The Impact of Homogeneous and Heterogeneous Parceling Strategies on Hierarchical Multidimensional Models

Abstract

Applying structural equation modeling to item parcels from a higher-order factor can result in the extraction of a qualitatively different latent variable, depending upon the parceling strategy that is used. The decision between homogeneous and heterogeneous parceling strategies should be made a priori based on the researcher’s theoretical understanding of the latent variable to be extracted; however, the choice about parceling strategy comes with statistical consequences for model convergence, model fit, and estimates of structural paths. Homogeneous parceling models are more likely to fail-to-converge than heterogeneous parcels when higher-order factor loadings are small or medium. Converged models, for both parceling strategies, are likely to result in good-fitting models with plausible solutions; however, converged models with Heywood cases are more likely to occur in homogeneous parceling models than heterogeneous parceling. Homogeneous models that converge with plausible solutions are likely to have a slightly better χ^2, SRMR, and RMSEA fit indices when higher-order factor loadings are small. On the other hand, heterogeneous parceling models are likely to have a slightly better CFI when higher-order factor loadings are medium strength. Homogeneous parceling was often associated with less biased estimates of gamma; however, gamma estimates tended to have large standard errors (compared with heterogeneous parceling models). Taken together, homogeneous parceling models tended to have better coverage, but heterogeneous parceling models tended to have more power.