Besides moderating the variance decomposition of trait T, the moderator itself may be correlated with the trait T via A, C, and/or E. The full bivariate moderation model (depicted in Fig. 1a), in which the variances of both trait T and moderator M, as well as their covariance, are decomposed into the three sources of variation (A, C, and E), allows one to test both the presence of moderation on the variance components unique to trait T, and the presence of moderation effects on the variance components common to trait T and moderator M, i.e., on the cross paths. Investigation of moderation of the covariance between the M and T, such as modeled via the 3 cross paths, is of interest if one wishes to understand the nature of, or the process underlying, the relation between M and T. With 17 parameters (15 describing the variance part of the model: 3 parameters unique to the moderator, 6 to describe the covariance between T and M, and 6 to describe the variance decomposition unique to T; and 2 parameters describing the
