Statistical Modeling of Latent Change

Abstract

The focus of this chapter is on a selected class of statistical models: latent change models. They are especially eligible for typical applications in cognitive training research with two or three groups (e.g., training, active control, passive control) and two or three time points (pretest, posttest, follow-up). Latent variable models have a long tradition in cognitive science because they can separate task-, paradigm-, and ability-specific variance in performance tasks. Latent change modeling allows to study latent means, latent intraindividual mean changes, and interindividual differences in both. This chapter addresses how the effectiveness of training programs can be evaluated with latent change models and typical misunderstandings in this context. Statistical power considerations and measurement invariance across experimental groups and time points are discussed. The benefits and risks of analyzing predictors and correlates of latent change variables are particularly relevant for cognitive training research. They provide valuable correlative information about possible mechanisms moderating training outcomes (e.g., compensation or magnification effects) but are no causal test of these mechanisms. Taken together, latent change modeling does not only allow testing whether a cognitive training works on average, but also studying interindividual differences in training outcomes.