A procedure for generating non-normal data for simulation of structural equation models is proposed. A simple transformation of univariate random variables is used for the generation of data on latent and error variables under some restrictions for the elements of the covariance matrices for these variables. Data on the observed variables is then computed from latent and error variables according to the model. It is shown that by controlling univariate skewness and kurtosis on pre-specified random latent and error variables, observed variables can be made to have a relatively wide range of univariate skewness and kurtosis characteristics according to the pre-specified model. Univariate distributions are used for the generation of data which enables a user to choose from a large number of different distributions. The use of the proposed procedure is illustrated for two different structural equation models and it is shown how PRELIS can be used to generate the data.

Similar articles

A Simple Simulation Technique for Nonnormal Data with Prespecified Skewness, Kurtosis, and Covariance Matrix.

Foldnes N, et al. Multivariate Behav Res. 2016.

Effects of skewness and kurtosis on normal-theory based maximum likelihood test statistic in multilevel structural equation modeling.

Ryu E, et al. Behav Res Methods. 2011.

Generating Multivariate Ordinal Data via Entropy Principles.

Lee Y, et al. Psychometrika. 2018.

Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation.

Cain MK, et al. Behav Res Methods. 2017.

Bayesian Analysis of Structural Equation Models With Nonlinear Covariates and Latent Variables.

Song XY, et al. Multivariate Behav Res. 2006.

https://www.ncbi.nlm.nih.gov/m/pubmed/26777072/

Regards!

Dear Adriana Santos-Caballero

Thank you very much for your interesting answer, very clear and very satisfying

I am very convinced

very pleased , madam