Structural Equation Modeling
The structural equation modeling techniques are used
to study relations among variables. The relations are typically assumed
to be linear. In social and behavioral research most phenomena are influenced
by a large number of determinants which typically have a complex pattern
of interrelationships. To understand the relative importance of these
determinants their relations must be adequately represented in a model,
which may be done with structural equation modeling.
A structural equation model may apply to one group of cases or to multiple
groups of cases. When multiple groups are analyzed parameters may be
constrained to be equal across two or more groups. When two or more groups
are analyzed, means on observed and latent variables may also be included
in the model.
As an application, how do you test the equality of regression slopes
coming from the same sample using 3 different measuring methods? You
could use a structural modeling approach.
1  Standardize all three data sets prior to the analysis because b weights
are also a function of the variance of the predictor variable and with
standardization, you remove this source.
2  Model the dependent variable as the effect from all three measures
and obtain the path coefficient (b weight)
for each one.
3  Then fit a model in which the three path coefficients are constrained
to be equal. If a significant decrement in fit occurs, the paths are
not equal.
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