Tetrad

Tetrad implements Confirmatory Tetrad Analysis (CTA) in Stata to evaluate and compare structural equation models (SEMs) by testing model-implied vanishing tetrads for model fit in models with continuous endogenous variables.

Key Features:

• Model Fit Testing: The tetrad command applies CTA to assess SEM fit by testing model-implied vanishing tetrads (specific combinations of covariances that should be zero).
• Model Comparison: Tetrad compares two tetrad-nested SEMs to determine relative fit for models with continuous endogenous variables.
• Flexible Input Options: The tetrad_matrix command accepts sample covariance matrices as input instead of raw data.
• Handling Diverse Data Types: tetrad_matrix accepts polychoric correlation matrices to enable CTA for SEMs involving dichotomous, ordinal, or censored outcomes.
• Enhanced Statistical Rigor: The tetrad_bootstrap extension provides a bootstrapped p-value for the CTA chi-square test statistic.

Scientific Applications:

• Psychology: Testing measurement models and latent-construct hypotheses within SEM frameworks using vanishing tetrads.
• Sociology: Evaluating competing structural models of social processes via CTA and tetrad-based model comparison.
• Economics: Comparing SEMs that represent alternative theorized relationships among economic variables using tetrad constraints.
• Cross-disciplinary SEM research: Applying CTA to datasets with continuous, dichotomous, ordinal, or censored outcomes to test model-implied covariance restrictions.

Methodology:

Performs Confirmatory Tetrad Analysis by testing vanishing tetrads (covariance combinations equal to zero), accepts raw data or sample covariance matrices and polychoric correlation matrices via tetrad_matrix, compares tetrad-nested SEMs, and can compute a bootstrapped p-value for the CTA chi-square test statistic via tetrad_bootstrap.