Several statistical approaches for the analysis of longitudinal data require that models be correctly specified for the association between a current outcome and the full history of past outcomes and time-dependent exposures. It is empirically challenging to determine the specific aspects of the outcome and/or exposure history that are predictive of a current outcome because the potential number of variables representing the history can be quite large. The purpose of this article is to outline statistical methods that can characterize lagged effects and to provide a structured approach for data analysis with the goal of appropriate model development. One of the main contributions of the article is to emphasize the possibility that in practice transition models may frequently require more than simple additive and linear models for the predictors representing the history of the outcome and covariate processes. We illustrate the concepts using an example from anemia treatment for dialysis patients and show how linear models can be specified with flexible dependence on exposure and/or outcome histories.