Research Article
BibTex RIS Cite

Asymptotic Relative Efficiency Comparison for some Fit Indices in Structural Equation Modeling

Year 2024, , 164 - 167, 28.03.2024

İlkay Doğan , İsmet Doğan , Nurhan Dogan

https://doi.org/10.17776/csj.1328880

Abstract

There are many fit statistics used in the structural equation modeling, and new ones are consistently being developed. Because of the variety of fit statistics, it is very important to be able to decide which fit statistics are appropriate to use in studies. When comparing any two statistics, the asymptotic relative efficiency (ARE) between them is used. The ARE can use as a power of the fit indices is one of the familiar optimal criteria. It is frequently more convenient, and also more suggestive, to use a measure of relative merit called the relative efficiency. This study aimed to compare of fit indices using Fraser’s asymptotic relative efficiency. The data sets were derived from the multivariate normal distribution using the mean vector and covariance matrix. It was determined that the most efficient fit indices in terms of asymptotic relative efficiency were Z-Test of Wilson & Hilferty (W&H), Root Mean Square Error of Approximation (RMSEA), and Chi-Square indices, respectively.

Keywords

Asymptotic relative efficiency Structural equation model Fit indices

References

  • [1] Wheatcroft E., Interpreting the skill score form of forecast performance metrics. Int. J. Forecast., 35 (2) (2019) 573-579.
  • [2] Sitthiyot T., Holasut K., On the evaluation of skill in binary forecast. Thailand and The World Economy, 40 (3) (2022) 33-54.
  • [3] Baringhaus L., Gaigall D., On an asymptotic relative efficiency concept based on expected volumes of confidence regions, Statistics, 53 (6) (2019) 1396–1436.
  • [4] Nikitin Y., Asymptotic Relative Efficiency in Testing, University of Saint-Petersburg, (2010).
  • [5] Pitman E.J.G., Mimeographed Lecture Notes on Nonparametric Statistics, Columbia University, New York, (1948) 52-59.
  • [6] Chernoff H.A., Measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, Ann. Math. Stat., 23 (1952) 493–507.
  • [7] Hodges J.L., Lehmann E.L., The efficiency of some nonparametric competitors of the t –test, Ann. Math. Stat., 27 (1956) 324–335.
  • [8] Bahadur R.R., Stochastic comparison of tests. Ann. Math. Stat., 31 (1960) 276–295.
  • [9] Yuan A., Fan R., Xu J., Xue Y., Li Q., Asymptotic relative efficiencies of the score and robust tests in genetic association studies, The Open Statistics & Probability, 9 (2018) 26-41.
  • [10] Fraser D.A.S., Nonparametric Methods in Statistics, John Wiley & Sons Inc, (1957) 270-276.
