hoyle RH. (Ed.) Handbook of Structural Equation Modeling, Guilford Press, 2012; pp 195-208.
  • [47] Gazeloğlu C., Methods for Estimating Weighted and Unweighted Parameters and Informatıon criteria used in structural equation modeling of ordinal categorical data and comparison of results with different sample sizes. Unpublished doctoral thesis, Anadolu University, 2016.
  • [48] Doğan İ. and Özdamar K., The effect of different data structures, sample sizes on model fit measures. Communication in Statistics-Simulation and Computation., 46(9) (2017) 7525-7533 .

Comparison of weighted least squares and robust estimation in structural equation modeling of ordinal categorical data with larger sample sizes

Year 2020, , 193 - 211, 22.03.2020

Cengiz Gazeloglu , Zerrin Aşan Greenacre

https://doi.org/10.17776/csj.648054
Cited By: 4

Abstract

The effect of different sample sizes on estimation methods such as weighted least squares and robust weighted least squares that are used in structural equation modeling was studied and compared using information criteria such as Akaike Information Criteria in this study. The simulations were repeated 1000 times with two estimation methods and the average values of criteria were calculated with different sample sizes. The study includes a construct of four factors, with four questions of each that are measured on a five-point Likert scale. Different sample sizes, ranging from 300 to 5000 were selected. According to the simulations results, it is concluded that the robust estimation method provides more effective results at lower sample size. In addition, it was found that as the sample size increases, the efficiency difference between two methods gradually decreases. Moreover, it was detected that there is almost no difference between the two methods for sample sizes over 3000.

