Examining Chi-Square Test Statistics Under Conditions of Large Model Size and Ordinal Data

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
• Asparouhov, T., & Muthén, B. (2010). Simple second order chi-square correction. Retrieved from https://www.statmodel.com/download/WLSMV_new_chi21.pdf
   Google Scholar
• Bandalos, D. L. (2008). Is parceling really necessary? A comparison of results from item parceling and categorical variable methodology. Structural Equation Modeling, 15(2), 211–240. doi:10.1080/10705510801922340
   Web of Science ®Google Scholar
• Bandalos, D. L. (2014). Relative performance of categorical diagonally weighted least squares and robust maximum likelihood estimation. Structural Equation Modeling, 21(1), 102–116. doi:10.1080/10705511.2014.859510
   Web of Science ®Google Scholar
• Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus means and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling, 13(2), 186–203. doi:10.1207/s15328007sem1302_2
   Web of Science ®Google Scholar
• Beaujean, A. A. (2014). Latent variable modeling using R: A step-by-step guide. New York, NY: Routledge.
   Google Scholar
• Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: John Wiley & Sons.
   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. (1982). Covariance structures. In D. M. Hawkins (Ed.), Topics in applied multivariate analysis (pp. 72–141). Cambridge, UK: Cambridge University Press.
   Google Scholar
• Curran, P., West, S., & Finch, J. (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1(1), 16–29. doi:10.1037/1082-989X.1.1.16
   Web of Science ®Google Scholar
• Curran, P. J., Bollen, K. A., Paxton, P., Kirby, J., & Chen, F. (2002). The noncentral chi-square distribution in misspecified structural equation models: Finite sample results from a Monte Carlo simulation. Multivariate Behavioral Research, 37(1), 1–36. doi:10.1207/S15327906MBR3701_01
   PubMed Web of Science ®Google Scholar
• DiStefano, C., Liu, J., Jiang, N., & Shi, D. (2017). Examination of the weighted root mean square residual: Evidence for trustworthiness?. Structural Equation Modeling, 1–14. doi:10.1080/10705511.2017.1390394
   Web of Science ®Google Scholar
• DiStefano, C., McDaniel, H., Zhang, Y., & Shi, D. (2018). Fitting large factor analysis models with ordinal data. Manuscript submitted for publication.
   Google Scholar
• DiStefano, C., & Morgan, G. B. (2014). A comparison of diagonal weighted least squares robust estimation techniques for ordinal data. Structural Equation Modeling, 21(3), 425–438. doi:10.1080/10705511.2014.915373
   Web of Science ®Google Scholar
• Fan, X., Thompson, B., & Wang, L. (1999). Effects of sample size, estimation methods, and model specification on structural equation modeling fit indexes. Structural Equation Modeling, 6(1), 56–83. doi:10.1080/10705519909540119
   Web of Science ®Google Scholar
• Finney, S., & Distefano, C. (2006). Nonnormal and categorical data in structural equation modeling. In G. Hancock, & R. Mueller (Eds.), Structural equation modeling: A second course. Greenwich, CT: Information Age Publishing.
   Google Scholar
• Flora, D. B., & Curran, P. J. (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9(4), 466–491. doi:10.1037/1082-989X.9.4.466
   PubMed Web of Science ®Google Scholar
• Forero, C. G., Maydeu-Olivares, A., & Gallardo-Pujol, D. (2009). Factor analysis with ordinal indicators: A Monte Carlo study comparing DWLS and ULS estimation. Structural Equation Modeling, 16(4), 625–641. doi:10.1080/10705510903203573
   Web of Science ®Google Scholar
• Herzog, W., Boomsma, A., & Reinecke, S. (2007). The model-size effect on traditional and modified tests of covariance structures. Structural Equation Modeling, 14(3), 361–390. doi:10.1080/10705510701301602
   Web of Science ®Google Scholar
• Jackson, D. L., Gillaspy, J. A., & Purc-Stephenson, R. (2009). Reporting practices in confirmatory factor analysis: An overview and some recommendations. Psychological Methods, 14(1), 6–23. doi:10.1037/a0014694
   PubMed Web of Science ®Google Scholar
• Kenny, D. A., & McCoach, D. B. (2003). Effect of the number of variables on measures of fit in structural equation modeling. Structural Equation Modeling, 10(3), 333–351. doi:10.1207/S15328007SEM1003_1
   Web of Science ®Google Scholar
• Kline, R. B. (2011). Principles and practice of structural equation modeling. New York, NY: Guilford Press.
