ABSTRACT
Measurement in psychological science often focuses on some form of latent trait measurement. A common problem in latent variable models in general, and factor models specifically, is the issue of indeterminacy. In confirmatory factor models, this indeterminacy manifests through the related concept of model equivalence. Factor analysis and structural equation modeling are incredibly flexible techniques that are centered on reproducing an observed covariance matrix, or equivalently, maximizing the likelihood of raw continuous or categorical data under and expected covariance structure. Despite the utility of extending measurement evaluation into longitudinal data, several statistical issues prevent a researcher from simply throwing repeated measurements into a standard exploratory factor analysis program. The chapter argues for a specific modeling approach, which should further be extended to include testing, empirical example, and software development. Valid measures should demonstrate longitudinal convergent and divergent validity, showing coincident changes with constructs that should change together and no relationship with constructs that should not be related.
