, 72:309

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

Theory and Methods

DOI: 10.1007/s11336-007-9006-3

Cite this article as:
Bollen, K.A. & Maydeu-Olivares, A. Psychometrika (2007) 72: 309. doi:10.1007/s11336-007-9006-3


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.


latent variables ordinal variables dichotomous variables instrumental variables two-stage least squares (2SLS) factor analysis 

Copyright information

© Psychometric Society 2007

Authors and Affiliations

  1. 1.Odum Institute for Research in Social Science, CB 3355 Manning HallUniversity of North CarolinaChapel HillUSA

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