Hess_rho | R Documentation |

Hessian matrix of LCV and LAML wrt rho (log smoothing parameters)

```
Hess_rho(
X_GL,
X_GL_Q,
GL_temp,
haz_GL,
deriv2_rho_beta,
deriv_rho_beta,
weights,
tm,
nb_smooth,
p,
n_legendre,
deriv_rho_inv_Hess_beta,
deriv_rho_Hess_unpen_beta,
S_list,
minus_eigen_inv_Hess_beta,
temp_LAML,
temp_LAML2,
Vp,
S_beta,
beta,
inverse_new_S,
X,
X_Q,
temp_deriv3,
temp_deriv4,
event,
expected,
type,
Ve,
deriv_rho_Ve,
mat_temp,
deriv_mat_temp,
eigen_mat_temp,
method
)
```

`X_GL` |
list of matrices ( |

`X_GL_Q` |
list of transformed matrices from X_GL in order to calculate only the diagonal of the fourth derivative of the likelihood |

`GL_temp` |
list of vectors used to make intermediate calculations and save computation time |

`haz_GL` |
list of all the matrix-vector multiplications X.GL[[i]]%*%beta for Gauss Legendre integration in order to save computation time |

`deriv2_rho_beta` |
second derivatives of beta wrt rho (implicit differentiation) |

`deriv_rho_beta` |
firt derivatives of beta wrt rho (implicit differentiation) |

`weights` |
vector of weights for Gauss-Legendre integration on [-1;1] |

`tm` |
vector of midpoints times for Gauss-Legendre integration; tm = 0.5*(t1 - t0) |

`nb_smooth` |
number of smoothing parameters |

`p` |
number of regression parameters |

`n_legendre` |
number of nodes for Gauss-Legendre quadrature |

`deriv_rho_inv_Hess_beta` |
list of first derivatives of Vp wrt rho |

`deriv_rho_Hess_unpen_beta` |
list of first derivatives of Hessian of unpenalized log likelihood wrt rho |

`S_list` |
List of all the rescaled penalty matrices multiplied by their associated smoothing parameters |

`minus_eigen_inv_Hess_beta` |
vector of eigenvalues of Vp |

`temp_LAML` |
temporary matrix used when method="LAML" to save computation time |

`temp_LAML2` |
temporary matrix used when method="LAML" to save computation time |

`Vp` |
Bayesian covariance matrix |

`S_beta` |
List such that S_beta[[i]]=S_list[[i]]%*%beta |

`beta` |
vector of estimated regression parameters |

`inverse_new_S` |
inverse of the penalty matrix |

`X` |
design matrix for the model |

`X_Q` |
transformed design matrix in order to calculate only the diagonal of the fourth derivative of the likelihood |

`temp_deriv3` |
temporary matrix for third derivatives calculation when type="net" to save computation time |

`temp_deriv4` |
temporary matrix for fourth derivatives calculation when type="net" to save computation time |

`event` |
vector of right-censoring indicators |

`expected` |
vector of expected hazard rates |

`type` |
"net" or "overall" |

`Ve` |
frequentist covariance matrix |

`deriv_rho_Ve` |
list of derivatives of Ve wrt rho |

`mat_temp` |
temporary matrix used when method="LCV" to save computation time |

`deriv_mat_temp` |
list of derivatives of mat_temp wrt rho |

`eigen_mat_temp` |
vector of eigenvalues of mat_temp |

`method` |
criterion used to select the smoothing parameters. Should be "LAML" or "LCV"; default is "LAML" |

Hessian matrix of LCV or LAML wrt rho

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