Testing Pattern Hypotheses On Correlation Matrices: Alternative Statistics And Some Empirical Results

Abstract

Abstract The goodness-of-fit of correlational pattern hypotheses has traditionally been assessed either with a likelihood ratio statistic (in conjunction with maximum likelihood estimation) or with a quadratic form statistic (in conjunction with generalized least squares estimates). In the present paper, several alternative statistics, based on the use of the Fisher r-to-z transform, are proposed, and their performance (as well as that of the traditional statistics) is assessed in a Monte Carlo experiment. The new statistics are shown to have Type I error rate performance at smaller sample sizes which is notably superior to their more traditional counterparts.