Finds the solution path of logistic functional additive regression with log-contrast constrain and FLiRTI strategy

Logistic_FAR_FLiRTI_Path finds the solution path of logistic functional additive regression with log-contrast constrain. It will NOT perform within-group orthonormalization as preprocession of the data. NOTE: This documentation needs to be double checked and updated!

Usage

Logistic_FAR_FLiRTI_Path(
  y_vec,
  x_mat,
  h,
  kn,
  p,
  p_type,
  p_param,
  lambda_seq,
  lambda_length,
  min_lambda_ratio = 0.01,
  mu2,
  a = 1,
  bj_vec = 1,
  cj_vec = sqrt(kn),
  rj_vec = 10^(-6),
  weight_vec = 1,
  delta_init,
  eta_stack_init,
  mu1_init,
  tol = 10^(-6),
  max_iter = 500,
  verbose = 0,
  svd_thresh = 10^{
-7
 }
)

Arguments

y_vec: response vector, 0 for control, 1 for case. n = length(y_vec) is the number of observations.
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.
h, kn, p: dimension information for the dataset(x_mat).
p_type: an character variable indicating different types of the penalty
p_param: numerical vector for the penalty function. p_param[1] store sthe lambda value and will be provided by lambda_seq.
lambda_seq: a non-negative sequence of lambda, along which the solution path is searched. It is RECOMMENED to not supply this parameter and let the function itself determines it from the given data.
lambda_length: length of the lambda sequence when computing lambda_seq. If lambda_seq is provided, then of course lambda_length = length(lambda_seq).
mu2: quadratic term in the ADMM algorithm
a, bj_vec, cj_vec, rj_vec: parameters for the algorithm. See Algorithm_Details.pdf for more information.
delta_init, eta_stack_init, mu1_init: initial values for the algorithm.
tol, max_iter: convergence tolerance and max number of iteration of the algorithm.
verbose: integer, indicating level of information to be printed during computation, currently supports: always: some info if something went wrong, e.g. when no penalty function is matched 1: information about the start and stop of the iteration 2. How the loss value is changed during each iteration
svd_thresh: not used
min_lam_ratio:: min(lambda_seq) / max{lambda_seq}. This function uses this parameter to determine the minimal value of lambda_seq. If p > n, then it is recommended to set this no smaller than 0.01 (sometimes even 0.05), otherwise you can set it to 0.001 or even smaller.

Value

A list containing the solution path of delta, eta_stack, mu1 and some computation information such as convergency, iteration number and the lambda sequence of this solution path.