Mean and Variance Corrected Test Statistics for Structural Equation Modeling with Many Variables

References

• Bartlett, M. S. (1954). A note on the multiplying factors in various χ2 approximations. Journal of the Royal Statistical Society B, 16, 296–298.
   Google Scholar
• Bentler, P. M., & Yuan, K.-H. (1999). Structural equation modeling with small samples: Test statistics. Multivariate Behavioral Research, 34, 181–197. doi:10.1207/S15327906Mb340203
   PubMed Web of Science ®Google Scholar
• Cribari-Neto, F., & Cordeiro, G. M. (1996). On Bartlett and Bartlett-type corrections. Econometric Reviews, 15, 339–367. doi:10.1080/07474939608800361
   Google Scholar
• Deng, L., Yang, M., & Marcoulides, K. M. (2018). Structural equation modeling with many variables: A systematic review of issues and developments. Frontiers in Psychology, 9, 580. doi:10.3389/fpsyg.2018.00580
   PubMed Web of Science ®Google Scholar
• Forbes, C., Evans, M., Hastings, N., & Peacock, B. (2011). Statistical distributions (4th ed.). Hoboken, NJ: Wiley.
   Google Scholar
• Hu, L. T., Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112, 351–362. doi:10.1037/0033-2909.112.2.351
   PubMed Web of Science ®Google Scholar
• Huang, P. H., Chen, H., & Weng, L. J. (2017). A penalized likelihood method for structural equation modeling. Psychometrika, 82, 329–354. doi:10.1007/s11336-017-9566-9
   PubMed Web of Science ®Google Scholar
• Jackson, D. L. (2001). Sample size and number of parameter estimates in maximum likelihood confirmatory factor analysis: A Monte Carlo investigation. Structural Equation Modeling, 8, 205–223. doi:10.1207/s15328007sem0802_3
   Web of Science ®Google Scholar
• Jacobucci, R., Grimm, K. J., & McArdle, J. J. (2016). Regularized structural equation modeling. Structural Equation Modeling, 23, 555–566. doi:10.1080/10705511.2016.1154793
   PubMed Web of Science ®Google Scholar
• Jiang, G., & Yuan, K.-H. (2017). Four new corrected statistics for SEM with small samples and nonnormally distributed data. Structural Equation Modeling, 24, 479–494. doi:10.1080/10705511.2016.1277726
   Web of Science ®Google Scholar
• Mardia, K. V. (1970). Measure of multivariate skewness and kurtosis with applications. Biometrika, 57, 519–530. doi:10.1093/biomet/57.3.519
   Web of Science ®Google Scholar
• Maronna, R. A., Martin, R. D., & Yohai, V. J. (2006). Robust statistics: Theory and methods. New York, NY: Wiley.
   Google Scholar
• Moshagen, M. (2012). The model size effect in SEM: Inflated goodness-of-fit statistics are due to the size of the covariance matrix. Structural Equation Modeling, 19, 86–98. doi:10.1080/10705511.2012.634724
   Web of Science ®Google Scholar
• Nevitt, J., & Hancock, G. R. (2004). Evaluating small sample approaches for model test statistics in structural equation modeling. Multivariate Behavioral Research, 39, 439–478. doi:10.1207/s15327906mbr3903_3
   Web of Science ®Google Scholar
• Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399–419). Thousand Oaks, CA: Sage. doi:10.2307/2291370
   Google Scholar
• Shi, D., Lee, T., & Terry, R. A. (2018). Revisiting the model size effect in structural equation modeling. Structural Equation Modeling, 25, 21–40. doi:10.1080/10705511.2017.1369088
   Web of Science ®Google Scholar
• Swain, A. J. (1975). Analysis of parametric structures for variance matrices ( Doctoral dissertation). University of Adelaide, Adelaide, Australia.
   Google Scholar
• Tong, X., & Bentler, P. M. (2013). Evaluation of a new mean scaled and moment adjusted test statistic for SEM. Structural Equation Modeling, 20, 148–156. doi:10.1080/10705511.2013.742403
   PubMed Web of Science ®Google Scholar
• Tong, X., Zhang, Z., & Yuan, K.-H. (2014). Evaluation of test statistics for robust structural equation modeling with nonnormal missing data. Structural Equation Modeling, 21, 553–565. doi:10.1080/10705511.2014.919820
   Web of Science ®Google Scholar
• Wakaki, H., Eguchi, S., & Fujikoshi, Y. (1990). A class of tests for a general covariance structure. Journal of Multivariate Analysis, 32, 313–325. doi:10.1016/0047-259x(90)90089-z
   Web of Science ®Google Scholar
• Weisberg, S. (1985). Applied linear regression (2nd ed.). New York, NY: John Wiley.
   Google Scholar
• Yang, M., Jiang, G., & Yuan, K.-H. (2018). The performance of ten modified rescaled statistics as the number of variables increases. Structural Equation Modeling, 25, 414–438. doi:10.1080/10705511.2017.1389612
   Web of Science ®Google Scholar
• Yuan, K.-H., & Bentler, P. M. (1998). Structural equation modeling with robust covariances. Sociological Methodology, 28, 363–396. doi:10.1111/0081-1750.00052
   Web of Science ®Google Scholar
• Yuan, K.-H., & Chan, W. (2008). Structural equation modeling with near singular covariance matrices. Computational Statistics & Data Analysis, 52, 4842–4858. doi:10.1016/j.csda.2008.03.030
   Web of Science ®Google Scholar
• Yuan, K.-H., & Chan, W. (2016). Structural equation modeling with unknown population distributions: Ridge generalized least squares. Structural Equation Modeling, 23, 163–179. doi:10.1080/10705511.2015.1077335
   Web of Science ®Google Scholar
• Yuan, K.-H., Chan, W., & Bentler, P. M. (2000). Robust transformation with applications to structural equation modelling. British Journal of Mathematical and Statistical Psychology, 53, 31–50.
   PubMed Web of Science ®Google Scholar
• Yuan, K.-H., Jiang, G., & Yang, M. (2018). Mean and mean-and-variance corrections with big data. Structural Equation Modeling, 25, 214–229. doi:10.1080/10705511.2017.1379012
   Web of Science ®Google Scholar
• Yuan, K.-H., Tian, Y., & Yanagihara, H. (2015). Empirical correction to the likelihood ratio statistic for structural equation modeling with many variables. Psychometrika, 80, 379–405. doi:10.1007/s11336-013-9386-5
   PubMed Web of Science ®Google Scholar
• Yuan, K.-H., Yang, M., & Jiang, G. (2017). Empirically corrected rescaled statistics for SEM with small N and large P. Multivariate Behavioral Research, 52, 673–698. doi:10.1080/00273171.2017.1354759
   PubMed Web of Science ®Google Scholar
• Yuan, K.-H., & Zhong, X. (2013). Robustness of fit indices to outliers and leverage observations in structural equation modeling. Psychological Methods, 18, 121–136. doi:10.1037/a0031604
   PubMed Web of Science ®Google Scholar