A Polychoric Instrumental Variable (PIV) Estimator for Structural Equation Models with Categorical Variables

This paper presents a new polychoric instrumental variable (PIV) estimator to use in structural equation models (SEMs) with categorical observed variables. The PIV estimator is a generalization of Bollen’s (Psychometrika 61:109–121, 1996) 2SLS/IV estimator for continuous variables to categorical endogenous variables. We derive the PIV estimator and its asymptotic standard errors for the regression coefficients in the latent variable and measurement models. We also provide an estimator of the variance and covariance parameters of the model, asymptotic standard errors for these, and test statistics of overall model fit. We examine this estimator via an empirical study and also via a small simulation study. Our results illustrate the greater robustness of the PIV estimator to structural misspecifications than the system-wide estimators that are commonly applied in SEMs. Kenneth Bollen gratefully acknowledges support from NSF SES 0617276, NIDA 1-RO1-DA13148-01, and DA013148-05A2. Albert Maydeu-Olivares was supported by the Department of Universities, Research and Information Society (DURSI) of the Catalan Government, and by grant BSO2003-08507 from the Spanish Ministry of Science and Technology. We thank Sharon Christ, John Hipp, and Shawn Bauldry for research assistance. The comments of the members of the Carolina Structural Equation Modeling (CSEM) group are greatly appreciated. An earlier version of this paper under a different title was presented by K. Bollen at the Psychometric Society Meetings, June, 2002, Chapel Hill, North Carolina.