Outlier Screening and a Distribution-Free Test for Vanishing Tetrads

The TETRAD search procedure has several limitations: It does not screen data for outliers; it relies on Wishart's test for vanishing tetrads that assumes a multinormal distribution for the random variables; and the significance tests do not take into account that multiple tetrad differences are being tested. I propose several ways to overcome these problems. First, I present several diagnostic statistics to help identify outliers and influential cases. Then I develop new, more general asymptotic tests for vanishing tetrads for variables with nonnormal distributions and derive a simultaneous test for multiple tetrad differences. Finally, the tests are extended to apply to tetrad differences of covariances as well as differences of correlations computed for random variables with “arbitrary” distributions.