[1] P.M. Bentler and D.G. Bonett, Significance tests and goodness of fit in the analysis of covariance structures,
Psycho. Bull. 88 (1980) 588–606.
[2] P.M. Bentler, EQS 6 structural equations program manual, In Los Angeles: BMDP Statistic Software, 2006
[3] P.M. Bentler and P. Dudgeon, Covariance structure analysis: statistical practice, theory, and directions, Annual
Rev. Psycho. 47 (1996) 563–592.
[4] P.M. Bentler and K.H. Yuan, Structural equation modeling with small samples:Test statistics, Mult. Behav. Res.
34 (1999) 181–197.
[5] J. Biggs, Evaluation of the effect of outliers on the GFI quality adjustment index in structural equation models
and proposal of alternative quality indices, Commun. Stat. Simul. Comput. 46 (2013) 5–9.
[6] K.A. Bollen, Outliers and improper solutions: A confirmatory factor analysis example, Socio. Meth. Res. 15
(1987) 375–384.
[7] K.A. Bollen, Structural Equations with Latent Variables, John Wiley & Sons, 1989.
[8] P.E. Brosseau-Liard and V. Savalei, Adjusting incremental fit indices for nonnormality, Mult. Behav. Res. 49
(2014) 460–470.
[9] P.E. Brosseau-Liard, V. Savalei and L. Li, An investigation of the sample performance of two nonnormality
corrections for RMSEA, Mult. Behav. Res. 47 (2012) 904–930.
[10] M.W. Browne, Asymptotically distribution-free methods for the analysis of covariance structures, British J. Math.
Stat. Psycho. 37 (1984) 62–83.
[11] W.M. Browne, Generalized Least Squares Estimators in the Analysis of Covariance Structures, ETS Res. Bull.
Ser. 1973 (1) 1–36.[12] W.M. Browne and R. Cudeck, Alternative ways of assessing model fit, Socio. Meth. Res. 21 (1992) 230–258.
[13] B.M. Byrne, Structural Equation Modeling with Mplus: Basic Concepts, Applications and Programming, Routledge, 2013
[14] S. Cangur and I. Ercan, Comparison of model fit indices used in structural equation modeling under multivariate
normality, J. Modern Appl. Stat. Meth. 14 (2015) 152–167.
[15] C. Cheng and H. Wu, Confidence Intervals of Fit Indexes by Inverting a Bootstrap Test, Struct. Equ. Mod. 24
(2017) 870–880.
[16] M.A. Cirillo and L.P. Barroso, Effect of outliers on the GFI quality adjustment index in structural equation model
and proposal of alternative indices, Commun. Stat. Simul. Comput. 64 (2017) 1895–1905.
[17] J.E. Collier, Applied structural equation modeling using AMOS: Basic to advanced techniques, Routledge, 2020.
[18] A. Crisci, Estimation methods for the structural equation models: maximum likelihood, partial least squares and
generalized maximum entropy, J. Appl. Quant. Meth. 7 (2012) 7–10.
[19] S.J. Devlin, R. Gnanadesikan and J.R. Kettenring, Robust estimation of dispersion matrices and principal components, J. Amer. Stat. Assoc. 76 (1981) 354–362.
[20] M. Harwell, A strategy for using bias and RMSE as outcomes in Monte Carlo studies in statistics, J. Modern
Appl. Stat. Meth. 17 (2018).
[21] L. Hildreth, Residual Analysis for Structural Equation Modeling, Statistics, PhD., 2013.
[22] L.T. Hu and P.M. Bentler, Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria
versus new alternatives, Struct. Equ. Model. 6 (1999) 1–55.
[23] S.R. HutChinson and A. Olmos, Behavior of descriptive fit indexes in confirmatory factor analysis using ordered
categorical data, Struct. Equ. Model. 5 (1998) 344–364.
[24] S. Jalal and P.M. Bentler, Using Monte Carlo normal distributions to evaluate structural models with nonnormal
data, Struct. Equ. Model. 25 (2018) 541–557.
[25] R.B. Kline, Principles and practices of structural equation modelling, In Methodology in the social sciences, (4th
ed.). Guilford publications, 2016.
[26] S.Y. Lee, Structural Equation Modeling A Bayesian Approach, John Wiley & Sons, 2007.
[27] C.H. Li, The performance of MLR, USLMV, and WLSMV estimation in structural regression models with ordinal
variables, J. Chem. Inf. Model. 53 (2014) 1689–1699.
[28] R. J. Magnus and H. Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics,
John Wiley & Sons, 2019.
[29] A. Maydeu-Olivares, D. Shi and Y. Rosseel, Assessing fit in structural equation models: A Monte-Carlo evaluation
of RMSEA versus SRMR confidence intervals and tests of close fit, Struc. Equ. Model. 25 (2018) 389–402.
[30] H. Midi, H.T. Hendi, J. Arasan and H. Uraibi,Fast and robust diagnostic technique for the detection of high
leverage points, Pertanika J. Sci. Tech. 28 (2020) 1203–1220.
