Exploratory SEM on longitudinal data: Causal modeling in the absence of a priori hypotheses

Structural Equations Models (SEM) are normally used to test the agreement between the data and a hypothesized model of causal relationships among multiple variables. However, in many circumstances it is hard to define one or several causal models to test, either because there is insufficient understanding of the field or because too many variables are involved. A prominent example is studies using biomarkers in population health, where the biomarkers are presumably parts of physiological regulatory networks that are still poorly understood. In this case, an exploratory version of SEM is needed to define a limited subset of models that are in agreement with the data, and which can be further tested. Here, we present such a method using longitudinal biomarker data. The algorithm explores all identified three-variable models and uses these results to eliminate as many non-supported causal relationships as possible. The model then proceeds systematically through 4-variable and larger models, incorporating the results of the lower-order models. Gradually this process builds a consensus set of models in which all non-supported relationships have been eliminated, but which may still contain ambiguous relationships. These models can then be tested in independent or test data sets set aside for this purpose.