  • [11] Jammalamadaka S.R., Wells M.T., A test of goodness of fit based on extreme spacings with some efficiency comparisons, Metrika, 35 (1988) 223-232.
  • [12] Puri M.L., Rao J.S., Yoon Y., A simple test for goodness of fit based on spacings with some efficiency comparisons (Report No.441). University of Wisconsin, (1976) 11-13.
  • [13] Anderson J.C., Gerbing D.W., The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis, Psychometrica, 49 (1984) 155–173. [14] Curran P.J., West, S.G., Finch J.F., The robustness of test statistics to non-normality and specification error in confirmatory factor analysis, Psychol. Methods, 1 (1) (1996) 16–29.
  • [15] Doğan İ., Özdamar K., The effect of different data structures, sample sizes on model fit measures, Commun. Stat-Simul. C., 46 (9) (2017) 7525-7533.
  • [16] Doğan İ., Farklı veri yapısı ve örneklem büyüklüklerinde yapısal eşitlik modellerinin geçerliği ve güvenirliğinin değerlendirilmesi, PhD Thesis, Eskişehir Osmangazi University, Institute of Health Sciences, (2015).
  • [17] Fan X., Thompson B., Wang L., Effects of sample size, estimation methods and model specification on structural equation modeling fit indexes, Struct. Equ. Modeling, 6 (1) (1999) 56–83.
  • [18] Doğan İ., Doğan, N., Model Performans Kriterlerinin Kronolojisine ve Metodolojik Yönlerine Genel Bir Bakış: Bir Gözden Geçirme, Türkiye Klinikleri J. Biostat., 12 (1) (2020) 114-125).
  • [19] Fan X., Sivo S.A., Sensitivity of fit indices to model misspecification and model types, Multivar. Behav. Res., 42 (3) (2007) 509–529.
  • [20] Liu C., White M., Newell G., Measuring and comparing the accuracy of species distribution models with presenceabsence data. Ecography, 34 (2) (2011) 232-243.
  • [21] Fan X., Fan X., TEACHER'S CORNER: Using SAS for Monte Carlo Simulation Research in SEM, Struct. Equ. Modeling, 12 (2) (2005) 299-333.
  • [22] Schumacker R.E., Lomax R.G., A beginner’s guide to structural equation modeling (2nd ed.). Mahlah, New Jersey,London: Lawrence Erlbaum Associates. (2004) 79-84.
  • [23] Erkorkmaz Ü., Etikan İ., Demir O., Özdamar K., Sanisoğlu S.Y., Doğrulayıcı faktör analizi ve uyum indeksleri, Turk. Klin. J. Med. Sci., 33(1) (2013) 210-223.
  • [24] Bollen, K.A. Structural equations with latent variables, New York: John Wiley & Sons, Inc., (1989) 256-289.
  • [25] Kline B.R., Principles and practice of structural modeling. New York-London: The Guilford Press, (2011) 189-230.
  • [26] Pereira H.R., Meschiatti M.C., Pires R.C.M., Blain G.C., On the performance of three indices of agreement: an easy-to-use r-code for calculating the Willmott indices, Bragantia, 77(2) (2018) 394-403.
  • [27] Weng L.J., Cheng C.P., Why might relative fit indices differ between estimators?, Struct. Equ. Modeling, 4 (2) (1997) 121-128.

