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 means part of the model: the estimated means of M and T, respectively), this bivariate moderation model describes the relations between T and M in great detail. In practice, describing (decomposing) a small covariance between M and T with as much as 6 parameters, can be computationally challenging, and solutions can be quite sensitive to starting values. Also, Rathouz et al. (2008) have shown that this model sometimes produces spurious moderation effects. More practically, programs like Mx (Neale et al. 2006) do not allow the simultaneous modeling of categorical and continuous variables, which complicates this bivariate parameterization of T and M if the two variables do not have the same measurement level.4 Finally, when the moderator of interest is a family-level variable, i.e., a variable that is by definition equal for twin 1 and twin 2, such as socioeconomic status in childhood (SES) or parental educational attainment level, then a bivariate parameterization is infeasible as the moderator does not show
