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Description: When multiple items are used to measure cluster-level constructs with individual-level responses, multilevel confirmatory factor models are useful. How to model constructs across levels is still an active area of research with competing methods being available to capture what can be interpreted as a valid representation of cluster-level phenomena. Moreover, the terminology used for the cluster-level constructs in such models varies across researchers. In this paper we provide an overview of used terminology and modeling approaches for cluster-level constructs measured through individual responses. We classify the constructs based on whether (a) the target of measurement is at the cluster level or at the individual level and (b) the construct requires a measurement model or not. Next, we discuss various two-level factor models that have been proposed for multilevel constructs that require a measurement model, and we show that the so-called doubly latent model with cross-level invariance of factor loadings is appropriate for all types of constructs that require a measurement model. We provide two illustrations using empirical data from students and organizational teams on stimulating teaching and on conflict in organizational teams, respectively.


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