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

1 2 |

`data_m` |
An |

`data_d` |
An |

`knot_a` |
The number of interior knots of the B-spline for the A component. The default value is 8. |

`knot_c` |
The number of interior knots of the B-spline for the C component. The default value is 8. |

`knot_e` |
The number of interior knots of the B-spline for the E component. The default value is 8. |

`eps` |
Tolerance for convergence of the EM algorithm iterations. The default value is 0.1. |

`mod` |
A character vector of length 3. Each element specifies the function for the A, C or E component respectively. The components can be 'd'(dynamic), 'c'(constant) or 'l'(linear). The default is c('d','d','d'). |

`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. |

When the 'mod' argument for a component is 'd'(dynamic), the corresponding 'beta' is the spline coefficients. When the 'mod' argument for a component is 'l'(linear), the corresponding 'beta' is a vector of two values, the exponential of which (exp(beta)) are the variances at the minimum and maximum age (or other covariates) provided in the data. When the 'mod' argument for a component is 'c'(constant), the corresponding 'beta' has only one value and exp(beta) is the variance.

`var_b_a ` |
The estimated variance for the penalized coefficient for the A components. |

`var_b_c ` |
The estimated variance for the penalized coefficient for the C components. |

`var_b_e ` |
The estimated variance for the penalized coefficient for the E components. |

`beta_a ` |
The estimated spline coefficients of the A component. See 'details' for more information. |

`beta_c ` |
The estimated spline coefficients of the C component. See 'details' for more information. |

`beta_e ` |
The estimated spline coefficients of the E component. See 'details' for more information. |

`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 marginal likelihood. |

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

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

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

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.

1 2 3 | ```
# data(data_ace)
# result <- AtCtEtp(data_ace$mz, data_ace$dz, knot_e = 7, knot_c = 5, mod=c('d','d','d'))
``` |

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