Simulating Multivariate Random Normal Data using Statistical Computing Platform R

Abstract

Many faculty members, as well as students, in the area of educational research methodology, sometimes have a need for generating data to use for simulation and computation purposes, demonstration of multivariate analysis techniques, or construction of student projects or assignments. As a great teaching tool, using simulated data helps us understand the intricacies of statistical concepts and techniques. The process of generating multivariate normal data is a nontrivial process and practical guides without dense mathematics are limited in the literature (Nissen and Saft, 2014). Hence, the purpose of this paper is to offer researchers a practical guide for and a quick access to generating multivariate random data with a given mean and variance-covariance structure. A detailed outline of simulating multivariate normal data with a given mean and variancecovariance matrix using Eigen (or spectral) and Cholesky decompositions is presented and implemented in statistical computing platform R version 3.4.4 (R Core Team, 2018).