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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