Optimizing Ridge Generalized Least Squares for Structural Equation Modeling

References

• Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49(2), 155–173. doi:10.1007/BF02294170
   Web of Science ®Google Scholar
• Blanca, M. J., Arnau, J., López-Montiel, D., Bono, R., & Bendayan, R. (2013). Skewness and kurtosis in real data samples. Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 9(2), 78–84. doi:10.1027/1614-2241/a000057
   Web of Science ®Google Scholar
• Boomsma, A. (1982). The robustness of lisrel against small sample sizes in factor analysis models. In K. G. Jöreskog & H. Wold (Eds.), Systems under indirect observation: Causality, structure, prediction (Part I) (pp. 149–173). Amsterdam, The Netherlands: North-Holland.
   Google Scholar
• Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37(1), 62–83. doi:10.1111/bmsp.1984.37.issue-1
   PubMed Web of Science ®Google Scholar
• Browne, M. W., MacCallum, R. C., Kim, C.-T., Andersen, B. L., & Glaser, R. (2002). When fit indices and residuals are incompatible. Psychological Methods, 7(4), 403–421. doi:10.1037/1082-989X.7.4.403
   PubMed Web of Science ®Google Scholar
• Cain, M. K., Zhang, Z., & Yuan, K.-H. (2017). Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence, and estimation. Behavior Research Methods, 49(5), 1716–1735. doi:10.3758/s13428-016-0814-1
   PubMed Web of Science ®Google Scholar
• Drezner, Z., Marcoulides, G. A., & Salhi, S. (1999). Tabu search model selection in multiple regression analysis. Communications in Statistics-Simulation and Computation, 28(2), 349–367. doi:10.1080/03610919908813553
   Web of Science ®Google Scholar
• Friedman, J., Hastie, T., & Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33(1), 1–22. doi:10.18637/jss.v033.i01
   PubMed Web of Science ®Google Scholar
• Glover, F. (1986). Future paths for integer programming and links to artificial intelligence. Computers & Operations Research, 13(5), 533–549. doi:10.1016/0305-0548(86)90048-1
   Web of Science ®Google Scholar
• Hu, L., Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112(2), 351–362. doi:10.1037/0033-2909.112.2.351
   PubMed Web of Science ®Google Scholar
• Jöreskog, K. G., & Sörbom, D. (1996). Lisrel 8: User’s reference guide. Chicago, IL: Scientific Software International.
   Google Scholar
• Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156–166. doi:10.1037/0033-2909.105.1.156
   Web of Science ®Google Scholar
• Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. V. Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399–419). Thousand Oaks, CA: Sage.
   Google Scholar
• Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological), 58(1), 267–288.
   Web of Science ®Google Scholar
• Yang, M., Jiang, G., & Yuan, K.-H. (2017). The performance of ten modified rescaled statistics as the number of variables increases. Structural Equation Modeling, 25(3), 414–438. doi:10.1080/10705511.2017.1389612
   Web of Science ®Google Scholar
• Yuan, K.-H., & Bentler, P. M. (1997). Improving parameter tests in covariance structure analysis. Computational Statistics & Data Analysis, 26(2), 177–198. doi:10.1016/S0167-9473(97)00025-X
   Web of Science ®Google Scholar
• Yuan, K.-H., & Bentler, P. M. (1998). Normal theory based test statistics in structural equation modelling. British Journal of Mathematical and Statistical Psychology, 51(2), 289–309. doi:10.1111/bmsp.1998.51.issue-2
   PubMedGoogle Scholar
• Yuan, K.-H., & Bentler, P. M. (2017). Improving the convergence rate and speed of fisher-scoring algorithm: Ridge and anti-ridge methods in structural equation modeling. Annals of the Institute of Statistical Mathematics, 69(3), 571–597. doi:10.1007/s10463-016-0552-2
   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(2), 163–179. doi:10.1080/10705511.2015.1077335
   Web of Science ®Google Scholar
• Yuan, K.-H., Jiang, G., & Cheng, Y. (2017). More efficient parameter estimates for factor analysis of ordinal variables by ridge generalized least squares. British Journal of Mathematical and Statistical Psychology, 70(3), 525–564. doi:10.1111/bmsp.2017.70.issue-3
   PubMed 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(2), 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(6), 673–698. doi:10.1080/00273171.2017.1354759
   PubMed Web of Science ®Google Scholar
• Yung, Y.-F., & Bentler, P. M. (1996). Bootstrapping techniques in analysis of mean and covariance structures. In G. A. Marcoulides & R. E. Schumacker (Eds.), Advanced structural equation modeling: Techniques and issues (pp. 195–226). Hillsdale, NJ: Erlbaum.
   Google Scholar