Model Misspecification and Goodness-of-fit in Latent Variable and Structural Equations Models

• Activity Number: 190
• Type: Contributed
• Date/Time: Monday, August 8, 2005 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Brisa N. Sanchez*+ and Louise Ryan
• Companies: Harvard School of Public Health and Harvard University
• Keywords: multiple outcomes ; multiple predictors ; measurement error ; LISREL

Abstract

Latent variable models are used frequently to analyze multivariate data and accommodate multiple closely related predictors. In the psychometrics and econometrics literature, the approach has been well developed and goes under the name of Structural Equation models (SEM). It has been shown that, by changing the assumed relationships between latent variables in a given SEM, it is possible to develop alternative models that lead to different scientific conclusions, yet also are statistically correct. We show that alternative models also can be attained by changing the relationships between the latent and observed variables. An implication is that the various well-established goodness-of-fit indices developed for SEMs, which focus on the difference between the empirical and model covariance for the data, cannot distinguish the scientifically misspecified model from the correct model. We apply a novel diagnostic tool developed for correlated data based on rotated residuals and evaluate its ability to distinguish between statistically equivalent models. Our findings underscore the critical role of subject matter and statistical considerations for latent variable modeling.