Variability or trait change? On the relationship between latent state-trait and multivariate latent growth curve models
Latent state-trait (LST) models and latent growth curve (LGC) models are latent variable models for analyzing longitudinal data that have emerged in different traditions. The European tradition has developed models for measuring variability based on LST theory (e.g., Steyer, Ferring, & Schmitt, 1992), whereas the North American tradition has mainly focused on LGC models. Although attempts have been made to draw connections between the two modeling traditions (e.g., Tisak & Tisak, 2000), many researchers are still puzzled about the formal and conceptual relationships between LST models and LGC models as well as the question as to when each model should be applied. In this talk, I show that different versions of the multivariate (i.e., multiple indicator) LGC model (McArdle, 1988) can be defined on the basis of the fundamental theoretical concepts of LST theory and that LST models can be conceived of as special cases of multivariate LGC models. I illustrate some important insights that follow from this, for example, the fact that the inclusion of a mean structure and testing of measurement invariance are important analysis steps not only in models for measuring trait changes (LGC models), but also in models for measuring variability (LST models). I outline a useful modeling strategy for deciding between variability and trait change models (or a combination of both) and the implementation of this strategy in Mplus.