References
- Asparouhov, T., & Muthén, B. (2010). Simple second order chi-square correction ( Unpublished manuscript). Retrieved from www.statmodel.com/download/WLSMV_new_chi21.pdf
- Bedford, T., Cooke, R. M., & Roger M. (2002). Vines–A new graphical model for dependent random variables. The Annals of Statistics, 30, 1031–1068. doi:10.1214/aos/1031689016
- Bentler, P. (2006). Eqs 6 structural equations program manual. Encino, CA: Multivariate Software.
- Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144–152. doi:10.1111/bmsp.1978.31.issue-2
- Christoffersson, A. (1975). Factor analysis of dichotomized variables. Psychometrika, 40, 5–32. doi:10.1007/BF02291477
- Claeskens, G., & Hjort, N. L. (2008). Model selection and model averaging. Cambridge: Cambridge University Press.
- Efron, B., & Tibshirani, R. J. (1994). An introduction to the bootstrap. Boca Raton, FL: CRC press.
- 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. doi:10.1037/1082-989X.9.4.466
- Foldnes, N., & Grønneberg, S. (2015). How general is the Vale–Maurelli simulation approach?. Psychometrika, 80, 1066–1083. doi:10.1007/s11336-014-9414-0
- Foldnes, N., & Grønneberg, S. (2017a). Approximating test statistics using eigenvalue block averaging. Structural Equation Modeling, 25, 1–14.
- Foldnes, N., & Grønneberg, S. (2017b). The asymptotic covariance matrix and its use in simulation studies. Structural Equation Modeling, 24, 1–16.
- Foldnes, N., & Grønneberg, S. (2019). On identification and non-normal simulation in ordinal covariance and item response models. Psychometrika. doi:10.1007/s11336-019-09688-z
- Foldnes, N., & Olsson, U. H. (2015). Correcting too much or too little? The performance of three chi-square corrections. Multivariate Behavioral Research, 50, 533–543. doi:10.1080/00273171.2015.1036964
- Grønneberg, S., & Foldnes, N. (2017). Covariance model simulation using regular vines. Psychometrika, 84, 1–17.
- Grønneberg, S., & Foldnes, N. (2019). A problem with discretizing Vale-Maurelli in simulation studies. Psychometrika, 84, 554–561. doi:10.1007/s11336-019-09663-8
- Hofert, M., Kojadinovic, I., Maechler, M., & Yan, J. (2013). copula: Multivariate dependence with copulas [Computer software manual] (R package version 0.999-7). Retrieved from http://CRAN.R-project.org/package=copula
- Jia, F., & Wu, W. (2019). Evaluating methods for handling missing ordinal data in structural equation modeling. Behavior Research Methods, 1–19.
- Jin, S., & Yang-Wallentin, F. (2017). Asymptotic robustness study of the polychoric correlation estimation. Psychometrika, 82, 67–85. doi:10.1007/s11336-016-9512-2
- Joe, H. (1997). Multivariate models and multivariate dependence concepts (Vol. 73). Boca Raton, FL: Chapman & Hall/CRC.
- Jöreskog, K. G. (2005). Structural equation modeling with ordinal variables using lisrel. Technical report. Lincolnwood, IL: Scientific Software International, Inc.
- Jöreskog, K. G., & Sörbom, D. (2015). Lisrel 9.20 for windows [computer software]. Skokie, IL: Scientific Software International.
- Li, C.-H. (2016a). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48, 936–949. doi:10.3758/s13428-015-0619-7
- Li, C.-H. (2016b). The performance of ml, dwls, and uls estimation with robust corrections in structural equation models with ordinal variables. Psychological Methods, 21, 369. doi:10.1037/met0000093
- Maydeu-Olivares, A. (2006). Limited information estimation and testing of discretized multivariate normal structural models. Psychometrika, 71, 57–77. doi:10.1007/s11336-005-0773-4
- Maydeu-Olivares, A., Garcia-Forero, C., Gallardo-Pujol, D., & Renom, J. (2009). Testing categorized bivariate normality with two-stage polychoric correlation estimates. Methodology, 5, 131–136. doi:10.1027/1614-2241.5.4.131
- Monroe, S. (2018). Contributions to estimation of polychoric correlations. Multivariate Behavioral Research, 53, 247–266. doi:10.1080/00273171.2017.1419851
- Muthén, B. (1978). Contributions to factor analysis of dichotomous variables. Psychometrika, 43, 551–560. doi:10.1007/BF02293813
- Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators. Psychometrika, 49, 115–132. doi:10.1007/BF02294210
- Muthén, B., & Muthén, L. (2012). Mplus version 7: User’s guide. Los Angeles, CA: Muthén & Muthén.
- Nelsen, R. B. (2007). An introduction to copulas. New York, NY: Springer Science & Business Media.
- Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 44, 443–460. doi:10.1007/BF02296207
- Pearson, K. (1901). Mathematical contributions to the theory of evolution. vii. on the correlation of characters not quantitatively. Philos. Trans. R. Soc. SA, 196, 1–47.
- R Core Team. (2018). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. Retrieved from https://www.R-project.org/
- Raykov, T., & Marcoulides, G. A. (2015). On examining the underlying normal variable assumption in latent variable models with categorical indicators. Structural Equation Modeling, 22, 581–587. doi:10.1080/10705511.2014.937846
- Rhemtulla, M., Brosseau-Liard, P. É., & 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. doi:10.1037/a0029315
- Rice, J. A. (2006). Mathematical statistics and data analysis. Belmont, CA: Cengage Learning.
- Robitzsch, A. (2019). sirt: Supplementary item response theory models [Computer software manual] (R package version 3.4-64). Retrieved from https://CRAN.R-project.org/package=sirt
- Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48, 1–36. doi:10.18637/jss.v048.i02
- Satorra, A. (1989). Alternative test criteria in covariance structure analysis: A unified approach. Psychometrika, 54, 131–151. doi:10.1007/BF02294453
- Satorra, A., & Bentler, P. (1988). Scaling corrections for statistics in covariance structure analysis (UCLA statistics series 2). Los Angeles, CA: University of California at Los Angeles, Department of Psychology.
- Schepsmeier, U., Stoeber, J., Brechmann, E. C., Graeler, B., Nagler, T., & Erhardt, T. (2018). Vinecopula: Statistical inference of vine copulas [Computer software manual] (R package version 2.1.8). Retrieved from https://CRAN.R-project.org/package=VineCopula
- Sklar, M. (1959). Fonctions de repartition a n dimensions et leurs marges. Paris, France: Université Paris 8.
- Takane, Y., & De Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393–408. doi:10.1007/BF02294363
- Vale, C. D., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48, 465–471. doi:10.1007/BF02293687