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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. The tetrad command allows researchers to use model-implied vanishing tetrads to test the overall fit of structural equation models (SEMs) and the relative fit of two SEMs 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. Researchers can also use the tetrad_matrix command to input a polychoric correlation matrix and conduct CTA for SEMs involving dichotomous, ordinal, or censored outcomes. Another extension of the command, tetrad_bootstrap, provides a bootstrapped p value for the chi-square test statistic. With Stata’s recently developed 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.