Fig. 1.

a Bivariate Choleksy with GxM model with the parent–child relationship variable moderating genetic and environmental effects on the mental health variable (model displayed for single member of a twin pair). A additive genetic effects, C shared environmental variance, E nonshared environmental influences. a_M, c_M, and e_M represent genetic, shared environmental, and nonshared environmental parameter estimates, respectively, for the moderator variable. a_c, c_c, and e_c signify variance shared between the moderator variable and the outcome variable. a_u, c_u, and e_u represent residual variance unique to the outcome variable. b Nonlinear main effects with GxM model with the parent–child relationship variable moderating genetic and environmental effects on the mental health variable (displayed for one member of a twin pair). A additive genetic effects, C shared environmental variance, E nonshared environmental influences. a_M, c_M, and e_M represent genetic, shared environmental, and nonshared environmental estimates for the moderator variable. a_u, c_u, and e_u denote residual variance unique to the outcome variable. α_u, κ_u, and ε_u denote interactions between the moderator (M) and the genetic and environmental influences on the outcome variable. β₁ and β₂ represent the linear and non-linear main effects of the moderator variable on the outcome variable