Keywords

Structural equation modeling categorical data information criteria simulation

Project Number

1506F501

References

  • [1] Agresti A., Categorical Data Analysis, Second edition, John Wiley Sons, 2003.
  • [2] Edward C., Wirht R.J., Houts C.R. and Xi N., Categorical Data in The Structural Equation Modeling Framework. Hoyle RH. (Ed.) Handbook of Structural Equation Modeling. Guilford Press, 2012;. 195-208.
  • [3] Arıcıgil Ç., Sosyal Bilimlerde Kategorik Verilerle İlişki Analizi, (Second Edition), Ankara, Pegem Akademi, 2013.
  • [4] Kateri M., Contingency Table Analysis Methods and Implementation Using R, New York, Springer, 2014.
  • [5] Agresti A., Booth J.G., Hobert J.P. and Caffo B., Random-Effects modeling of Categorical Response Data. Sociological Methodology., 30 (2000) 27-80.
  • [6] Akıncı E.D., Yapısal eşitlik modellerinde bilgi kriterleri, Doctoral Thesis, Fen Bilimleri Enstitüsü, İstanbul, Mimar Sinan Güzel Sanatlar Üniversitesi, 2007.
  • [7] Schumacker R.E. and Lomax R.G., A beginner's guide to structural equation modeling, Third edition, Routledge, Taylor and Francis Group, LLC 2010.
  • [8] Likert R., A Technique for the Measurement of Attitudes, New York University 1932.
  • [9] Lee S.Y., Structural Equation Modeling A Bayesian Approach, England, John Wiley Sons, 2007.
  • [10] Arslan M.S.T., Ordinal değişkenli yapısal eşitlik modellerinde kullanılan parametre tahmin yöntemlerinin karşılaştırılması, Master Thesis, Fen Bilimleri Enstitüsü, Eskişehir, Eskişehir Osmangazi Üniversitesi, 2011.
  • [11] Jörekog K.G. and Sörbom D., LISREL 8: Structural Equation Modelling with the Simples Command Language, Scientific Sofware International, 1993.
  • [12] Kline R.B., Principles and Practice of Structural Equation Modelling, London, Guilford Press, 2011.
  • [13] Kline R.B., Principles and Practice of Structural Equation Modelling, London, Guilford Press, 2005.
  • [14] Schumacker R.E. and Lomax R.G., A beginner's guide to structural equation modeling, Second edition, Mahwah, Lawrence Erlbaum Associates, 2004.
  • [15] Çelik H.E., Yapısal eşitlik modellemesi ve bir uygulama: genişletilmiş online alışveriş kabul modeli, Doctoral Thesis, Fen Bilimleri Enstitüsü, Eskişehir Osman Gazi Üniversitesi, Eskişehir, 2009.
  • [16] Agresti A. , Analysis of Ordinal Categorical Data, John Wiley Sons, 2010.
  • [17] Bollen K.A., Structural Equation with Latent Variables, New York, John Wiley Sons, 1989.
  • [18] Çelik H.E., Yılmaz V., LISREL 9.1 ile Yapısal Eşitlik Modellemesi, Ankara, Anı Yayıncılık, 2013.
  • [19] Muthén B. O., A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika., 49 (1984) 115–132.
  • [20] Doğan İ., Farklı veri yapısı ve örneklem büyüklüklerinde yapısal eşitlik modellerinin geçerliliği ve güveniliğinin değerlendirilmesi. Doktora Tezi. Sağlık Bilimleri Enstitüsü. Eskişehir: Eskişehir Osmangazi Üniversitesi, 2015.
  • [21] Akaike H., A new look at the statistical model identification, IEEE Transactions on Automatic Control., 19(6) (1974), 716–723.
  • [22] Akaike H., Information theory as an extension of the maximum likelihood principle. In. B.N. Petrov and F. Csaki (Eds.), Proceedings of the Second International Symposium on Information Theory, Akademiai Kiado, Budapest, 1973; pp 267–28.
  • [23] Akaike H., Likelihood of a model and information criteria, Journal of Econometrics., 16 (1981) 3-14.
  • [24] Bozdogan H., Model selection and Akaike’s information criterion (AIC): the general theory and its analytical extensions. Psychometrika., 52(3) (1987), 345-370.
  • [25] Browne M.W. and Cudeck R., Alternative ways of assessing model fit. In: K. A. Bollen & J. S. Long (Eds.), Testing structural equation models, Beverly Hills, CA: Sage Publication, 1993; pp136-162.
  • [26] Bozdogan H., Akaike's Information Criterion and Recent Developments in Information Complexity. Journal of Mathematical Psychology., 44 (2000) 62-91.
  • [27] Bozdogan H., Choosing the number of component clusters in the mixture-model using a new informational complexity criterion of the inverse-fisher information matrix. Information and Classification, Concepts, Methods and Applications Proceedings of the 16th Annual Conference of the “Gesellschaft für Klassifikation e.V.” University of Dortmund, April 1–3, 1992.
  • [28] Scharwz G., Estimating the dimension of a model, The Annals of Statistics, 6 (1978) 461-464.
  • [29] Mallows C.L., Some commet on Cp, Technometrics., 8 (1973) 661-675.
  • [30] Cheung G.W. and Rensvold R.B., Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance, Structural Equation Modeling., 9(2) (2002), 233-255.
  • [31] Anderson D.R., Burnham K.P. and White G.C., Comparison of akaike information criterion and consistent Akaike information criterion for model selection and statistical inference from capture-recapture studies. Journal of Applied Statistics,. 25(2) (1998), 263-282.
  • [32] Muthén B.O., Latent variable structural equation modeling with categorical data. Journal of Econometrics., 22 (1983) 48-65.
  • [33] Muthén B.O. and Kaplan D., A comparison of some methodologies for the factor analysis of non- normal Likert variables. British Journal of Mathematical and Statistical Psychology., 38 (1985) 171-189.
  • [34] Jöreskog K.G., Latent variable modeling with ordinal variables. Paper presented at the international Workshop on statistical Modeling and Latent Variables in Trento, Italy, 1991.
  • [35] Muthén B.O. and Satorra A., Technical aspects of Muthen’s LISCOMP approach to estimation of latent variable relations with a comprehensive measurement model. Psychometrika, 60 (1995) 489-503.
  • [36] J.R. Hipp J.R. and Bollen K.A., Model fit in structural equation models with censored, ordinal, and dichotomous variables: Testing vanishing tetrads, Sociological Methodology., 33(1) (2003), 267-305.
  • [37] Flora D.B. and Curran P.J., An emprical evaluation of Alternative methods of estimation for confirmatory factor analysis with ordinal data. Psyco Methods., 9(4) (2004), 466-491.
  • [38] Forero C. G., Maydeu-Olivares M. and Gallardo-Pujol D., Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling., 16 (2009) 625–641.
  • [39] Beauducel A., and Herzberg P: Y., On the performance of maxi- mum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling., 13 (2006) 186– 203.
  • [40] DiStefano C., The impact of categorization with confirmatory factor analysis. Structural Equation Modeling., 9 (2002) 327–346.
  • [41] Yang-Wallentin F., Jöreskog K.G. and H. Luo H., Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling., 17 (2010) 392–423.
  • [42] Savalei V. and Rhemtull M., The performance of robust test statistics with categorical data, British Journal of Mathematical and Statistical Psychology., 66 (2013) 201-223.
  • [43] Rhemtulla M., Brosseau-Liard P.E. and Savalei V., 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) (2012) 354-373.
  • [44] DiStefano C. and Morgan B.G., A comparison of diagonal weighted least squares robust estimation techniques for ordinal data, Structural Equation Modeling: A Multidisciplinary Journal., 21(3) (2014) 425-438.
  • [45] Li C.H., Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavioral Research., 48 (2016) 936–949.
  • [46] Byrne M.B., Equation modeling Computer Software Snapshots of LISREL, EQS, Amos, and Mplus. Hoyle RH. (Ed.) Handbook of Structural Equation Modeling, Guilford Press, 2012; pp 195-208.
  • [47] Gazeloğlu C., Methods for Estimating Weighted and Unweighted Parameters and Informatıon criteria used in structural equation modeling of ordinal categorical data and comparison of results with different sample sizes. Unpublished doctoral thesis, Anadolu University, 2016.
  • [48] Doğan İ. and Özdamar K., The effect of different data structures, sample sizes on model fit measures. Communication in Statistics-Simulation and Computation., 46(9) (2017) 7525-7533 .
There are 48 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Natural Sciences
Authors

Cengiz Gazeloglu 0000-0002-8222-3384

Zerrin Aşan Greenacre 0000-0002-2098-3118

Project Number 1506F501
Publication Date March 22, 2020
Submission Date November 18, 2019
Acceptance Date January 13, 2020
Published in Issue Year 2020

Cite

APA Gazeloglu, C., & Aşan Greenacre, Z. (2020). Comparison of weighted least squares and robust estimation in structural equation modeling of ordinal categorical data with larger sample sizes. Cumhuriyet Science Journal, 41(1), 193-211. https://doi.org/10.17776/csj.648054

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