Understanding Dyad, Person, and Contextual Effects in Dyadic Analysis

Several interesting variations on the Common Fate Model (CFM) for dyadic analysis have emerged over the past decade. For instance, the multilevel-CFM is characterized by directional paths between Person level observed X and Y variables in addition to the Dyad level direct path between the corresponding latent variables. Although this model appears to provide a decomposition of the Y on X regression into Dyad and Person level components, close examination reveals that this specification yields a Dyad level coefficient that captures the contextual effect, or the discrepancy in the between- and within-cluster coefficients. The present work elucidates key features of the multilevel-CFM that produce the contextual effect parametrization, and introduces an alternative specification, the between-within-CFM that yields a decomposition of the Y on X regression consistent with the general multilevel SEM literature. These variations on the CFM are illustrated using empirical examples, supported by syntax for commonly used SEM software.