Post-selection estimation — Logistic_FAR_FLiRTI_Path_Further

This function performs post-selection estimation on a given solution.

Usage

Logistic_FAR_FLiRTI_Path_Further_Improve(
  x_mat,
  y_vec,
  h,
  k_n,
  p,
  delta_vec_init,
  eta_stack_init,
  mu1_vec_init,
  mu2,
  a = 1,
  lam = 0.1,
  weight_vec = NULL,
  tol = 10^(-5),
  max_iter = 1000
)

Arguments

x_mat: covariate matrix, consists of two parts. dim(x_mat) = (n, h + p * kn) First h columns are for demographical covariates(can include an intercept term) Rest columns are for p functional covariates, each being represented by a set of basis functions resulting kn covariates.
y_vec: response vector, 0 for control, 1 for case. n = length(y_vec) is the number of observations.
h, k_n, p: dimension information for the dataset(x_mat).
delta_vec_init, eta_stack_init, mu1_vec_init: Initial values for the algorithm. This function uses these initial values to find out the active functional covariates. And the post-selection estimation begins with these initial values.
mu2: quadratic term in the ADMM algorithm
a: parameters for the algorithm. The 1st term in the loss function is 1 / a * loglik. See Algorithm_Details.pdf for more information.
lam: A scalar for the regularize in ridge penalty form in case of model saturation.
tol, max_iter: convergence tolerance and max number of iteration of the algorithm.