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Hess_rho

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

Description

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

Usage

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
)

Arguments

X_GL

list of matrices (length(X.GL)=n.legendre) for Gauss-Legendre quadrature
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"

Value

Hessian matrix of LCV or LAML wrt rho

survPen

Multidimensional Penalized Splines for Survival and Net Survival Models

v1.5.1
GPL-3 | file LICENSE
Authors
Mathieu Fauvernier [aut, cre], Laurent Roche [aut], Laurent Remontet [aut], Zoe Uhry [ctb], Nadine Bossard [ctb]
Initial release

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