A Taxonomy of Joint Longitudinal Models

For most longitudinal processes of interest to prevention scientists, there is at least one other related longitudinal process at work in the variable system over time.  By utilizing a joint model, the associations between two (or more) processes be explicitly evaluated.  In this paper, we present a taxonomy of joint longitudinal models to provide a unifying framework for existing models and to assist in identifying joint process settings for which the analytic approaches are under-developed.   Each primary model type in the taxonomy is motivated by a substantively-relevant question from the current prevention research literature.

We distinguish three primary axes for the model taxonomy: 1) the longitudinal outcome metric (e.g., continuous) for each process; 2) the temporal ordering of the processes, (e.g., sequential, concurrent, etc.); and 3) the nature of the cross-process covariation (e.g., causal, reciprocal, etc.).   In general, the analytic techniques that exist for joint modeling involve concurrent or partially-concurrent processes.  In the most common among these, the exogenous influence joint models, one of the two processes represents an exogenous source of variability (i.e., a time-varying covariate) for the remaining process.  For approaches that explicitly model both concurrent processes, the dominant techniques utilize the same analytic model for each outcome across time. We refer to these models as symmetric models for dual longitudinal processes (SDPs). The most widely used symmetric dual-process models are for repeated continuous outcomes, e.g., dual (or parallel) latent growth models (DLGM). These SDP models may be well-suited for certain research questions but are all limited by the necessary assumptions that the same model specification for the change process is valid for both of the repeated outcomes and that the relationship between the two processes over time can be accurately captured exclusively by the dual-process covariation permitted by that particular symmetric model.  Using our joint model taxonomy, we expand the category of SDP to include dual ordinal growth models and dual survival models.  We further expand the broader category of dual-process models to include asymmetric dual-process models (ADPs) to accommodate situations for which it is more theoretically or empirically desirable to have different specifications of change process models for each of the longitudinal outcomes.  We round out the taxonomy by extending both the symmetric and asymmetric joint models to sequential processes. 

Throughout this paper, as we consider the different joint model typologies, we discuss how these alternate joint models can be used to evaluate the direct and indirect effects of risk and protective factors on each process.