A Copula Approach to Generate Non-Normal Multivariate Data for SEM

The present paper develops a procedure based on multivariate copulas for simulating multivariate non-normal data that satisfies a pre-specified covariance matrix. The covariance matrix used, can comply with a specific moment structure form (e.g., a factor analysis or a general SEM model). So the method is particularly useful for Monte Carlo evaluation of SEM models in the context of non-normal data. The new procedure for non-normal data simulation is theoretically described and also implemented on the widely used R environment. The quality of the method is assessed by performing Monte Carlo simulations. Within this context a one-sample test on the observed VC-matrix is involved. This test is robust against normality violations. This test is defined through a particular SEM setting. Finally, an example for Monte Carlo evaluation of SEM modeling of non-normal data using this method is presented.