HOW TO GENERATE NONNORMAL DATA FOR SIMULATION OF STRUCTURAL EQUATION MODELS

A procedure for generating non-normal data for simulation of structura l equation models is proposed. A simple transformation of univariate r andom 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 c omputed from latent and error variables according to the model. Tt is shown that by controlling univariate skewness and kurtosis on pre-spec ified random latent and error variables, observed variables can be mad e to have a relatively wide range of univariate skewness and kurtosis characteristics according to the pre-specified model. Univariate distr ibutions are used for the generation of data which enables a user to c hoose from a large number of different distributions. The use of the p roposed procedure is illustrated for two different structural equation models and it is shown how PRELIS can be used to generate the data.