REFERENCES
- Asparouhov, T., & Muthén, B. (2010). Computing the strictly positive Satorra-Bentler chi-square test in Mplus. Retrieved from http://www.statmodel.com/download/webnotes/webnote12.pdf
- Bandalos, D. L. (2008). Is parceling really necessary? A comparison of results from item parceling and categorical variable methodology. Structural Equation Modeling, 15, 211–240.
- Bandalos, D. L. (2011). Performance of the ML, MLMV, WLSMV, and WLS estimators under model misspecification, nonnormality, and coarse categorization. Unpublished manuscript.
- Bandalos, D. L., & Webb, M. (2005, April). Efficacy of the WLSMV estimator for coarsely categorized and nonnormally distributed data. Paper presented at the annual meeting of the American Educational Research Association, Montreal, Canada.
- Beauducel, A., & Herzberg, P. Y. (2006). On the performance of maximum likelihood versus mean and variance adjusted weighted least squares estimation in CFA. Structural Equation Modeling, 13, 186–203.
- Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley.
- DiStefano, C. (2002). The impact of categorization with confirmatory factor analysis. Structural Equation Modeling, 9, 327–346.
- DiStefano, C., & Hess, B. (2005). Using confirmatory factor analysis for construct validation: An empirical review. Journal of Psychoeducational Assessment, 23, 225–241.
- DiStefano, C., & Seaman, M. A. (2007, April). A comparison of three robust estimators using categorical data. Paper presented at the annual conference of the American Educational Research Association, Chicago, IL.
- Finney, S. J., & DiStefano, C. (2006). Nonnormal and categorical data in structural equation modeling. In G. R. Hancock & R. O. Mueller (Eds.), Structural equation modeling: A second course (pp. 269–314). Greenwich, CT: Information Age.
- 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, 466–491.
- 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, 625–641.
- Foss, T., Jöreskog, K. G., & Olsson, U. H. (2011). Testing structural equation models: The effect of kurtosis. Computational Statistics and Data Analysis, 55, 2263–2275.
- Hoogland, J. J., & Boomsma, A. (1998). Robustness studies in covariance structure modeling: An overview and a meta-analysis. Sociological Methods & Research, 26, 329–367.
- Hutchinson, S. R., & Olmos, A. (1998). Behavior of descriptive fit indices in confirmatory factor analysis using ordered categorical data. Structural Equation Modeling, 5, 344–364.
- Jackson, D. L., Gillaspy, J. A., & Purc-Stephenson, R. (2009). Reporting practices in confirmatory factor analysis: An overview and some recommendations. Psychological Methods, 14, 6–23.
- Jöreskog, K. G. (1994). On chi-squares for the independence model and fit measures in LISREL. Retrieved from http://www.ssicentral.com/lisrel/techdocs/ftb.pdf
- Jöreskog, K. G. (2004). On chi-squares for the independence model and fit measures in LISREL Retrieved from http://ssicentral.com/lisrel/techdocs/ordinal.pdf
- Jöreskog, K., & Sörbom, D. (1996). PRELIS 2: User’s reference guide. Chicago, IL: Scientific Software International.
- Jöreskog, K., Sörbom, D., du Toit, S., & du Toit, M. (2000). LISREL 8: New statistical features. Chicago: Scientific Software International.
- Kaplan, D. (2000). Structural equation modeling: Foundations and extensions. Thousand Oaks, CA: Sage.
- Lei, P. W. (2009). Evaluating estimation methods for ordinal data in structural equation modeling. Quality & Quantity, 43, 495–507.
- Maydeu-Olivares, A. (2006). Limited information estimation and testing of discretized multivariate normal structural models. Psychometrika, 71, 57–77.
- Muthén, B. O. (1993). Goodness of fit with categorical and other nonnormal variables. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 205–243). Newbury Park, CA: Sage.
- Muthén, B. O. (1998–2004). Mplus technical appendices. Los Angeles, CA: Muthén & Muthén. Retrieved from http://www.statmodel.com/download/techappen.pdf
- Muthén, B. O., du Toit, S., & Spisic, D. (1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Unpublished manuscript.
- Muthén, B. O., & Kaplan, D. (1985). A comparison of some methodologies for the factor analysis of nonnormal Likert variables. British Journal of Mathematical and Statistical Psychology, 38, 171–189.
- Muthén, L. (2008). Baseline model in Mplus. Retrieved from http://www.statmodel.com/discussion/messages/11/3602.html?1223049639
- Muthén, L. K., & Muthén, B. O. (2006). Mplus user’s guide (4th ed.). Los Angeles, CA: Muthén & Muthén.
- Olsson, U. H., Foss, T., Troye, S. V., & Howell, R. D. (2000). The performance of ML, GLS, and WLS estimation in structural equation modeling under conditions of misspecification and nonnormality. Structural Equation Modeling, 7, 557–595.
- Oranje, A. (2003, April). Comparison of estimation methods in factor analysis with categorized variables: Applications to NAEP data. Paper presented at the annual conference of the American Educational Research Association, Chicago, IL.
- Potthast, M. J. (1993). Confirmatory factor analysis of ordered categorical variables with large models. British Journal of Mathematical & Statistical Psychology, 46, 273–286.
- Rhemtulla, M., Brosseau-Liard, P., & 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, 354–373.
- Satorra, A., & Bentler, P. M. (1988). Scaling corrections for chi-square statistics in covariance structure analysis. Proceedings of the Business and Economic Statistics Section of the American Statistical Association, 308–313.
- Schreiber, J. B., Stage, F. K., King, J., Nora, A., & Barlow, E. A. (2006). Reporting structural equation modeling and confirmatory factor analysis results: A review. Journal of Educational Research, 99, 323–337.
- West, S. G., Finch, J. F., & Curran, P. J. (1995). Structural equation models with nonnormal variables: Problems and remedies. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications (pp. 56–75). Thousand Oaks, CA: Sage.
- Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: Current approaches and future directions. Psychological Methods, 12(3), 58–79.
- Yang-Wallentin, F., Jöreskog, K. G., & Luo, H. (2010). Confirmatory factor analysis of ordinal variables with misspecified models. Structural Equation Modeling, 17, 392–423.
- Yu, C.-Y., & Muthén, B. (2002, April). Evaluation of model fit indices for latent variable models with categorical and continuous outcomes. Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA.