A Note on the Specification of Error Structures in Latent Interaction Models

Latent interaction models have motivated a great deal of methodological research, mainly in the area of estimating such models. Product-indicator methods have been shown to be competitive with other methods of estimation in terms of parameter bias and standard error accuracy, and their continued popularity in empirical studies is due, in part, to their straightforward implementation and relative ease of estimation in mainstream structural equation modeling software. In recent years, the impact of different specifications of the mean structure of the structural model has been the focus of a fair amount of investigation in this area. Yet the effects of misspecification of the error structure of the observed variables implied by the model have not been investigated. In this study, the authors demonstrate algebraically the ramifications of misspecifying these error structures for the unconstrained product-indicator approach. Recommendations to practitioners based on these results are discussed.