GENERATING MULTIVARIATE DATA FROM NONNORMAL DISTRIBUTIONS - MIHAL ANDBARRETT REVISITED

An algorithm described by Graybill (1969) factors a population correla tion matrix, R, into an upper and lower triangular matrix, T and T', s uch that R = T'T. The matrix T is used to generate multivariate data s ets from a multinormal distribution. When this algorithm is used to ge nerate data for nonnormal distributions, however, the sample correlati ons are systematically biased downward. We describe an iterative techn ique that removes this bias by adjusting the initial correlation matri x, R, factored by the Graybill algorithm. The method is illustrated by simulating a multivariate study by Mihal and Barrett (1976). Large-N simulations indicate that the iterative technique works: multivariate data sets generated with this approach successfully model both the uni variate distributions of the individual variables and their multivaria te structure (as assessed by intercorrelation and regression analyses) .