R/akaike_adjusted_rsq.R

In AICcPermanova: Model Selection of PERMANOVA Models Using AICc

#' Akaike-Adjusted R Squared Calculation with Model Averaging
#'
#' Calculates the adjusted R squared for each predictor using the Akaike
#' Information Criterion (AIC) and model averaging. AIC is used to compare the
#' performance of candidate models and select the best one. Then, the R squared
#' is adjusted based on the weight of evidence in favor of each model. The final
#' result is a long-format table of variable names and corresponding adjusted
#' R squared values.
#'
#' @param DF A data.frame containing the variables to calculate the adjusted
#'           R squared for. The data.frame should include the columns:
#'           "form", "AICc", "max_vif", "k", "DeltaAICc", "AICWeight", and "N".
#' @return A data.frame with columns "Variable" and "Full_Akaike_Adjusted_RSq".
#'         Each row represents a predictor, and its corresponding adjusted R
#'         squared value based on the Akaike-adjusted model averaging process.
#' @details The adjusted R squared is calculated as:
#'          \deqn{Adjusted R^2 = 1 - (RSS / (N - k - 1)) * ((N - 1) / (N - k - 1))}
#'          where RSS is the residual sum of squares, N is the sample size, and
#'          k is the number of predictors. The R squared is adjusted based on the
#'          weight of evidence in favor of each model, which is calculated as:
#'          \deqn{w_i = exp(-0.5 * DeltaAICc_i) / sum(exp(-0.5 * DeltaAICc))}
#'          where w_i is the weight of evidence in favor of the ith model, and
#'          DeltaAICc_i is the difference in AICc between the ith model and the
#'          best model. Model averaging uses the weights to combine the
#'          performance of different models in the final calculation of the
#'          adjusted R squared.
#'
#' @importFrom dplyr mutate_at vars matches everything select summarise_if
#' @importFrom tidyr pivot_longer
#'
#' @examples
#' library(data.table)
#' df <- data.table(form = c(1,2,3),
#'                  AICc = c(10,20,30),
#'                  max_vif = c(3,4,5),
#'                  k = c(1,2,3),
#'                  DeltaAICc = c(2,5,8),
#'                  AICWeight = c(0.2,0.5,0.3),
#'                  N = c(100,100,100),
#'                  A1 = c(0.3, 0.5, NA),
#'                  A2 = c(0.7, NA, 0.2),
#'                  A3 = c(0.2, 0.3, 0.6))
#' akaike_adjusted_rsq(df)
#'
#' @export

akaike_adjusted_rsq <- function(DF) {
  AICc <- DeltaAICc <- max_vif <- AICWeight <- Model <- k <- N <- NULL
  Result <- DF |>
    dplyr::mutate_at(dplyr::vars(-dplyr::matches("form|max_vif|AICc|k|DeltaAICc|N|AICWeight")), ~ifelse(is.na(.x), 0, .x))|>
    dplyr::mutate_at(dplyr::vars(-dplyr::matches("form|max_vif|AICc|k|DeltaAICc|N|AICWeight")), ~.x * AICWeight)|>
    dplyr::summarise_if(is.numeric, sum)|>
    dplyr::select(-AICc, -DeltaAICc, -AICWeight, -matches("Model"), -max_vif, -k, -N)|>
    tidyr::pivot_longer(dplyr::everything(), names_to = "Variable", values_to = "Full_Akaike_Adjusted_RSq")

  return(Result)
}