tetrad: A Program for Confirmatory Tetrad Analysis

Confirmatory tetrad analysis (CTA) is a method of testing and comparing the fit of Structural Equation Models (SEMs) based on tetrads (differences in the product of pairs of covariance of observed variables). CTA has a few benefits over alternative methods of testing SEM model fit, including (1) some underidentified SEMs are still testable using their vanishing tetrads, (2) some SEMs are nested in their vanishing tetrads and can be directly compared while they are not nested using alternative estimators, and (3) researchers can perform tests on parts of the model as well as the whole model. We have developed a Stata command that conducts CTA based on the approach outlined in Bollen (1990) and Bollen and Ting (1993). The approach involves 4 steps: (1) identify vanish tetrads (tetrads that equal 0) for a given model, (2) compute the asymptotic covariance matrix for the vanishing tetrads, (3) identify non redundant vanishing tetrads, and (4) compute the tetrad test statistic. The Stata command takes as input the set of observed variables and an implied covariance matrix from a hypothesized model (or two implied covariance matrices if a nested test) that can be obtained following the sem command and returns the tetrad test statistic.