[31] H. Ogasawara, Standard errors of fit indices using residuals in structural equation modeling, Psychometrika 66
(2001) 421–436.
[32] D.J. Olive and D. Hawkins, Robust multivariate location and dispersion, Unpublished Manuscript Available From
(Http://Www. Math. Siu. Edu/Olive/Pphbmld.Pdf), (2010) 1–30.
[33] D.J. Olive, Robust Multivariate Analysis, Springer, 2017.
[34] D.J. Olive and D.M. Hawkins, High breakdown multivariate estimators, (2008) 1–29.
[35] J. Palomo, D.B. Dunson and K. Bollen, Bayesian Structural Equation Modeling, In Handbook of Latent Variable
and Related Models, 2007.
[36] M. Rhemtulla, P.E. Brosseau-Liard and V. Savalei, When can categorical variables be treated as continuous? A
comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions, Psycho.
Meth. 17 (2012) 354–373.
[37] E.E. Rigdon, CFI versus RMSEA: A comparison of two fit indexes for structural equation modeling, Struct. Equ.
Model. 3 (1996) 369–379.
[38] P.J. Rousseeuw and K. VanDriessen, A fast algorithm for the minimum covariance determinant estimator, Technom. 41 (1999) 212–223.
[39] V. Savalei, Expected versus observed information in SEM with incomplete normal and nonnormal data, Psycho.
Meth. 15 (2010) 352–367.
[40] V. Savalei, Understanding robust corrections in structural equation modeling, Struct. Equ. Model. 21 (2014) 149–
160.
[41] K. Schermelleh-Engel, H. Moosbrugger and H. M¨uller, Evaluating the fit of structural equation models: Tests of
significance and descriptive goodness-of-fit measures, MPR-Online, 8 (2003) 23–74.
[42] R.E. Schumacker and R. G. Lomax,A Beginner’s Guide to Structural Equation Modeling, New York, NY: Taylorand Francis Group, LLC, 2010.
[43] J.D. Schweig, Multilevel factor analysis and student ratings of instructional practice, UCLA. 2014.
[44] D. Shi, A. Maydeu-Olivares and Y. Rosseel, Assessing Fit in Ordinal Factor Analysis Models: SRMR vs. RMSEA,
Struct. Equ. Model. 27 (2020) 1–15.
[45] B.G. Tabachnick and L.S. Fidell, Using Multivariate Statistics, Pearson Boston, 2014
[46] N.H. Timm, Applied Multivariate Analysis, Springer,New York Berlin Heidelberg, 2002
[47] X. Tong, Evaluation of the Robustness of Modified Covariance Structure Test Statistics, University of California,
Los Angeles, 2012
[48] H. S. Uraibi and H. Midi, On robust bivariate and multivariate correlation coefficient, Econ. Comput. Econ.
Cyber. Stud. Res. 53 (2019) 221–239.
[49] H.S. Uraibi, H. Midi and S. Rana, Robust multivariate least angle regression, Sci. Asia 43 (2017) 56–60.
[50] C.D. Vale and V.A. Maurelli, Simulating multivariate nonnormal distributions, Psychometrika 48 (1983) 465–471.
[51] J. Wang and X. Wang,Structural equation modeling: Applications using Mplus, John Wiley & Sons, 2020.
[52] Y. Xia and Y. Yang, RMSEA, CFI, and TLI in structural equation modeling with ordered categorical data: The
story they tell depends on the estimation methods, Behav. Res. Meth. 51 (2019) 409–428.
[53] F. Yang-Wallentin, K.G. J¨oreskog and H. Luo, Confirmatory factor analysis of ordinal variables with misspecified
models, Struct. Equ. Model. 17 (2010) 392–423.
[54] K.H. Yuan and P. Bentler, Normal theory based test statistics in structural equation modelling, British J. Math.
Stat. Psycho. 51 (1998) 289–309.
[55] K. H. Yuan and P. Bentler, Effect of outliers on estimators and tests in covariance structure analysis, British J.
Math. Stat. Psycho. 54 (2001) 161–175.
[56] K. H. Yuan, P. M. Bentler and W. Zhang, The effect of skewness and kurtosis on mean and covariance structure
analysis: The univariate case and its multivariate implication, Soc. Meth. Res. 34 (2005) 240–258.
[57] K. H. Yuan, W. Chan and P.M. Bentler, Robust transformation with applications to structural equation modelling,
British J. Math. Stat. Psycho. 53 (2000) 31–50.
[58] K. H. Yuan and K. Hayashi, Standard errors in covariance structure models: Asymptotics versus bootstrap, British
J. Math. Stat. Psycho. 59 (2006) 397–417.
[59] J. Zhang, Applications of a robust dispersion estimator, Doctoral dissertation, Southern Illinois University Carbondale, 2011.
[60] J. Zhang, D. J. Olive and P. Ye,Robust covariance matrix estimation with canonical correlation analysis, Int. J.
Stat. Prob. 1 (2012) 119–136.