The Separation of Between-Person and Within-Person Components of Individual Change Over Time: A Latent Curve Model With Structured Residuals

Objective: Although recent statistical and computational developments allow for the empirical testing of psychological theories in ways not previously possible, one particularly vexing challenge remains: how to optimally model the prospective, reciprocal relations between 2 constructs as they developmentally unfold over time. Several analytic methods currently exist that attempt to model these types of relations, and each approach is successful to varying degrees. However, none provide the unambiguous separation over time of between-person and within-person components of stability and change, components that are often hypothesized to exist in the psychological sciences. Our goal in this article is to propose and demonstrate a novel extension of the multivariate latent curve model to allow for the disaggregation of these effects. Method: We begin with a review of the standard latent curve models and describe how these primarily capture between-person differences in change. We then extend this model to allow for regression structures among the time-specific residuals to capture within-person differences in change. Results: We demonstrate this model using an artificial data set generated to mimic the developmental relation between alcohol use and depressive symptomatology spanning 5 repeated measures. Conclusions: We obtain a specificity of results from the proposed analytic strategy that is not available from other existing methodologies. We conclude with potential limitations of our approach and directions for future research.