Implications of Parcel-Allocation Variability for Comparing Fit of Item-Solutions and Parcel-Solutions

Abstract

This article relates a still-popular motivation for using parceling to an unrecognized cost. The still-popular motivation is improvement in fit with respect to the item-solution. The cost is uncertainty in fit due to the selection of one out of many possible item-to-parcel allocations. A theoretical framework establishes the reason for this relationship: The same mechanisms that cause larger item- versus parcel-solution differences in the minimized discrepancy function also cause larger allocation to allocation variability in the parcel-solution's minimized discrepancy function. Study 1 illustrates that these shared causal mechanisms lead to a strong positive association between average item–parcel differences in minimized discrepancy function values and parcel-allocation variability in those values. Study 2 extends these results from discrepancy function values to fit indexes, showing that the association remains positive, but varies in magnitude depending on what quantities other than the discrepancy function are involved in computing the fit index. The important implication for practice is that when item–parcel fit differences are large enough to alter conclusions about model adequacy, parcel-allocation variability tends to be large enough for parcel-solution model adequacy to depend on the particular allocation chosen.