MM Versus Ml Estimates of Structural Equation Models with Interaction Terms: Robustness to Non-Normality of the Consistency Property

• Activity Number: 584
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Albert Satorra*+ and Ab Mooijaart
• Companies: Universitat Pompeu Fabra and Leiden University
• Keywords: maximum-likelihood ; method of moments ; third-order moment ; asymptotic bias ; latent-variable ; structural relation

Abstract

A standard assumption in structural equation models with interaction terms is the normality of all the random constituents of the model. In applications, however, there may be predictors, disturbance terms of equations, or measurement errors, deviating from normality. The present paper investigates how deviation from normality affects the consistency of two alternative estimators; namely, the maximum likelihood (ML) and the method of moments (MM) estimators. The ML approach requires full specification of the distribution of observable variables while this is not required in the MM approach. It will be seen that while the MM estimator is insensitive to departures from normality of all the random constituents of the model not involved in the interaction terms, such deviation from normality distorts considerably the consistency property of the ML estimator. The paper provides analytical results showing the consistency of MM when using a proper selection of moments up to order three, and presents a Monte Carlo illustration showing how the consistency of the ML estimator breaks down when there is deviation from normality. It is concluded that for a va