Primary Submission Category: Methodological approaches to studying public health
A Comparison of Methods for Detecting Invalid Instruments in Structural Equation Models Estimated with Model Implied Instrumental Variable Two Stage Least Squares
Authors: Adam Lilly
Presenting Author: Adam Lilly*
Structural equation modeling is used in the social and population health sciences to estimate models containing latent variables, evaluate measures, control for measurement error, conduct mediation analyses, investigate multiple outcomes simultaneously, and for many other purposes. When all endogenous variables are continuous, maximum likelihood is the most popular estimator, but the model implied instrumental variable two-stage least squares (MIIV-2SLS) estimator is an attractive alternative. The MIIV-2SLS estimator transforms every equation in a SEM that includes latent variables into an equation with the original parameters but only observed variables, and then uses the model structure to locate instruments already in the model to estimate each equation. When a model is estimated using MIIV-2SLS, the Sargan overidentification test can be used to identify equations with invalid instruments, but the test does not provide information regarding which instruments are invalid. In this paper, I adapt a Lagrangian multiplier (LM) test developed by Wooldridge and the MR-PRESSO test developed by Verbanck and colleages to the MIIV-2SLS setting. The primary ingredient in the LM test is the r-squared from a regression of the residuals from an equation estimated by 2SLS on the predicted values of the regressors in a modified form of that equation that includes one or more of the instruments from the original specification. The MR-PRESSO test was originally developed to detect genetic variants that display evidence of horizontal pleiotropy in applications of two-sample Mendelian randomization. I will simulate 500 sample datasets from a population model for each of seven different sample sizes ranging from 75 to 2000. Incorrect models that constrain one or more of the population parameters to zero will then be estimated with MIIV-SEM in the sample data to determine which method performs better in detecting invalid instruments caused by the misspecification.