A Unified Framework of Longitudinal Models to Examine Reciprocal Relations

Inferring reciprocal effects or causality between variables is a central aim of behavioral and psychological research. To address reciprocal effects, a variety of longitudinal models that include cross-lagged relations have been proposed in different contexts and disciplines. However, the relations between these cross-lagged models have not been systematically discussed in the literature. This lack of insight makes it difficult for researchers to select an appropriate model when analyzing longitudinal data, and some researchers do not even think about alternative cross-lagged models. The present research provides a unified framework that clarifies the conceptual and mathematical similarities and differences between these models. The unified framework shows that existing longitudinal models can be effectively classified based on whether the model posits unique factors and/or dynamic residuals and what types of common factors are used to model changes. The latter is essential to understand how cross-lagged parameters are interpreted. We also present an example using empirical data to demonstrate that there is great risk of drawing different conclusions depending on the cross-lagged models used.