MissImp: Missing Data Imputation

#' MCAR Test
#' @description \code{mcar_test_combined} shows if a missing data mechanism is
#' MCAR by performing three classical statistic tests:
#' - the dummy variable test \code{dummy_test}, Little's MCAR test
#' \code{mcar_test} from package \code{naniar} and
#' - the normality tests (Hawkin's test and non-parametric test included)
#' - \code{TestMCARNormality} from package \code{MissMech}.
#' Our null hypothesis H0 is that the missing data mechanism is MCAR.
#' These three tests focus on testing different aspects of MCAR mechanism.
#' The dummy variable test is to verify if the value of one variable is
#' correlated with the missingnness of another variable. Little's MCAR tet
#' focuses on testing the if the mean vector for each missig pattern is part of
#' the total mean vector. And the normality tests focuses on testing the
#' normality and homoscedasticity according to the variance matrix.
#' The conclusion of these three tests as well as their statistics will be
#' returned.
#' @param df Incomplete dataframe.
#' @param col_cat Categorical columns index.
#' @param p_val Significance level.
#' @return \code{test_results} The final results from the three tests mentioned
#' in 'Description'. \code{TRUE} means that we don't have enough evidence to
#' reject our H0: the missing data mechanism is MCAR. And \code{FALSE} means
#' that H0 is rejected, the missing data mechanism is not MCAR.
#' @return \code{p_values} The p-values of our three tests.
#' @return \code{result_dummy_test} The detailed result from dummy variable
#' test.
#' @return \code{result_little_test} The detailed result from Little's MCAR
#' test.
#' @return \code{result_missmech} The detailed result from the normality tests
#' (Hawkin's test and non-parametric test).
#' @export
#' @examples
#' n <- 10000
#' mu.X <- c(1, 2, 3)
#' Sigma.X <- matrix(c(9, 3, 2, 3, 4, 0, 2, 0, 1), nrow = 3)
#' X.complete.cont <- MASS::mvrnorm(n, mu.X, Sigma.X)
#' rs <- generate_miss(X.complete.cont, 0.5, mechanism = "MAR1")
#' mcar_test_combined(data.frame(rs$X.incomp))$test_result
mcar_test_combined <- function(df, col_cat = c(), p_val = 0.1) {
  is_naniar_package_installed()
  out_dummy <- dummy_test(df, col_cat)
  out_little <- naniar::mcar_test(df)
  exist_cat <- !all(c(0, col_cat) == c(0))
  if (exist_cat) {
    print("The normality test is written for numerical dataframes.
          Here the test is performed on only the numerical part of the input
          dataframe.\n")
    df <- subset(df, select = -col_cat)
  }
  out_missmech <- TestMCARNormality(df)
  p_values <- data.frame(
    "Dummy variable test" = out_dummy$p.value,
    "Little's MCAR test" = out_little$p.value,
    "Hawkin's test" = out_missmech$pvalcomb,
    "Non parametric test" = out_missmech$pnormality
  )
  test_results <- data.frame(
    "Dummy variable test" = (out_dummy$p.value > p_val),
    "Little's MCAR test" = (out_little$p.value > p_val),
    "MissMech test" = ((out_missmech$pvalcomb < p_val) * (
      out_missmech$pnormality < p_val) == 0)
  )
  return(list(
    test_results = test_results, p_values = p_values,
    result_dummy_test = out_dummy, result_little_test = out_little,
    result_missmech = out_missmech
  ))
}