We first tested whether variance components could be constrained to be equal across the sexes in the saturated model. This resulted in a significant deterioration in fit (Δ χ2 = 42.58, Δdf = 16, AIC = + 10.58) (Table 3) so subsequent models did not incorporate this constraint. We next tested an AE model, in which shared environment does not contribute to variance, and a CE model, in which genetic factors do not contribute to variance. The AE model fit well (Δχ2 = 9.63, Δdf = 10, p = 0.473, AIC = −10.37); however, the CE model fit significantly worse (Δχ2 = 219.66, Δdf = 10, p < 0.001, AIC = + 199.66) and was rejected. We subsequently tested a series of models nested within the full AE model, e.g. to assess whether the genetic and environmental correlations between traits could be removed without a deterioration in fit. Ultimately, only the environmental correlation path between MD and regular cigarette use (path e2,1) could be removed, and only in males. Parameter estimates of the best-fitting models for these analyses are depicted in Figs. 2a and b.
