Evaluating the impact of partial factorial invariance on selection in two populations

Studies of factorial invariance examine whether a common factor model holds across multiple populations with identical parameter values. Partial factorial invariance exists when some, but not all, parameters are invariant. The literature on factorial invariance is unclear about what should be done if partial invariance is found. One approach to this problem evaluates the impact of partial invariance on accuracy of selection on the basis of a composite of the measures whose factor structure is being studied. Assuming a single-factor model holds, accuracy of selection using the composite is evaluated under varying degrees of partial invariance. A variety of examples are presented with discussion of extensions and limitations.