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.

Refining the vulnerability model of low self-esteem and depression: Disentangling the effects of genuine self-esteem and narcissism.

“…Cole & Maxwell, 2003). To measure the latent factors, we used item parcels as indicators because parcels produce more reliable latent variables than individual items (Little, Cunningham, Shahar, & Widaman, 2002; but see Marsh, Lüdtke, Nagengast, Morin, & Von Davier, 2013). For each latent factor, we aggregated the items into three parcels.…”

Achievement goal profiles among adolescent males and females.

“…ESEM offers the possibility to integrate features of CFA, structural equation modeling (SEM), and exploratory factor analysis (EFA) in a single framework. This decision is based on the results from simulation studies Sass & Schmitt, 2010;Schmitt & Sass, 2011) and studies of simulated data (Marsh, Lüdtke, Nagengast, Morin, & Von Davier, 2013;Morin, Arens, & Marsh, 2015) showing that forcing cross loadings (even as small as .100, Marsh et al, 2013) present in the population model to be exactly zero according to typical CFA specification forces these cross loadings to be expressed through an inflation of the factor correlations. In contrast, these same studies show that the free estimation of cross-loadings, even when none are present in the population model, still provides unbiased estimates of the factor correlations (also see Asparouhov, Muthén, & Morin, 2015;.…”

Self-esteem development across the life span: A longitudinal study with a large sample from Germany.

“…Given that the use of item parcels is not unequivocally supported in the methodological literature (for the debate, see, e.g., Little et al, 2013;Marsh, Lüdtke, Nagengast, Morin, & Von Davier, 2013), we also tested for measurement invariance on the item level. We accounted for the Likert-type response scale of the RSE by using item factor analysis with categorical indicators (Wirth & Edwards, 2007).…”

“…Models 5 and 6 tested weak and strong invariance across cohorts by progressively constraining the loadings and intercepts of indicators. As indicated by the test of small difference in fit, the constraints did not significantly worsen model fit, suggesting strong measurement invariance across birth cohorts.Given that the use of item parcels is not unequivocally supported in the methodological literature (for the debate, see, e.g., Little et al, 2013;Marsh, Lüdtke, Nagengast, Morin, & Von Davier, 2013), we also tested for measurement invariance on the item level. We accounted for the Likert-type response scale of the RSE by using item factor analysis with categorical indicators (Wirth & Edwards, 2007).…”