Quasi-Maximum Likelihood Estimation of Structural Equation Models With Multiple Interaction and Quadratic Effects

Abstract

In this article, a nonlinear structural equation model is introduced and a quasi-maximum likelihood method for simultaneous estimation and testing of multiple nonlinear effects is developed. The focus of the new methodology lies on efficiency, robustness, and computational practicability. Monte-Carlo studies indicate that the method is highly efficient and that the likelihood ratio test of nonlinear effects is robust and outperforms alternative testing procedures. The new method is applied to empirical data of middle-aged men, where a latent interaction between physical fitness and flexibility in goal adjustment on complaint level is hypothesized. A model with 5 simultaneous nonlinear effects is analyzed, and the hypothesized interaction is quantified and tested positively against an additive model with quadratic and linear effects.

ACKNOWLEDGMENTS

This research was supported by the National Institute on Alcohol Abuse and Alcoholism (NIAAA) under Grant K02 AA 00230-01; by the National Institute of Mental Health (NIMH) and the National Institute on Drug Abuse (NIDA) under Grant MH40859; and by the Research Board of the University of Illinois, Urbana-Champaign, under Grant 03269. The Quasi-ML software is available from Andreas G. Klein upon request.