A method for generating realistic correlation matrices

Simulating sample correlation matrices is important in many areas of statistics. Approaches such as generating Gaussian data and finding their sample correlation matrix or generating random uniform [−1, 1] deviates as pairwise correlations both have drawbacks. We develop an algorithm for adding noise, in a highly controlled manner, to general correlation matrices. In many instances, our method yields results which are superior to those obtained by simply simulating Gaussian data. Moreover, we demonstrate how our general algorithm can be tailored to a number of different correlation models. Using our results with a few different applications, we show that simulating correlation matrices can help assess statistical methodology. SRG partially supported by National Science Foundation Grant DMS-1001614. JH and DG partially supported by the Institute for Pure and Applied Mathematics, National Science Foundation Grant DMS-0931852. DG was also supported in part by a fellowship from the Edmond J. Safra center for Bioinformatics at Tel-Aviv University. R code available at http://pages.pomona.edu/~jsh04747/research/simcor.r.