ABSTRACT
The general model framework unifies and generalizes the multilevel, factor, item response, latent class, structural equation and longitudinal models discussed in Chapter 3.
In that chapter we were mainly concerned with models having continuous responses. Here we describe latent variable models accommodating all the response processes discussed in Chapter 2. As we shall see, and in contrast to the models in Chapter 3, random coefficients and factors can now be included in the same model. Latent variables are also allowed to vary at several levels, yielding for instance multilevel factor models. Multilevel structural equations can be specified to regress latent variables on same and higher level latent and observed variables. We will also relax the assumption of multivariate normality of the latent variables by using other continuous or discrete distributions or nonparametric maximum likelihood. Different kinds of latent class models are also accommodated. The model framework mostly corresponds to the class of Generalized Linear Latent And Mixed Models (GLLAMM) described in RabeHesketh et al. (2004a); see also Rabe-Hesketh et al. (2001a). However, we also discuss model types not accommodated within that class such as multilevel latent class models.
