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 Cole, D. A., Perkins, C. E., &; Zelkowitz, R. L. (2016). Impact of homogeneous and heterogeneous parceling strategies when latent variables represent multidimensional constructs. Psychological Methods, 21(2), 164–174. doi: 10.1037/met0000047Crossref], PubMed], Web of Science ®] , Google Scholar]; Little, Rhemtulla, Gibson, &; Shoemann, 2013 Little, T. D., Rhemtulla, M., Gibson, K., &; Schoemann, A. M. (2013). Why the items versus parcels controversy needn't be one. Psychological Methods, 18(3), 285–300. doi: 10.1037/a0033266Crossref], PubMed], Web of Science ®] , Google Scholar]; Marsh, Ludtke, Nagengast, Morin, &; von Davier, 2013 Marsh, H. W., Lüdtke, O., Nagengast, B., Morin, A., &; von Davier, M. (2013). Why item parcels are (almost) never appropriate: Two wrongs do not make a right—camouflaging misspecification with item parcels in CFA models. Psychological Methods, 18(3), 257–284. doi: 10.1037/a0032773Crossref], PubMed], Web of Science ®] , Google Scholar]; Rhemtulla, 2016 Rhemtulla, M. (2016). Population performance of SEM parceling strategies under measurement and structural model misspecification. Psychological Methods, 21(3), 348–368. doi: 10.1037/met0000072Crossref], PubMed], Web of Science ®] , Google Scholar]) 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.