Improving generalizability coefficient estimate accuracy: A way to incorporate auxiliary information

Initially proposed by Marcoulides and further expanded by Raykov and Marcoulides, a structural equation modeling approach can be used in generalizability theory estimation. This article examines the utility of incorporating auxiliary variables into the structural equation modeling approach when missing data is present. In particular, the authors assert that by adapting a saturated correlates model strategy to structural equation modeling generalizability theory models, one can reduce any biased effects caused by missingness. Traditional approaches such as an analysis of variance do not possess such a feature. This article provides detailed instructions for adding auxiliary variables into a structural equation modeling generalizability theory model, demonstrates the corresponding benefits of bias reduction in generalizability coefficient estimate via simulations, and discusses issues relevant to the proposed approach.