Residual-Based
Diagnostics for Structural Equation Models
Brisa N. Sanchez Assistant Research Professor Department of Biostatistics School of Public Health University of Michigan Abstract
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 |