covsim: An R Package for Simulating Non-normal Data for Structural Equation Models Using Copulas

Abstract

In factor analysis and structural equation modeling non-normal data simulation is traditionally performed by specifying univariate skewness and kurtosis together with the target covariance matrix. However, this leaves little control over the univariate distributions and the multivariate copula of the simulated vector. In this paper we explain how a more flexible simulation method called vine-to-anything (VITA) may be obtained from copula-based techniques, as implemented in a new R package, covsim. VITA is based on the concept of a regular vine, where bivariate copulas are coupled together into a full multivariate copula. We illustrate how to simulate continuous and ordinal data for covariance modeling, and how to use the new package discnorm to test for underlying normality in ordinal data. An introduction to copula and vine simulation is provided in the appendix.