Latent Variable Models Under Misspecification: Two-Stage Least Squares (2SLS) and Maximum Likelihood (ML) Estimators

TLDR

The study compares maximum likelihood estimation with three variants of two‑stage least squares in structural equation models. The authors simulate correctly and incorrectly specified models to evaluate bias, efficiency, and hypothesis‑test accuracy. When models are correctly specified, 2SLS with reduced IV sets matches ML in bias and efficiency, but under misspecification 2SLS shows lower bias and more accurate tests, suggesting researchers consider 2SLS unless highly confident in model correctness.

Abstract

This article compares maximum likelihood (ML) estimation to three variants of two-stage least squares (2SLS) estimation in structural equation models. The authors use models that are both correctly and incorrectly specified. Simulated data are used to assess bias, efficiency, and accuracy of hypothesis tests. Generally, 2SLS with reduced sets of instrumental variables performs similarly to ML when models are correctly specified. Under correct specification, both estimators have little bias except at the smallest sample sizes and are approximately equally efficient. As predicted, when models are incorrectly specified, 2SLS generally performs better, with less bias and more accurate hypothesis tests. Unless a researcher has tremendous confidence in the correctness of his or her model, these results suggest that a 2SLS estimator should be considered.