Presents a necessary and sufficient condition for the equivalence of structural-equation models that is applicable to models with parameter restrictions and models that may or may not fulfill assumptions of the rules. Illustrates the application of the approach for studying model equivalence. (SLD)

It is shown that, for equivalent structural equation models that have been extended to multigroup models, imposing cross-group equality constraints on no parameters, all parameters, or any number of parameters for which the models are identical preserves the model equivalence property. Results are illustrated with two-group cognitive intervention…

A general structural equation model for measuring residualized true change and studying patterns of true growth or decline is described. This approach allows consistent and efficient estimation of the degree of interrelationship between residualized change in a repeatedly assessed psychological construct and other variables. (SLD)