grad_rho_mult: Gradient vector of LCV and LAML wrt rho (log smoothing parameters). Version for multiplicative decomposition : relative mortality ratio model

Description

Gradient vector of LCV and LAML wrt rho (log smoothing parameters). Version for multiplicative decomposition : relative mortality ratio model

Usage

grad_rho_mult(
  X_GL,
  GL_temp,
  haz_GL,
  deriv_rho_beta,
  weights,
  tm,
  nb_smooth,
  p,
  n_legendre,
  S_list,
  temp_LAML,
  Vp,
  S_beta,
  beta,
  inverse_new_S,
  X,
  event,
  expected,
  Ve,
  mat_temp,
  method
)

Value

List of objects with the following items:

grad_rho: gradient vector of LCV or LAML
deriv_rho_inv_Hess_beta: List of first derivatives of Vp wrt rho
deriv_rho_Hess_unpen_beta: List of first derivatives of the Hessian of the unpenalized log-likelihood wrt rho

Arguments

X_GL: list of matrices (length(X.GL)=n.legendre) for Gauss-Legendre quadrature
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
deriv_rho_beta: firt derivative 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
S_list: List of all the rescaled penalty matrices multiplied by their associated smoothing parameters
temp_LAML: 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
event: vector of right-censoring indicators
expected: vector of expected hazard rates
Ve: frequentist covariance matrix
mat_temp: temporary matrix used when method="LCV" to save computation time
method: criterion used to select the smoothing parameters. Should be "LAML" or "LCV"; default is "LAML"