ABSTRACT
Social science theories refer to characteristics (and associated measured variables) that are either continuous (or nearly so) or categorical. For categorical characteristics, we may then distinguish among theories that refer to measurement at a single time point (static) or measurements at two or more time points (dynamic). For dynamic theories, interest centers around the initial distribution of people across categories, and how people transition from a category at each time point to a category (either the same or different) at another time point. The measurements at different time points might be of the same characteristic or of different characteristics (e.g., how does personality type measured at an early age relate to whether a person ends up in a white-collar or blue-collar job later). To complicate the situation further, observed measurements may be thought to be imperfect indicators of an underlying (latent) characteristic. We may now define latent transition analysis (LTA) as a statistical model in which (i) latent categorical constructs are defined at two or more time points, (ii) parameters are included that assess initial status and transition probabilities from time i to time i + 1 (for most models; for others, we predict further into the future), and (iii) observed variables are imperfect indicators of the hypothesized latent variables. As a simple example, we might theorize that at each age, children either can or cannot conserve volume (in accordance with Piaget’s theory). We could give a three-item test to each of a large number of children at ages 3, 4, 5, 6, and 7, and then see whether the data are consistent with the theory, and if so, assess the rate at which children transition from being nonconservers to conservers at each age. The distinguishing characteristics of this study are that (i) the model allows children to be in one of two true states at each time, (ii) the observed test items are categorical (scored right/wrong), and (iii) each child is measured several times (here, over a four-year period).
