utils-distribution-comparison.R

#' Compare Empirical Data to Distributions
#'
#' @family Empirical
#'
#' @author Steven P. Sanderson II, MPH
#'
#' @details The purpose of this function is to take some data set provided and
#' to try to find a distribution that may fit the best. A parameter of
#' `.distribution_type` must be set to either `continuous` or `discrete` in order
#' for this the function to try the appropriate types of distributions.
#'
#' The following distributions are used:
#'
#' Continuous:
#' -  tidy_beta
#' -  tidy_cauchy
#' -  tidy_chisquare
#' -  tidy_exponential
#' -  tidy_gamma
#' -  tidy_logistic
#' -  tidy_lognormal
#' -  tidy_normal
#' -  tidy_pareto
#' -  tidy_uniform
#' -  tidy_weibull
#'
#' Discrete:
#' -  tidy_binomial
#' -  tidy_geometric
#' -  tidy_hypergeometric
#' -  tidy_poisson
#'
#' The function itself returns a list output of tibbles. Here are the tibbles that
#' are returned:
#' -  comparison_tbl
#' -  deviance_tbl
#' -  total_deviance_tbl
#' -  aic_tbl
#' -  kolmogorov_smirnov_tbl
#' -  multi_metric_tbl
#'
#' The `comparison_tbl` is a long `tibble` that lists the values of the `density`
#' function against the given data.
#'
#' The `deviance_tbl` and the `total_deviance_tbl` just give the simple difference
#' from the actual density to the estimated density for the given estimated distribution.
#'
#' The `aic_tbl` will provide the `AIC` for liklehood of the distribution.
#'
#' The `kolmogorov_smirnov_tbl` for now provides a `two.sided` estimate of the
#' `ks.test` of the estimated density against the empirical.
#'
#' The `multi_metric_tbl` will summarise all of these metrics into a single tibble.
#'
#'
#' @description Compare some empirical data set against different distributions
#' to help find the distribution that could be the best fit.
#'
#' @param .x The data set being passed to the function
#' @param .distribution_type What kind of data is it, can be one of `continuous`
#' or `discrete`
#' @param .round_to_place How many decimal places should the parameter estimates
#' be rounded off to for distibution construction. The default is 3
#'
#' @examples
#' xc <- mtcars$mpg
#' output_c <- tidy_distribution_comparison(xc, "continuous")
#'
#' xd <- trunc(xc)
#' output_d <- tidy_distribution_comparison(xd, "discrete")
#'
#' output_c
#' output_d
#'
#' @return
#' An invisible list object. A tibble is printed.
#'
#' @export
#'

tidy_distribution_comparison <- function(.x, .distribution_type = "continuous",
                                         .round_to_place = 3) {

  # Tidyeval ----
  x_term <- as.numeric(.x)
  n <- length(x_term)
  dist_type <- tolower(as.character(.distribution_type))
  rt <- as.numeric(.round_to_place)

  if (!dist_type %in% c("continuous", "discrete")) {
    rlang::abort(
      message = "The '.distribution_type' parameter must be either 'continuous'
      or 'discrete'.",
      use_cli_format = TRUE
    )
  }

  # Get parameter estimates for distributions
  if (dist_type == "continuous") {
    b <- try(util_beta_param_estimate(x_term)$parameter_tbl |>
               dplyr::filter(method == "NIST_MME") |>
               dplyr::select(dist_type, shape1, shape2) |>
               purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(b, "try-error")) {
      tb <- tidy_beta(.n = n, .shape1 = round(b[[2]], rt), .shape2 = round(b[[3]], rt))
    }

    c <- try(util_cauchy_param_estimate(x_term)$parameter_tbl |>
               dplyr::select(dist_type, location, scale) |>
               purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(c, "try-error")) {
      tc <- tidy_cauchy(.n = n, .location = round(c[[2]], rt), .scale = round(c[[3]], rt))
    }

    chi <- try(util_chisquare_param_estimate(x_term)$parameter_tbl |>
                 dplyr::select(dist_type, dof, ncp) |>
                 purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(chi, "try-error")) {
      tchi <- tidy_chisquare(.n = n, .df = round(chi[[2]], rt), .ncp = round(chi[[3]], rt))
    }

    e <- try(util_exponential_param_estimate(x_term)$parameter_tbl |>
               dplyr::select(dist_type, rate) |>
               dplyr::mutate(param_2 = NA) |>
               purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(e, "try-error")) {
      te <- tidy_exponential(.n = n, .rate = round(e[[2]], rt))
    }