   Google Scholar
• Lei, P. W. (2009). Evaluating estimation methods for ordinal data in structural equation modeling. Quality & Quantity, 43(3), 495–507. doi:10.1007/s11135-007-9133-z
   Web of Science ®Google Scholar
• Marsh, H. W., Hau, K. T., Balla, J. R., & Grayson, D. (1998). Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research, 33(2), 181–220. doi:10.1207/s15327906mbr3302_1
   PubMed Web of Science ®Google Scholar
• Maydeu-Olivares, A., Fairchild, A. J., & Hall, A. G. (2017). Goodness of fit in item factor analysis: Effect of the number of response alternatives. Structural Equation Modeling, 24(4), 495–505. doi:10.1080/10705511.2017.1289816
   Web of Science ®Google Scholar
• Maydeu-Olivares, A., Shi, D., & Rosseel, Y. (2017). Assessing fit in structural equation models: A Monte-Carlo evaluation of RMSEA versus SRMR confidence intervals and tests of close fit. Structural Equation Modeling, 1–14. doi:10.1080/10705511.2017.1389611
   Web of Science ®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(1), 86–98. doi:10.1080/10705511.2012.634724
   Web of Science ®Google Scholar
• Muthén, B., Kaplan, D., & Hollis, M. (1987). On structural equation modeling with data that are not missing completely at random. Psychometrika, 52, 431–462.
   Web of Science ®Google Scholar
• Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 9, 599–620.
   Web of Science ®Google Scholar
• Pornprasertmanit, S., Miller, P., & Schoemann, A. (2012). R Package Simsem: Simulated structural equation modeling. Retrieved from http://cran.r-project.org
   Google Scholar
• R Development Core Team. (2015). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
   Google Scholar
• Rhemtulla, M., Brosseau-Liard, P. É. E., & Savalei, V. (2012). 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), 354–373.
   Google Scholar
• Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36. doi:10.18637/jss.v048.i02
   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 variable analysis. Applications for developmental research (pp. 399–419). Thousand Oaks, CA: Sage.
   Google Scholar
• Savalei, V., & Rhemtulla, M. (2013). The performance of robust test statistics with categorical data. British Journal of Mathematical and Statistical Psychology, 66(2), 201–223. doi:10.1111/bmsp.2013.66.issue-2
   PubMed Web of Science ®Google Scholar
• Shi, D., Lee, T., & Maydeu-Olivares, A. (2018). Understanding the model size effect on SEM fit indices. Manuscript submitted for publication.
   Google Scholar
• Shi, D., Lee, T., & Terry, R. A. (2015). Abstract: Revisiting the model size effect in structural equation modeling (SEM). Multivariate Behavioral Research, 50(1), 142. doi:10.1080/00273171.2014.989012
   PubMed Web of Science ®Google Scholar
• Shi, D., Lee, T., & Terry, R. A. (2018). Revisiting the model size effect in structural equation modeling. Structural Equation Modeling, 25(1), 21–40. doi:10.1080/10705511.2017.1369088
   Web of Science ®Google Scholar
• Shi, D., Song, H., & Lewis, M. D. (2017). The impact of partial factorial invariance on cross-group comparisons. Assessment. Advance online publication. doi:10.1177/1073191117711020
   PubMedGoogle Scholar
• Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling, 17(3), 392–423. doi:10.1080/10705511.2010.489003
   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