Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes

Latent variable structural equation modeling with categorical data

Journal of Econometrics, 1983, 22, 48-65.

A structural probit model with latent variables

Journal of the American Statistical Association, 74, 807-811

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

Sociological Methods and Research 36:46-86.

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.