Comparison of Different Parceling Approaches in Structural Equation Modeling Using Simulation Methods

Structural equation modeling (SEM) is commonly used to create latent variables from a set of manifest variables. When relationships between the manifest and latent variables are accurately specified and estimated, latent variables produce more reliable estimates of association between constructs by modeling measurement error. When there are a large number of manifest variables (e.g., >4), model fit problems often occur due to increased chance of dual factor loadings or correlated residuals and sources of sampling error. A strategy that can potentially address this problem is parceling, which is a method of reducing the number of items by creating composite scales with the manifest variables. Despite misgivings recently expressed by Marsh et al. (2013), parceling is an important tool that is often appropriate for use with SEM (Little et al., 2013).According to the domain representative concept (Kishton & Widaman, 1994), manifest items are assumed to be drawn from a single domain and any lack of correlation between manifest variables is due to lack of reliability. Thus created parcels included as manifest variables in SEM should also be representative of the whole domain. Based on this concept, we propose an optimal domain representative (ODR) approach to create parcels by performing all the possible assignments of items to parcels. The combination with the highest average correlation between parcels would have the highest coefficient alpha and thus maximize internal consistency.

To illustrate the benefits of the ODR approach, we conducted a set of simulations to compare this approach with other parceling approaches, including the domain representative (DR) approach, unidimensional (UNI) approach, radial approach, random approach, and factorial approach (Rogers & Schmitt, 2004), in terms of parameter estimates, model stability and ease of use.

Preliminary simulation analysis showed that the ODR approach is superior to the random and UNI approach and is comparable to the DR and radial approach in term of parameter estimates.  The radial approach is not easy to implement and is also not very stable: factor loadings on created parcels have large variances. The DR approach is not easy to implement when the number of items is not balanced across factors. The proposed ODR approach showed advantage to other parceling approaches and is easily implemented with the developed R function.