R/regress_select.R

In EvanWie/regNselect:

## usethis namespace: start
#' @useDynLib regNselect, .registration = TRUE
## usethis namespace: end
NULL

## usethis namespace: start
#' @importFrom Rcpp sourceCpp
## usethis namespace: end
NULL

#' 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 of coefficients, estimate standard errors, test statistics, and p-values
#'
#' @export
lin_model = function(formula, data, weights= NULL){
  if(length(formula[[2]]) != 1){
    stop("y must be univariate")
  }

  modframe = model.frame(formula = formula, data = data)

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

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

  n = length(y)

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

    res = y - x%*%beta

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

    varcov_beta = solve(t(x)%*%x)*sigma_sq
  } else {

    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
    #beta = betaRcpp(y,x)

    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))

  test_stat = beta/se_beta

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

  results = cbind.data.frame(coefficients = round(beta,6), St.Error = round(se_beta,6),
                             test_statistic = round(test_stat,3), p_value = p)
  row.names(results) = colnames(x)

  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).
#'
#' @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 Dataframe of coefficients, estimate standard errors, test statistics, and p-values
#' for parameters remaining in the model following backwards selection.
#'
#' @export
back_select = function(formula, data, prem = .1){
  if(length(formula[[2]]) != 1){
    stop("y must be univariate")
  }

  modframe = model.frame(formula = formula, data = data)

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

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

  n = length(y)

  beta = solve(t(x)%*%x)%*%t(x)%*%y
  #beta = betaRcpp(y,x)

  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()

  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}
  }

  results = cbind.data.frame(coefficients = round(beta,6), St.Error = round(se_beta,6),
                             test_statistic = round(test_stat,3), p_value = p)
  row.names(results) = c("Intercept",colnames(x)[2:max(2,q)])

  cat("Removed variables:\n", removed_vars, "\n")

  return(results)
}

#x = rnorm(10)
#x2 = rnorm(10)
#x3 = rnorm(10)
#y = rnorm(10)
#df = data.frame(y, x, x2, x3)
#lin_model(y~x*x2,df)

#back_select(y~x*x2,df,.5)

#summary(lm(y~x*x2, data = df))
#olsrr::ols_regress(y~x*x2, data = df)
#result = bench::mark(lin_model(y~x*x2,df)[1], as.vector(olsrr::ols_regress(y~x*x2, data = df)$beta)[1])
#plot(result)
#result2 = bench::mark(lin_model(y~x*x2,df)[1], as.vector(lm(y~x*x2, data = df)$coefficients[1]))
#plot(result2)

#result3 = bench::mark(lin_model(y~x*x2,df)[1], lin_model2(y~x*x2,df)[1])
#plot(result3)