RSAVS_Compute_BIC: Compute Modified BIC
In fenguoerbian/RSAVS: Robust Subgroup Analysis and Variable Selection

RSAVS_Compute_BIC

R Documentation

Compute Modified BIC

This function computes the modified BIC(mBIC), given a specific solution.

RSAVS_Compute_BIC(
  y_vec,
  x_mat,
  beta_vec,
  mu_vec,
  loss_type,
  loss_param,
  phi,
  a,
  double_log_lik = TRUE
)

`y_vec`	numerical vector of response. `n = length(y_vec)` is the number of observations.
`x_mat`	numerical matrix of covariates. `p = ncol(x_mat)` is the number of covariates.
`beta_vec`	numerical vector of covariate effects
`mu_vec`	numerical vector of subgroup effect(intercept term) for each observations
`loss_type`, `loss_param`	type and parameters of the loss function `loss_type = "L1"`: L-1 loss, no actual parameter is needed. `loss_type = "L2"`: L-2 loss, no actual parameter is needed. `loss_type = "Huber"`, Huber loss, and `c = loss_param[0]`, where `c` is the parameter needed by huber loss. A popular choice is `c = 1.345`.
`phi`	a positive constant.
`a`	a scalar controlling the regression part of mBIC. If not provided, then the number of observation(`n`) is used.
`double_log_lik`	boolen, whether to use log logLik(double log likelihood) in the regression part of mBIC. Defaults to `TRUE`.

BIC = log(1 / a * sum(loss(y - mu - x * beta)) + |S| * Phi ,

where

mu is the intercept term of each observation. And the number of subgroups is K = length(unique(mu_vec)).
beta is the covariate effect vector. And the number of active covariates is Q = sum(beta_vec != 0).
the loss function is determined by loss_type and loss_param.
|S| is the complexity of the model and |S| = K + Q.
Phi is a constant and Phi = phi * log(log(n + p)) * log(n) / n.