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Abstract:
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This study discusses difficulties of effect comparisons between equations in multilevel structural equation models with non-metric outcomes, such as nonlinear dyadic mixed-effects regression. In these models, the fixation of the level-1 error variances induces substantial drawbacks in the context of effect comparisons which align with the well-known problems of standard single and multilevel nonlinear models. Specifically, the level-1 and level-2 coefficients as well as the level-2 variance components are implicitly rescaled by the amount of unobserved level-1 residual variation and thus may apparently differ across equations despite of true effect equality. Against this background, the present study discusses a multilevel extension of the method proposed by Sobel and Arminger (1992) with which potential differences in level-1 residual variation can be taken into account within the imposed equality restrictions through the specification of non-linear parameter constraints. In this context, the advantages as well as limitations of the proposed technique will be exemplified within an empirical application.
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