R/GLM_gradient_constant.R

In Z1chenZhao/bis557: BIS557

#' GLM_gradient_constant
#'
#' @description Implement a first-order solution for the GLM maximum likelihood
#' problem using only gradient information, avoiding the Hessian matrix.
#' Constant step size.
#'
#' @param X The design matrix
#' @param Y Response variable
#' @param mu_fun A function to use eta get mu
#' @param maxit The maximum iteration times to allow the loop to exit, set default as 1e5
#' @param tol The difference between previous beta and new beta to allow
#' the loop to exit, set default as 1e-5.
#'
#' @details  The code is adapted from lecture notes.
#' @return A list of beta coefficients.
#' @importFrom utils tail
#' @export
#'

GLM_gradient_constant <- function(X,
                     Y,
                     mu_fun,
                     maxit = 1e5,
                     tol = 1e-5){

  beta <- matrix(rep(0, ncol(X), ncol = 1))
  beta_diff <- c()
  for (i in seq_len(maxit)) {
    beta_old <- beta
    eta <- X %*% beta
    mu <- mu_fun(eta)
    beta <- beta_old + t(X) %*% (Y - matrix(mu, ncol = 1))/10000
    beta_diff <- c(beta_diff, sum( (beta - beta_old)^2 ))

    if (tail(beta_diff, 1) < tol) {
      break
    }
  }
  return(list(coefficients = beta))
}