References
- Bates, D., & Maechler, M. (2019). Matrix: Sparse and dense matrix classes and methods [Computer software manual]. https://CRAN.R-project.org/package=Matrix(Rpackageversion1.2–18)
- Bentler, P. (2006). Eqs 6 structural equations program manual. Multivariate Software, Inc.
- Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62–83. https://doi.org/https://doi.org/10.1111/j.2044-8317.1984.tb00789.x
- Burkardt, J. (2014). The truncated normal distribution (Tech. Rep.). Department of Scientific Computing Website, Florida State University.
- 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, 1716–1735. https://doi.org/https://doi.org/10.3758/s13428-016-0814-1
- Cario, M. C., & Nelson, B. L. (1997). Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix (Tech. Rep.). Department of Industrial Engineering and Management Sciences, Northwestern University.
- Fleishman, A. (1978). A method for simulating non-normal distributions. Psychometrika, 43(4), 521–532. https://doi.org/https://doi.org/10.1007/BF02293811
- Foldnes, N., & Grønneberg, S. (2015). How general is the Vale–Maurelli simulation approach? Psychometrika, 80, 1066–1083. https://doi.org/https://doi.org/10.1007/s11336-014-9414-0
- Foldnes, N., & Grønneberg, S. (2017). The asymptotic covariance matrix and its use in simulation studies. Structural Equation Modeling: A Multidisciplinary Journal, 24, 881–896. doi:https://doi.org/10.1080/10705511.2017.1341320.
- Foldnes, N., & Grønneberg, S. (2019). On identification and non-normal simulation in ordinal covariance and item response models. Psychometrika, 84, 1000–1017. https://doi.org/https://doi.org/10.1007/s11336-019-09688-z
- Foldnes, N., & Grønneberg, S. (2020a). Pernicious polychorics: The impact and detection of underlying non- normality. Structural Equation Modeling: A Multidisciplinary Journal, 27, 525–543. doi:https://doi.org/10.1080/10705511.2019.1673168.
- Foldnes, N., & Grønneberg, S. (2020b). covsim: Simulate from distributions with given covariance matrix and marginal information [Computer software manual]. https://CRAN.R-project.org/package=covsim(Rpackageversion0.2.0)
- Foldnes, N., & Grønneberg, S. (2021). The sensitivity of structural equation modeling with ordinal data to underlying non-normality and observed distributional forms. Psychological Methods. (Online first). https://doi.org/https://doi.org/10.1037/met0000385
- Foldnes, N., & Olsson, U. H. (2016). A simple simulation technique for nonnormal data with prespecified skewness, kurtosis, and covariance matrix. Multivariate Behavioral Research, 51, 207–219. https://doi.org/https://doi.org/10.1080/00273171.2015.1133274
- Galarza, C. E., Kan, R., & Lachos, V. H. (2021). Momtrunc: Moments of folded and doubly truncated multivariate distributions [Computer software manual]. https://CRAN.R-project.org/package= MomTrunc (R package version 5.97)
- Grønneberg, S., & Foldnes, N. (2017). Covariance model simulation using regular vines. Psychometrika, 82, 1035–1051. https://doi.org/https://doi.org/10.1007/s11336-017-9569-6
- Grønneberg, S., & Foldnes, N. (2019). A problem with discretizing Vale-Maurelli in simulation studies. Psychometrika, 84, 554–561. https://doi.org/https://doi.org/10.1007/s11336-019-09663-8
- Grønneberg, S., & Foldnes, N. (2021). Factor analyzing ordinal items requires substantive knowledge of response marginals. Psychological Methods. (Submitted). https://doi.org/https://doi.org/10.1037/met0000385
- Grønneberg, S., Foldnes, N., & Marcoulides, K. M. (2021). covsim: An r package for simulating non-normal data for structural equation models using copulas. Journal of Statistical Software. forthcoming.
- Grønneberg, S., & Moss, J. (2021). Partial identification of latent correlations with polytomous data. Psychometrika. (Submitted).
- Higham, N. J. (2002). Computing the nearest correlation matrix—a problem from finance. IMA Journal of Numerical Analysis, 22, 329–343. https://doi.org/https://doi.org/10.1093/imanum/22.3.329
- Johnson, N. L., Kotz, S., & Balakrishnan, N. (1994). Continuous univariate distributions (Vol. 1). John Wiley & Sons.
- Jöreskog, K., & Sörbom, D. (2006). Lisrel version 8.8. lincolnwood, il: Scientific software international. Inc.
- Leppard, P., & Tallis, G. (1989). Algorithm as 249: Evaluation of the mean and covariance of the truncated multinormal distribution. Journal of the Royal Statistical Society. Series C, Applied Statistics, 38, 543–553.
- Mair, P., Satorra, A., & Bentler, P. M. (2012). Generating Nonnormal Multivariate Data Using Copulas: Applications to SEM. Multivariate Behavioral Research, 47, 547–565. https://doi.org/https://doi.org/10.1080/00273171.2012.692629
- Mardia, K. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519–530. https://doi.org/https://doi.org/10.1093/biomet/57.3.519
- Micceri, T. (1989). The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin, 105, 156.
- Ogasawara, H. (2021). A non-recursive formula for various moments of the multivariate normal distribution with sectional truncation. Journal of Multivariate Analysis, 183, 104729. https://doi.org/https://doi.org/10.1016/j.jmva.2021.104729
- Orjebin, E. (2014). A recursive formula for the moments of a truncated univariate normal distribution [Master’s thesis]. The University of Queensland. https://people.smp.uq.edu.au/YoniNazarathy/teaching_projects/studentWork/EricOrjebin_TruncatedNormalMoments.pdf
- Qu, W., Liu, H., & Zhang, Z. (2019). A method of generating multivariate non-normal random numbers with desired multivariate skewness and kurtosis. Behavior Research Methods, 51, 1–8. https://doi.org/https://doi.org/10.3758/s13428-018-1072-1
- Qu, W., & Zhang, Z. (2020). mnonr: A generator of multivariate non-normal random numbers [Computer software manual]. https://CRAN.R -project.org/package=mnonr (R package version 1.0.0)
- R Core Team. (2020). R: A language and environment for statistical computing [Computer software manual]. https://www.R-project.org/
- Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48, 1–36. https://doi.org/https://doi.org/10.18637/jss.v048.i02
- Shorack, G. R., & Wellner, J. A. (2009). Empirical processes with applications to statistics (Vol. 59). Society for Industrial and Applied Mathematics (SIAM.
- Touloumis, A. (2016). Simulating correlated binary and multinomial responses under marginal model specification: The simcormultres package. The R Journal, 8, 79–91. https://doi.org/https://doi.org/10.32614/RJ-2016-034
- Vale, C. D., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48, 465–471. https://doi.org/https://doi.org/10.1007/BF02293687
- Wilhelm, S., & Manjunath, B. G. (2015). tmvtnorm: Truncated multivariate normal and student t distribution [Computer software manual]. http://CRAN.R-project.org/package=tmvtnorm(Rpackageversion1.4–10)