R/ols-best-subsets-regression.R

In cmlopera/olsrr: Tools for Building OLS Regression Models

#' Best subsets regression
#'
#' Select the subset of predictors that do the best at meeting some
#' well-defined objective criterion, such as having the largest R2 value or the
#' smallest MSE, Mallow's Cp or AIC.
#'
#' @param model An object of class \code{lm}.
#' @param x An object of class \code{ols_step_best_subset}.
#' @param ... Other inputs.
#'
#' @return \code{ols_step_best_subset} returns an object of class \code{"ols_step_best_subset"}.
#' An object of class \code{"ols_step_best_subset"} is a data frame containing the
#' following components:
#'
#' \item{n}{model number}
#' \item{predictors}{predictors in the model}
#' \item{rsquare}{rsquare of the model}
#' \item{adjr}{adjusted rsquare of the model}
#' \item{predrsq}{predicted rsquare of the model}
#' \item{cp}{mallow's Cp}
#' \item{aic}{akaike information criteria}
#' \item{sbic}{sawa bayesian information criteria}
#' \item{sbc}{schwarz bayes information criteria}
#' \item{gmsep}{estimated MSE of prediction, assuming multivariate normality}
#' \item{jp}{final prediction error}
#' \item{pc}{amemiya prediction criteria}
#' \item{sp}{hocking's Sp}
#'
#' @references
#' Kutner, MH, Nachtscheim CJ, Neter J and Li W., 2004, Applied Linear Statistical Models (5th edition).
#' Chicago, IL., McGraw Hill/Irwin.
#'
#' @section Deprecated Function:
#' \code{ols_best_subset()} has been deprecated. Instead use \code{ols_step_best_subset()}.
#'
#' @family variable selection procedures
#'
#' @examples
#' model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
#' ols_step_best_subset(model)
#'
#' # plot
#' model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars)
#' k <- ols_step_best_subset(model)
#' plot(k)
#'
#' @export
#'
ols_step_best_subset <- function(model, ...) UseMethod("ols_step_best_subset")

#' @export
#'
ols_step_best_subset.default <- function(model, ...) {

  check_model(model)
  check_npredictors(model, 3)

  nam <- coeff_names(model)

  n <-
    nam %>%
    length()

  r <-
    n %>%
    seq_len(.)

  combs <- list()

  for (i in seq_len(n)) {
    combs[[i]] <- combn(n, r[i])
  }

  lc <-
    combs %>%
    length()

  varnames <- model_colnames(model)

  predicts <- nam

  len_preds <-
    predicts %>%
    length()

  gap <- len_preds - 1

  space <- coeff_length(predicts, gap)

  data <- mod_sel_data(model)

  colas <-
    combs %>%
    map_int(ncol)

  response <-
    varnames %>%
    extract(1)

  p <- colas
  t <- cumsum(colas)
  q <- c(1, t[-lc] + 1)
  mcount <- 0
  rsq <- list()
  adjr <- list()
  cp <- list()
  aic <- list()
  sbic <- list()
  sbc <- list()
  mse <- list()
  gmsep <- list()
  jp <- list()
  pc <- list()
  sp <- list()
  press <- list()
  predrsq <- list()
  preds <- list()
  lpreds <- c()

  for (i in seq_len(lc)) {
    for (j in seq_len(colas[i])) {
      predictors <- nam[combs[[i]][, j]]
      lp <- length(predictors)
      out <- ols_regress(paste(response, "~", paste(predictors, collapse = " + ")), data = data)
      mcount <- mcount + 1
      lpreds[mcount] <- lp
      rsq[[mcount]] <- out$rsq
      adjr[[mcount]] <- out$adjr
      cp[[mcount]] <- ols_mallows_cp(out$model, model)
      aic[[mcount]] <- ols_aic(out$model)
      sbic[[mcount]] <- ols_sbic(out$model, model)
      sbc[[mcount]] <- ols_sbc(out$model)
      gmsep[[mcount]] <- ols_msep(out$model)
      jp[[mcount]] <- ols_fpe(out$model)
      pc[[mcount]] <- ols_apc(out$model)
      sp[[mcount]] <- ols_hsp(out$model)
      predrsq[[mcount]] <- ols_pred_rsq(out$model)
      preds[[mcount]] <- paste(predictors, collapse = " ")
    }
  }

  ui <- data.frame(
    n = lpreds,
    predictors = unlist(preds),
    rsquare = unlist(rsq),
    adjr = unlist(adjr),
    predrsq = unlist(predrsq),
    cp = unlist(cp),
    aic = unlist(aic),
    sbic = unlist(sbic),
    sbc = unlist(sbc),
    msep = unlist(gmsep),
    fpe = unlist(jp),
    apc = unlist(pc),
    hsp = unlist(sp),
    stringsAsFactors = F
  )

  sorted <- c()

  for (i in seq_len(lc)) {
    temp <- ui[q[i]:t[i], ]
    temp <- temp[order(temp$rsquare, decreasing = TRUE), ]
    sorted <- rbind(sorted, temp[1, ])
  }

  mindex <-
    sorted %>%
    nrow() %>%
    seq_len(.)

  sorted <- cbind(mindex, sorted)

  class(sorted) <- c("ols_step_best_subset", "tibble", "data.frame")

  return(sorted)

}

#' @export
#' @rdname ols_step_best_subset
#' @usage NULL
#'
ols_best_subset <- function(model, ...) {
  .Deprecated("ols_step_best_subset()")
}


#' @export
#'
print.ols_step_best_subset <- function(x, ...) {
  print_best_subset(x)
}

#' @export
#' @rdname ols_step_best_subset
#'
plot.ols_step_best_subset <- function(x, model = NA, ...) {

  rsquare <- NULL
  adjr    <- NULL
  sbic    <- NULL
  aic     <- NULL
  sbc     <- NULL
  cp      <- NULL
  a       <- NULL
  b       <- NULL


  d <- tibble(mindex = x$mindex, rsquare = x$rsquare, adjr = x$adjr,
               cp = x$cp, aic = x$aic, sbic = x$sbic, sbc = x$sbc)

  p1 <- best_subset_plot(d, rsquare)
  p2 <- best_subset_plot(d, adjr, title = "Adj. R-Square")
  p3 <- best_subset_plot(d, cp, title = "C(p)")
  p4 <- best_subset_plot(d, aic, title = "AIC")
  p5 <- best_subset_plot(d, sbic, title = "SBIC")
  p6 <- best_subset_plot(d, sbc, title = "SBC")

  # grid.arrange(p1, p2, p3, p4, p5, p6, ncol = 2, top = "Best Subsets Regression")
  myplots <- list(plot_1 = p1, plot_2 = p2, plot_3 = p3,
                  plot_4 = p4, plot_5 = p5, plot_6 = p6)
  result <- marrangeGrob(myplots, nrow = 2, ncol = 2)
  result

}

#' Best subset plot
#'
#' Generate plots for best subset regression.
#'
#' @importFrom ggplot2 geom_line theme element_blank
#'
#' @param d1 A tibble.
#' @param title Plot title.
#'
#' @noRd
#'
best_subset_plot <- function(d, var, title = "R-Square") {

  mindex <- NULL
  a      <- NULL
  b      <- NULL

  varr   <- enquo(var)

  d %>%
    select(a = mindex, b = !! varr) %>%
    ggplot(aes(x = a, y = b)) +
    geom_line(color = "blue") +
    geom_point(color = "blue", shape = 1, size = 2) +
    xlab("") + ylab("") + ggtitle(title) +
    theme(axis.ticks = element_blank())

}