Multivariate longitudinal methods for studying developmental relationships between depression and academic achievement

Recent advances in methods and computer software for longitudinal data analysis have pushed researchers to more critically examine developmental theories. In turn, researchers have also begun to push longitudinal methods by asking more complex developmental questions. One such question involves the relationships between two developmental processes. In this situation, choosing a longitudinal method is not obvious and should depend on specific hypotheses and research questions. This article outlines three common bivariate longitudinal models, including the bivariate latent growth curve model, the latent growth curve with a time-varying covariate, and the bivariate dual change score growth model, and illustrates their use by modeling how the development of depression is related to the development of achievement. Each longitudinal model is fitted to repeated measurements of children's depression and achievement from the National Longitudinal Survey of Youth (NLSY) data set in order to examine differing developmental relationships, and show how the developmental questions are answered by each longitudinal technique. The results from the longitudinal models appear to be somewhat at odds with one another regarding the developmental relationships between achievement and depression, but the conclusions are actually correct solutions to different developmental questions. These results highlight the need for researchers to match their research questions with model selection.