Model-based manifest and latent composite scores in structural equation models

Abstract

Composite scores are commonly used in the social sciences as dependent and independent variables in statistical models. Typically, composite scores are computed prior to statistical analyses. In this paper, we demonstrate the construction of model-based composite scores that may serve as outcomes or predictors in structural equation models (SEMs). Model-based composite scores of manifest variables are useful in the presence of ignorable missing data, as full-information maximum likelihood estimation can be used for parameter estimation. Model-based composite scores of latent variables account for measurement error in the aggregated variables. We introduce the pseudo-indicator model (PIM) for the construction of three composite scores: (a) the sum score, (b) the weighted sum score, and (c) the average score of manifest and latent variables in SEM. The utility of manifest model-based composite scores in the case of missing values is shown by a simulation study. The use of multiple manifest and latent model-based composite scores in SEM is illustrated with data from motivation research.