Problems with Rationales for Parceling that Fail to Consider Parcel-Allocation Variability

In structural equation modeling applications, parcels-averages or sums of subsets of item scores-are often used as indicators of latent constructs. Parcel-allocation variability (PAV) is variability in results that arises within sample across alternative item-to-parcel allocations. PAV can manifest in all results of a parcel-level model (e.g., model fit, parameter estimates, standard errors, and inferential decisions). It is a source of uncertainty in parcel-level model results that can be investigated, reported, and accounted for. Failing to do so raises representativeness and replicability concerns. However, in recent methodological literature (Cole, Perkins, & Zelkowitz, 2016 ; Little, Rhemtulla, Gibson, & Shoemann, 2013 ; Marsh, Ludtke, Nagengast, Morin, & von Davier, 2013 ; Rhemtulla, 2016 ) parceling has been justified and recommended in several situations without quantifying or accounting for PAV. In this article, we explain and demonstrate problems with these rationales. Overall, we find that: (1) using a purposive parceling algorithm for a multidimensional construct does not avoid PAV; (2) passing a test of unidimensionality of the item-level model need not avoid PAV; and (3) a desire to improve power for detecting structural misspecification does not warrant parceling without addressing PAV; we show how to simultaneously avoid PAV and obtain even higher power by comparing item-level models differing in structural constraints. Implications for practice are discussed.