Why item parcels are (almost) never appropriate: Two wrongs do not make a right—Camouflaging misspecification with item parcels in CFA models.

Abstract

The present investigation has a dual focus: to evaluate problematic practice in the use of item parcels and to suggest exploratory structural equation models (ESEMs) as a viable alternative to the traditional independent clusters confirmatory factor analysis (ICM-CFA) model (with no cross-loadings, subsidiary factors, or correlated uniquenesses). Typically, it is ill-advised to (a) use item parcels when ICM-CFA models do not fit the data, and (b) retain ICM-CFA models when items cross-load on multiple factors. However, the combined use of (a) and (b) is widespread and often provides such misleadingly good fit indexes that applied researchers might believe that misspecification problems are resolved--that 2 wrongs really do make a right. Taking a pragmatist perspective, in 4 studies we demonstrate with responses to the Rosenberg Self-Esteem Inventory (Rosenberg, 1965), Big Five personality factors, and simulated data that even small cross-loadings seriously distort relations among ICM-CFA constructs or even decisions on the number of factors; although obvious in item-level analyses, this is camouflaged by the use of parcels. ESEMs provide a viable alternative to ICM-CFAs and a test for the appropriateness of parcels. The use of parcels with an ICM-CFA model is most justifiable when the fit of both ICM-CFA and ESEM models is acceptable and equally good, and when substantively important interpretations are similar. However, if the ESEM model fits the data better than the ICM-CFA model, then the use of parcels with an ICM-CFA model typically is ill-advised--particularly in studies that are also interested in scale development, latent means, and measurement invariance.