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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.
Klein et al. (Fri,) studied this question.