Effects of parceling on model selection: Parcel-allocation variability in model ranking.

Research interest often lies in comparing structural model specifications implying different relationships among latent factors. In this context parceling is commonly accepted, assuming the item-level measurement structure is well known and, conservatively, assuming items are unidimensional in the population. Under these assumptions, researchers compare competing structural models, each specified using the same parcel-level measurement model. However, little is known about consequences of parceling for model selection in this context-including whether and when model ranking could vary across alternative item-to-parcel allocations within-sample. This article first provides a theoretical framework that predicts the occurrence of parcel-allocation variability (PAV) in model selection index values and its consequences for PAV in ranking of competing structural models. These predictions are then investigated via simulation. We show that conditions known to manifest PAV in absolute fit of a single model may or may not manifest PAV in model ranking. Thus, one cannot assume that low PAV in absolute fit implies a lack of PAV in ranking, and vice versa. PAV in ranking is shown to occur under a variety of conditions, including large samples. To provide an empirically supported strategy for selecting a model when PAV in ranking exists, we draw on relationships between structural model rankings in parcel- versus item-solutions. This strategy employs the across-allocation modal ranking. We developed software tools for implementing this strategy in practice, and illustrate them with an example. Even if a researcher has substantive reason to prefer one particular allocation, investigating PAV in ranking within-sample still provides an informative sensitivity analysis. (PsycINFO Database Record
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