# Fitting the ACE(t)-p model

### Description

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

### Usage

1 2 | ```
AtCtEtp(data_m, data_d, knot_a = 8, knot_c = 8, knot_e = 8, eps = 0.1,
mod=c('d','d','d'), robust = 0)
``` |

### Arguments

`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. |

### Details

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.

### Value

`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. |

### 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

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'))
``` |