Title: Model Implied Instrumental Variables: An Alternative Orientation to Structural Equation Models

Abstract:  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 can spread bias through estimated parameters when the model is approximate. This talk presents the Model Implied Instrumental Variable (MIIV) approach to SEMs originally proposed in Bollen (1996). The MIIV estimator using Two Stage Least Squares (2SLS) or MIIV-2SLS has greater robustness to structural misspecifications and the conditions for robustness are better understood than other estimators. 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 (e.g., a new test of dimensionality). MIIV methods apply to higher order factor analyses, categorical measures, growth curve models, dynamic factor analysis, and nonlinear latent variables. Finally, it permits researchers to estimate and test only the latent variable model or any other subset of equations. Despite these promising features, research is needed to better understand its performance under a variety of conditions that represent real world empirical examples. In addition, other MIIV estimators beyond 2SLS are available. This presentation will provide an overview of this new orientation to SEMs and illustrate MIIVsem, an R package that implements it.