Hess_rho: Hessian matrix of LCV and LAML wrt rho (log smoothing...
In survPen: Multidimensional Penalized Splines for Survival and Net Survival Models

Hess_rho

R Documentation

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"