Structural equation modeling with instrumental variables

Y. Rosseel${}^a$

${}^a$Ghent University

Instrumental variables (IV) play a central role in econometrics and related disciplines, where they are widely used to address issues of endogeneity and causal identification. In contrast, their use in psychometrics has remained limited. Early contributions considered IV estimation in the context of the factor model, but a key development was the seminal work of [1], which demonstrated how instrumental variables can be employed to estimate directed parameters–such as factor loadings and path coefficients–within structural equation models (SEMs). Nevertheless, nearly three decades later, IV methods are still rarely used in SEM and psychometrics more generally.

In this presentation, I review recent methodological advances that may facilitate a wider adoption of IV estimation in SEM. First, after using IV estimation for the directed parameters in the model, noniterative methods can now be used to estimate the remaining undirected parameters (variances and covariances) in a second stage. Moreover, analytic standard errors can be obtained for all free parameters in the model. Second, the availability of complete parameter estimates allows the derivation of model-implied moments, which in turn enables formal goodness-of-fit testing. Third, the theoretical relationship between traditional IV estimation and SEM has become clearer; for example, Browne’s residual test can be shown to correspond to the Sargan test of overidentifying restrictions. Finally, IV estimation has recently been implemented in the lavaan package in R, further lowering the barrier to practical application.

Keywords: Structural Equation Modeling, Instrumental Variables.