MODEL IMPLIED INSTRUMENTAL VARIABLES (MIIVS): A NEW ORIENTATION TO STRUCTURAL EQUATION MODELS (SEMS)
Kenneth A. Bollen
University of North Carolina
at Chapel Hill
It is hardly controversial to say that our models are approximations to reality. Yet when it comes to estimating structural equation models (SEMs), we use estimators that assume true models (e.g., ML) and that readily spread bias through estimated parameters when the model is approximate. This talk presents the Model Implied Instrumental Variable (MIIV) approach to SEMs initially proposed in Bollen (1996). It has greater robustness to structural misspecifications and the conditions for robustness are well understood. In addition, the MIIV-2SLS estimator is asymptotically distribution free. Furthermore, MIIV-2SLS has equation based overidentification tests that can help pinpoint errors in specification. Beyond these features, the MIIV approach has other desirable qualities. It permits new tests of dimensionality and tests of causal vs. reflective indicators. MIIV methods apply to higher order factor analyses, categorical measures, growth curve models, and nonlinear latent variables. Finally, it permits researchers to estimate and test only the latent variable model or any other subset of equations. This presentation will provide an overview of this new orientation to SEMs and illustrate MIIVsem, an R package that implements it.