# Fitting the ACE(t) model

### Description

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

### Usage

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### Arguments

`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. |

### Details

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'.

### Value

`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 |

### Author(s)

Liang He

### References

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.

### Examples

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