Effect comparison in multilevel structural equation models with non-metric outcomes

This study discusses difficulties of effect comparisons 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 (and within) 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 through the specification of non-linear parameter constraints. The problems of effect comparisons in multilevel probit SEM's and the proposed correction method are exemplified with a simulation study.