Equivalent Structural Equation Models and Group Equality Constraints

This article is concerned with equivalent structural equation models that have been extended to multigroup models. It is shown that imposing cross-group equality constraints upon (a) no parameters or all parameters, or (b) any number of parameters in which the models are identical, preserves the model equivalence property. Alternatively, constraining for equality across groups some of those parameters in which the models differ can yield nonequivalent multiple-group models. The results are illustrated on two-group cognitive intervention data.