A Note on the Use of Bootstrap Tetrad Tests for Covariance Structures

Tetrad tests are a valuable tool for testing covariance structures, particularly when other tests such as the likelihood ratio test are not appropriate. However the implementation of tetrad tests is complicated by the fact that there are often multiple sets of nonredundant vanishing tetrads, and also by computational limitations, particularly for bootstrap tetrad tests for models with a large number of indicator variables. We show that a simple modification of a bootstrap tetrad test can overcome these limitations. Another beneficial result of this modification is that it can increase the power of the test.