tetrad: A Set of Stata Commands for Confirmatory Tetrad Analysis

This article provides a brief overview of Confirmatory Tetrad Analysis (CTA) and presents a new set of Stata commands for conducting CTA with supporting examples. The Stata command, tetrad, allows researchers to use modelimplied vanishing tetrads to test the overall fit of structural equation models (SEMs) with continuous endogenous variables and the relative fit of two SEMs with continuous endogenous variables that are tetrad-nested. An extension of the command, tetrad_matrix, allows researchers to conduct CTA using a sample covariance matrix as input rather than relying on raw data. In addition, researchers can use the tetrad_matrix command to input a polychoric correlation matrix and conduct CTA for SEMs involving dichotomous, ordinal, or censored outcomes. An additional extension of the command, tetrad_bootstrap, provides a bootstrapped p-value for the chi-square test statistic. By drawing on Stata's recently developed suite of commands for structural equation modeling, researchers can integrate CTA with data preparation, likelihood ratio tests for model fit, and the estimation of model parameters in a single statistical software package.