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

Kenneth A. Bollen · Alberto Maydeu‐Olivares

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Psychometric Methodologies and Testing Statistical Methods and Bayesian Inference Advanced Causal Inference Techniques

Abstract

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.

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1989Structural Equations with Latent Variables 1991Structural Equations with Latent Variables.1989EQS : structural equations program manual 1995Testing Structural Equation Models.1985Optimism, coping, and health: Assessment and implications of generalized outcome expectancies.2004An Empirical Evaluation of Alternative Methods of Estimation for Confirmatory Factor Analysis With Ordinal Data.1994Corrections to test statistics and standard errors in covariance structure analysis.1984A General Structural Equation Model with Dichotomous, Ordered Categorical, and Continuous Latent Variable Indicators

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2012A Monte Carlo study comparing PIV, ULS and DWLS in the estimation of dichotomous confirmatory factor analysis

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