The ACE(t) model with the A, C and E variance components as functions with respect to age modelled by B-splines.

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`data_m` |
An |

`data_d` |
An |

`mod` |
A character vector of length 3. Each element specifies the function for the A, C or E component respectively. The A and C components can be 'd'(dynamic), 'c'(constant) or 'n'(NA). The E component can only be 'd' or 'c'. Thus, |

`knot_a` |
The number of interior knots of the B-spline for the A component, which must be no less than 3. The default value is 5. |

`knot_c` |
The number of interior knots of the B-spline for the C component, which must be no less than 3. The default value is 5. |

`knot_e` |
The number of interior knots of the B-spline for the E component, which must be no less than 3. The default value is 5. |

`boot` |
A logical indicator of whether to use the bootstrap method to calculate the confidence interval. The default is FALSE. |

`num_b` |
The number of replicates when the bootstrap method is used (i.e. |

`init` |
A 3x1 vector of the initial values for the optimization. The default values are 1. |

`robust` |
An integer indicating the number of different initial values that the function will randomly generate and try in the optimization. The default value is 0. |

If the variance is close to the boundary (0), it is better to use the bootstrap method to get the CIs. The optimization algorithm may sometimes end up with a local minimum. It is recommended to try different random initial values by setting 'robust'.

`n_beta_a ` |
The number of spline coefficients for the A component. |

`n_beta_c ` |
The number of spline coefficients for the C component. |

`n_beta_e ` |
The number of spline coefficients for the E component. |

`beta_a ` |
The estimated spline coefficients (if the model parameter is 'd') or variance (if the model parameter is 'c') of the A component. |

`beta_c ` |
The estimated spline coefficients (if the model parameter is 'd') or variance (if the model parameter is 'c') of the C component. |

`beta_e ` |
The estimated spline coefficients (if the model parameter is 'd') or variance (if the model parameter is 'c') of the E component. |

`hessian_ap ` |
The approximated Hessian matrix from the quasi-Newton algorithm. |

`hessian ` |
The Hessian matrix calculated analytically. |

`con ` |
An indicator of convergence of the optimization algorithm. An integer code 0 indicates successful completion. See 'optim' for more details. |

`lik ` |
The minus log-likelihood. |

`knots_a ` |
A vector of the knot positions for the A component. |

`knots_c ` |
A vector of the knot positions for the C component. |

`knots_e ` |
A vector of the knot positions for the E component. |

`boot ` |
A list containing pointwise CIs estimated from the bootstrap method when |

Liang He

He, L., Sillanpää, M.J., Silventoinen, K., Kaprio, J. and Pitkäniemi, J., 2016. Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models. Genetics, 202(4), pp.1313-1328.

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