Hierarchical mean and covariance structure models

Purpose of this paper is the formulation of a generalized latent variable model. A variety of mixed measurement and structural relationship models for metric, classified metric, ordered categorical, dichotomous and one- and double-sided censored indicators is linked to metric latent variables by three construction principles. These involve the combination of threshold concepts, simultaneous equation systems and hierarchical factor analytical models. The LISREL model is shown to be a special case. While focusing on construction principles and important special cases of the general model, some references to estimation strategies are given. This research was partially supported by a dissertation grant of theStudienstiftung des Deutschen Volkes. Comments and suggestions on earlier drafts by Gerhard Arminger, Günter Bamberg, Bernd Korzen and Andreas Schepers are gratefully acknowleged.