Conducting Tetrad Tests of Model Fit and Contrasts of Tetrad-Nested Models: A New SAS Macro

This article describes a SAS macro to assess model fit of structural equation models by employing a test of the model-implied vanishing tetrads. Use of this test has been limited in the past, in part due to the lack of software that fully automates the test in a user-friendly way. The current SAS macro provides a straightforward method for researchers touse thevanishing tetrads impliedbymodels toassess the fitof (a) structural equation models containing continuous endogenous variables; (b) structural equation models containing continuous endogenous variables nested for vanishing tetrads; and (c) structural equation models containing dichotomous, ordinal, or censored endogenous variables. Besides providing an alternative assessment of model fit to the usual likelihood-ratio test (LRT), thevanishing tetrads testoccasionallyprovidesastatistical assessment of competing models nested for vanishing tetrads but not nested for the LRT. The macro permits formal comparisons between tetrad-nested structural equation models containing dichotomous, ordinal, or censored endogenous variables.