R/regSel_code.R

Defines functions back_select lin_model

Documented in back_select lin_model

#' Linear regression model
#'
#' Performs linear regression using Ordinary Least Squares (or Weighted Least Squares when weights are specified)
#'
#' @param formula Model formula using specified columns of DataFrame 'data'. Can include interactions and select no intercept
#' with -1
#' @param data Dataframe from which model variables are pulled.
#' @param weights Vector of weights to be used in Weighted Least Squares regression estimates. Default = NULL.
#' @return List containing the following elements
#' \itemize{
#' \item beta estimates
#' \item estimate standard errors
#' \item test statistics
#' \item p-values
#' \item residuals
#' }
#' @examples  x = rnorm(10)
#' x2 = rnorm(10)
#' y = rnorm(10)
#' df = data.frame(y,x,x2)
#'
#' lin_model(formula = y~x*x2, data = df, weights = 1:10)
#'
#' lin_model(formula = y~1, data = df)
#'
#' @export
lin_model = function(formula, data, weights= NULL){
  if(length(formula[[2]]) != 1){
    stop("y must be univariate")
  }

  #Parse formula into its response and covariates
  modframe = model.frame(formula = formula, data = data)

  y <- model.response(modframe, "numeric")

  x = model.matrix(formula, data = data)

  n = length(y)

  #OLS beta, variance calculations
  if(is.null(weights)){
    beta = solve(t(x)%*%x)%*%t(x)%*%y

    res = y - x%*%beta

    sigma_sq = sum(res^2)/(n-ncol(x))

    varcov_beta = solve(t(x)%*%x)*sigma_sq
  } else {
    #WLS beta, variance calculations

    if(!is.vector(weights) | length(weights) != n){
      stop("Weights must be written as a vector with length equal to length y")
    }

    w = diag(weights)
    beta = solve(t(x) %*% w %*% x) %*% t(x) %*% w %*% y

    res = y - x%*%beta

    sigma_sq <- sum(weights*res^2)/(n - ncol(x))

    varcov_beta = sigma_sq* solve(t(x)%*%w%*%x)
  }

  se_beta =sqrt(diag(varcov_beta))

  #Calculate test stats and p-values and gather results
  test_stat = beta/se_beta

  p = 2*pt(-abs(test_stat), n-1)

  results = list(betas = as.vector(beta), se_beta = as.vector(se_beta),
                 test_statistic = as.vector(test_stat), p_value = as.vector(p), res = as.vector(res))

  names(results$betas) = colnames(x)
  names(results$se_beta) = names(results$betas)
  names(results$test_statistic) = names(results$betas)
  names(results$p_value) = names(results$betas)

  return(results)
}


#' Backwards selcection of linear regression model
#'
#' Performs backwards selection of model parameters. Removes parameter with greatest p-value above "prem" threshold.
#' P-values are calculated using Ordinary Least Squares (no weighting option). Must have at least one non-intercept
#' covariate in the model.
#'
#' @param formula Model formula using specified columns of DataFrame 'data'. Can include interactions and select no intercept
#' with -1.
#' @param data Dataframe from which model variables are pulled.
#' @param prem Threshold at which a parameter will be removed from the model if it has the highest p-value above the threshold.
#' The default value is .1.
#' @return List containing the following elements
#' \itemize{
#' \item beta estimates
#' \item estimate standard errors
#' \item test statistics
#' \item p-values
#' \item residuals
#' \item covariates removed from model
#' }
#' @examples x = rnorm(10)
#' x2 = rnorm(10)
#' y = rnorm(10)
#' df = data.frame(y,x,x2)
#'
#' back_select(formula = y~x*x2, data = df, prem = .1)
#'
#' @export
back_select = function(formula, data, prem = .1){
  if(length(formula[[2]]) != 1){
    stop("y must be univariate")
  }

  if(formula[[3]]==1){
    stop("Model must have at least one covariate")
  }

  #Parse formula into response and covariates
  modframe = model.frame(formula = formula, data = data)

  y <- model.response(modframe, "numeric")

  x = model.matrix(formula, data = data)

  n = length(y)

  #Calculate initial OLS beta, variance, and p-values
  beta = solve(t(x)%*%x)%*%t(x)%*%y

  res = y - x%*%beta

  q = ifelse(is.matrix(x), ncol(x), 1)
  sigma_sq = sum(res^2)/(n-q)

  varcov_beta = solve(t(x)%*%x)*sigma_sq

  se_beta =sqrt(diag(varcov_beta))

  test_stat = beta/se_beta

  p = 2*pt(-abs(test_stat), n-1)

  removed_vars = c()

  #Repeat parameter estimation and variance calculations until maximum p-value less than removal threshold
  while(max(p[2:max(2,q)]) > prem){
    rem_col = which(p == max(p[2:ncol(x)]))

    removed_vars = c(removed_vars, colnames(x)[rem_col])

    x = x[,-rem_col]

    beta = solve(t(x) %*% x) %*% t(x) %*% y

    res = y - x%*%beta

    q = ifelse(is.matrix(x), ncol(x), 1)
    sigma_sq = sum(res^2)/(n-q)

    varcov_beta = solve(t(x)%*%x)*sigma_sq

    se_beta =sqrt(diag(varcov_beta))

    test_stat = beta/se_beta

    p = 2*pt(-abs(test_stat), n-1)

    if(q == 1){break}
  }

  #Gather results from final model

  results = list(betas = as.vector(beta), se_beta = as.vector(se_beta),
                 test_statistic = as.vector(test_stat), p_value = as.vector(p),
                 res = as.vector(res), removed_vars = removed_vars)

  names(results$betas) = c("(Intercept)",colnames(x)[2:max(2,q)])
  names(results$se_beta) = names(results$betas)
  names(results$test_statistic) = names(results$betas)
  names(results$p_value) = names(results$betas)

  return(results)
}
EvanWie/regSel documentation built on Nov. 26, 2019, 2:11 a.m.