Year 2024, , 164 - 167, 28.03.2024

İlkay Doğan , İsmet Doğan , Nurhan Dogan

https://doi.org/10.17776/csj.1328880

Abstract

References

  • [1] Wheatcroft E., Interpreting the skill score form of forecast performance metrics. Int. J. Forecast., 35 (2) (2019) 573-579.
  • [2] Sitthiyot T., Holasut K., On the evaluation of skill in binary forecast. Thailand and The World Economy, 40 (3) (2022) 33-54.
  • [3] Baringhaus L., Gaigall D., On an asymptotic relative efficiency concept based on expected volumes of confidence regions, Statistics, 53 (6) (2019) 1396–1436.
  • [4] Nikitin Y., Asymptotic Relative Efficiency in Testing, University of Saint-Petersburg, (2010).
  • [5] Pitman E.J.G., Mimeographed Lecture Notes on Nonparametric Statistics, Columbia University, New York, (1948) 52-59.
  • [6] Chernoff H.A., Measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations, Ann. Math. Stat., 23 (1952) 493–507.
  • [7] Hodges J.L., Lehmann E.L., The efficiency of some nonparametric competitors of the t –test, Ann. Math. Stat., 27 (1956) 324–335.
  • [8] Bahadur R.R., Stochastic comparison of tests. Ann. Math. Stat., 31 (1960) 276–295.
  • [9] Yuan A., Fan R., Xu J., Xue Y., Li Q., Asymptotic relative efficiencies of the score and robust tests in genetic association studies, The Open Statistics & Probability, 9 (2018) 26-41.
  • [10] Fraser D.A.S., Nonparametric Methods in Statistics, John Wiley & Sons Inc, (1957) 270-276.
  • [11] Jammalamadaka S.R., Wells M.T., A test of goodness of fit based on extreme spacings with some efficiency comparisons, Metrika, 35 (1988) 223-232.
  • [12] Puri M.L., Rao J.S., Yoon Y., A simple test for goodness of fit based on spacings with some efficiency comparisons (Report No.441). University of Wisconsin, (1976) 11-13.
  • [13] Anderson J.C., Gerbing D.W., The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis, Psychometrica, 49 (1984) 155–173. [14] Curran P.J., West, S.G., Finch J.F., The robustness of test statistics to non-normality and specification error in confirmatory factor analysis, Psychol. Methods, 1 (1) (1996) 16–29.
  • [15] Doğan İ., Özdamar K., The effect of different data structures, sample sizes on model fit measures, Commun. Stat-Simul. C., 46 (9) (2017) 7525-7533.
  • [16] Doğan İ., Farklı veri yapısı ve örneklem büyüklüklerinde yapısal eşitlik modellerinin geçerliği ve güvenirliğinin değerlendirilmesi, PhD Thesis, Eskişehir Osmangazi University, Institute of Health Sciences, (2015).
  • [17] Fan X., Thompson B., Wang L., Effects of sample size, estimation methods and model specification on structural equation modeling fit indexes, Struct. Equ. Modeling, 6 (1) (1999) 56–83.
  • [18] Doğan İ., Doğan, N., Model Performans Kriterlerinin Kronolojisine ve Metodolojik Yönlerine Genel Bir Bakış: Bir Gözden Geçirme, Türkiye Klinikleri J. Biostat., 12 (1) (2020) 114-125).
  • [19] Fan X., Sivo S.A., Sensitivity of fit indices to model misspecification and model types, Multivar. Behav. Res., 42 (3) (2007) 509–529.
  • [20] Liu C., White M., Newell G., Measuring and comparing the accuracy of species distribution models with presenceabsence data. Ecography, 34 (2) (2011) 232-243.
  • [21] Fan X., Fan X., TEACHER'S CORNER: Using SAS for Monte Carlo Simulation Research in SEM, Struct. Equ. Modeling, 12 (2) (2005) 299-333.
  • [22] Schumacker R.E., Lomax R.G., A beginner’s guide to structural equation modeling (2nd ed.). Mahlah, New Jersey,London: Lawrence Erlbaum Associates. (2004) 79-84.
  • [23] Erkorkmaz Ü., Etikan İ., Demir O., Özdamar K., Sanisoğlu S.Y., Doğrulayıcı faktör analizi ve uyum indeksleri, Turk. Klin. J. Med. Sci., 33(1) (2013) 210-223.
  • [24] Bollen, K.A. Structural equations with latent variables, New York: John Wiley & Sons, Inc., (1989) 256-289.
  • [25] Kline B.R., Principles and practice of structural modeling. New York-London: The Guilford Press, (2011) 189-230.
  • [26] Pereira H.R., Meschiatti M.C., Pires R.C.M., Blain G.C., On the performance of three indices of agreement: an easy-to-use r-code for calculating the Willmott indices, Bragantia, 77(2) (2018) 394-403.
  • [27] Weng L.J., Cheng C.P., Why might relative fit indices differ between estimators?, Struct. Equ. Modeling, 4 (2) (1997) 121-128.
There are 26 citations in total.

Details

Primary Language English
Subjects Biostatistics
Journal Section Natural Sciences
Authors

İlkay Doğan 0000-0001-7552-6478

İsmet Doğan 0000-0001-9251-3564

Nurhan Dogan 0000-0001-7224-6091

Publication Date March 28, 2024
Submission Date July 18, 2023
Acceptance Date March 12, 2024
Published in Issue Year 2024

Cite

APA Doğan, İ., Doğan, İ., & Dogan, N. (2024). Asymptotic Relative Efficiency Comparison for some Fit Indices in Structural Equation Modeling. Cumhuriyet Science Journal, 45(1), 164-167. https://doi.org/10.17776/csj.1328880