Residual-Based Diagnostics for Structural Equation Models

Brisa N. Sanchez
Assistant Research Professor
Department of Biostatistics
School of Public Health
University of Michigan


            We extend recently developed goodness of fit tests for correlated data to structural equation models with latent variables. The proposed tests lend themselves to graphical displays and are designed to detect misspecified distributional or linearity assumptions. To complement graphical displays, test statistics are defined; the null distributions of the test statistics are approximated using computationally efficient simulation techniques. Because the proposed diagnostics are based on subject-specific residuals and are graphical in nature, they are more advantageous than the available, classical diagnostic tools for structural equation models.  Classical diagnostics are based on aggregate forms of the data and are unequipped to diagnose misspecified distributions or linearity assumptions. The proposed methods are illustrated using data from a study of in-utero lead exposure.

This is joint work with Louise M. Ryan and E. Andres Houseman.  Partial funding was provided by a Predoctoral Fellowship from the Howard Hughes Medical Institute