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Most quantitative comparisons of interest are based on scores obtained from multi-item scales. In order for such comparisons to be valid and meaningful, conventional thinking dictates that simple structure and metric invariance must be satisfied at the level of individual items. However, it is proposed here that the use of multi-item scales requires only that conditions of simple structure and metric invariance be satisfied at the scale level, that is, for hypothesized sets of items as a whole rather than each item individually. The proposed concepts can be implemented within the context of confirmatory factor analysis (CFA) by imposing constraints on mean factor loadings and intercepts of item sets rather than loadings and intercepts of each individual item. Further, the present method is proposed as a conceptual alternative to the specification of measurement models that is currently predominant in CFA.
Labouvie et al. (Sun,) studied this question.