Multigroup analysis in the context of multilevel analysis to judge if a referent-shift model is needed for measurement of composition emergence
This study demonstrates how a multigroup analysis approach is used in the analysis of multilevel data to judge if a referent-shift consensus model is needed to measure a compositional property. A compositional property in multilevel context means that the forms of emergence from individual levels to group levels are isomorphic as individuals interact, communicate perspectives, and iteratively construct a common interpretation, so that all individuals in the collective are similar. The measurement principle for conceptualization of multilevel compositional properties is to use a referent-shift consensus model proposed by Chan(1998). However, if the researcher wants to use the samel construct in individual levels as well as in group levels, she needs to administer the same items to the same individuals again with a change of reference from “group” to “ individual”. It sounds bothersome and creates difficulties in reality. For that reason, researchers often collect data from individuals using self-referenced items, aggregate, and then use the aggregate scores as measures of group level variables. However in these cases, measurement invariance is tacitly assumed across the individual and group levels. We pointed out the problems of this unjustified assumption in analyses of multilevel data, and presented an analytic procedure to test the assumption using multigroup analysis framework. In sum, if measurement invariance across levels is established, researchers can use either a self-referent or a referent-shift data at individual levels and aggregate data at group levels without dual measurement. Moreover, in such a case, using a referent-shift data(‘we’ data) is more appropriate in light of construct validity because of its higher possibility to reveal group effects. If the measurement invariance across levels is not supported, researchers should collect data separately for individual level variables with a self-reference items and for group level variables with group-referenced items.