SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

The Quasi-ML approach for modeling nonlinear SEM

Andreas G. Klein
University of Illinois at Urbana-Champaign
Bengt O. Muthén
University of California Los Angeles

In a statistical research context, a linear model sometimes provides only a questionable representation of reality. This situation particularly arises when the size of an effect of an exogenous variable on an endogenous variable itself depends on the outcome of a third variable. Then, in addition to linear effects, an interaction effect becomes an integral part of the model structure.

The modeling of interaction or other nonlinear effects by using structural equation modeling has been an issue of ongoing research in recent years. In practice, theory-based hypothesized interactions have often failed to become replicated. With the Quasi-Ml estimation method, a newly developed estimation technique is presented. This method provides an approximate ML estimator, and first results indicate that it outperforms the currently available methodology particularly for more complex models with respect to statistical power and robustness, whereas for more elementary models the LMS method (Klein & Moosbrugger, 2000) has already proved to be statistically highly efficient.

In connection with the Quasi-ML method, a general nonlinear latent variable modeling framework is discussed which incorporates the flexible modeling of multiple nonlinear effects. The applicability of the new modeling framework and Quasi-ML estimation method is illustrated by an empirical data set.