Consult the above reference
for further details on this macro.
Abstract:
This paper describes a SAS macro to assess model fit of
structural equation models (SEM) 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 to use the vanishing tetrads implied by models to assess the fit
of: 1) SEMs containing continuous endogenous variables; 2) SEMs
containing continuous endogenous variables nested for vanishing tetrads; 3)
SEMs containing dichotomous, ordinal, or censored endogenous variables.
Besides providing an alternative assessment of model fit to the usual
likelihood-ratio test (LRT), the vanishing tetrads test occasionally provides a
statistical assessment of competing models nested for vanishing tetrads but not
nested for the LRT. The macro permits formal comparisons between
tetrad-nested SEMs containing dichotomous, ordinal, or censored endogenous
variables.
The SAS
macro available here is user-friendly in several ways and also includes many of
the recent important extensions of the vanishing tetrads test.
- First,
the current macro allows the researcher to assess the vanishing tetrads of
the model when the data come from dichotomous, ordinal, or censored
observed variables. In such a case, the researcher need only provide
the polychoric correlation (covariance) matrix and its accompanying asymptotic
covariance matrix.
- Second,
the macro automates many of the more onerous and analytically difficult
tasks required to perform the vanishing tetrad test. For instance,
the procedure of determining the vanishing tetrads implied by the model
(done manually in the Ting (1995) macro) has now been fully automated, a
considerable advantage, particularly for larger models. In addition,
given two models the program automatically detects whether the models are
tetrad-nested and selects the appropriate vanishing tetrads for the test
between models.
- Third,
Hipp and Bollen (2003) suggested that since there is generally not a
unique set of vanishing tetrads for any given model the researcher may
wish to pull random draws of vanishing tetrads to assess the sensitivity
of the results to such selection. This randomization procedure is a
fully automated feature of the current macro.
- Last,
this macro has adopted a new strategy for selecting the vanishing tetrads
implied by the model using the sweep operator. Hipp and Bollen (2003)
pointed out that this strategy is about sixty times faster than the
procedure suggested by Bollen and Ting (1993), a feature that becomes
particularly important in randomizing sets of tetrads, bootstrapping
applications, or conducting Monte Carlo
studies of the test.