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Abstract:
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Questionnaires and tests often use many items to measure a given domain or trait. In these cases, simpler structural equation models can be developed by using parcel scores (sums or means of item subsets-subscales, testlets, or item bundles) instead of the original items as the observed indicators of the latent variables. This paper uses hierarchical factor models and confirmatory component models to outline procedures for jointly modeling parcels and their items. Using real data examples, we demonstrate the specification of item-level models which produce the same fit, estimates, and standard errors as corresponding parcel-level models. We also describe methods for testing how well the observed associations between items in different parcels can be explained by the correlation between their parcel means.
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