Under the Cholesky decomposition model any covariance between PGD and CU is attributable to unmeasured correlated, latent liabilities. This model is agnostic in so far it does make predictions about the direction of causation. It is possible to use the same cross-twin cross-trait correlations to test hypotheses about the direction of causation at the phenotypic level between variables measured at the same time. This form of modeling assumes that (see 62) sibling cooperation or rivalry is absent, the relationship between PGD and CU is equivalent for twin 1 and twin 2, the twin pair correlations are different for PGD and CU (63), and there are no unmeasured variables which influence both measures thereby inflating the correlations arising through the causal influence of one variable on the other. Based on the methods described elsewhere (44, 62, 64) we fitted a series of uni-directional and reciprocal causation models to the twin data illustrated in Figure 2. Heath (62) has shown that the uni-directional and reciprocal causation models are nested within the Cholesky decomposition which permits model comparisons using goodness of fit statistics.
