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Title: A two-stage estimation procedure for nonlinear structural equation models Authors:  Klaus Holst - A.P. Moller-Maersk (Denmark) [presenting]
Esben Budtz-Jorgensen - Copenhagen University (Denmark)
Abstract: Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in nonlinear models may be complex and require numerical integration. Furthermore, ML inference is sensitive to distributional assumptions. We introduce a simple two-stage estimation technique for estimation of nonlinear associations between latent variables. Here both steps are based on fitting linear SEMs: first a linear model is fitted to data on the latent predictor and terms describing the nonlinear effects are predicted. In the second step, the predictions are included in a linear model for the latent outcome variable. We show that this procedure is consistent and identifies its asymptotic distribution. We also illustrate how this framework easily allows the association between latent variables to be modelled using restricted cubic splines and we develop a modified estimator which is robust to non-normality of the latent predictor. In a simulation study, we compare the proposed method to ML-analysis and a simple two-stage least squares technique.