Testing the degree of cross-sectional and longitudinal dependence between two discrete dynamic processes

Developmental research often involves studying change across 2 or more processes or constructs simultaneously. A natural question in this work is whether change in these 2 processes is related or independent. Associative latent transition analysis (ALTA) was designed to test hypotheses about the degree to which change in 2 discrete latent variables is related. The ALTA model is a type of latent class model, which is a categorical latent variable model based on categorical indicators. In the ALTA approach, level and change on 1 variable is predicted by level and change in another. Two types of hypotheses are discussed: (a) broad hypotheses of dependence between the 2 discrete latent variables and (b) targeted hypotheses comparing specific patterns of change between levels of the discrete variables. Both types of hypotheses are tested via nested model comparisons. Analyses of relations between psychological state and substance use illustrate the model. Recent psychological state and recent substance use were found to be associated cross-sectionally and longitudinally, implying that change in recent substance use was related to change in recent psychological state.