    g <- try(util_gamma_param_estimate(x_term)$parameter_tbl |>
               dplyr::filter(method == "NIST_MME") |>
               dplyr::select(dist_type, shape, scale) |>
               purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(g, "try-error")) {
      tg <- tidy_gamma(.n = n, .shape = round(g[[2]], rt), .scale = round(g[[3]], rt))
    }

    l <- try(util_logistic_param_estimate(x_term)$parameter_tbl |>
               dplyr::filter(method == "EnvStats_MME") |>
               dplyr::select(dist_type, location, scale) |>
               purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(l, "try-error")) {
      tl <- tidy_logistic(.n = n, .location = round(l[[2]], rt), .scale = round(l[[3]], rt))
    }

    ln <- try(util_lognormal_param_estimate(x_term)$parameter_tbl |>
                dplyr::filter(method == "EnvStats_MME") |>
                dplyr::select(dist_type, mean_log, sd_log) |>
                purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(ln, "try-error")) {
      tln <- tidy_lognormal(.n = n, .meanlog = round(ln[[2]], rt), .sdlog = round(ln[[3]], rt))
    }

    p <- try(util_pareto_param_estimate(x_term)$parameter_tbl |>
               dplyr::filter(method == "MLE") |>
               dplyr::select(dist_type, shape, scale) |>
               purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(p, "try-error")) {
      tp <- tidy_pareto(.n = n, .shape = round(p[[2]], rt), .scale = round(p[[3]], rt))
    }

    u <- try(util_uniform_param_estimate(x_term)$parameter_tbl |>
               dplyr::filter(method == "NIST_MME") |>
               dplyr::select(dist_type, min_est, max_est) |>
               purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(u, "try-error")) {
      tu <- tidy_uniform(.n = n, .min = round(u[[2]], rt), .max = round(u[[3]], rt))
    }

    w <- try(util_weibull_param_estimate(x_term)$parameter_tbl |>
               dplyr::select(dist_type, shape, scale) |>
               purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(w, "try-error")) {
      tw <- tidy_weibull(.n = n, .shape = round(w[[2]], rt), .scale = round(w[[3]], rt))
    }

    nn <- try(util_normal_param_estimate(x_term)$parameter_tbl |>
                dplyr::filter(method == "EnvStats_MME_MLE") |>
                dplyr::select(dist_type, mu, stan_dev) |>
                purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(n, "try-error")) {
      tn <- tidy_normal(.n = n, .mean = round(nn[[2]], rt), .sd = round(nn[[3]], rt))
    }

    comp_tbl <- tidy_combine_distributions(
      tidy_empirical(x_term, .distribution_type = dist_type),
      if (exists("tb") && nrow(tb) > 0) {
        tb
      },
      if (exists("tc") && nrow(tc) > 0) {
        tc
      },
      if (exists("tchi") && nrow(tchi) > 0) {
        tchi
      },
      if (exists("te") && nrow(te) > 0) {
        te
      },
      if (exists("tg") && nrow(tg) > 0) {
        tg
      },
      if (exists("tl") && nrow(tl) > 0) {
        tl
      },
      if (exists("tln") && nrow(tln) > 0) {
        tln
      },
      if (exists("tp") && nrow(tp) > 0) {
        tp
      },
      if (exists("tu") && nrow(tu) > 0) {
        tu
      },
      if (exists("tw") && nrow(tw) > 0) {
        tw
      },
      if (exists("tn") && nrow(tn) > 0) {
        tn
      }
    )
  } else {
    bn <- try(util_binomial_param_estimate(trunc(tidy_scale_zero_one_vec(x_term)))$parameter_tbl |>
                dplyr::select(dist_type, size, prob) |>
                purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(bn, "try-error")) {
      tb <- tidy_binomial(.n = n, .size = round(bn[[2]], rt), .prob = round(bn[[3]], rt))
    }

    ge <- try(util_geometric_param_estimate(trunc(x_term))$parameter_tbl |>
                dplyr::filter(method == "EnvStats_MME") |>
                dplyr::select(dist_type, shape) |>
                dplyr::mutate(param_2 = NA) |>
                purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(ge, "try-error")) {
      tg <- tidy_geometric(.n = n, .prob = round(ge[[2]], rt))
    }

    h <- try(util_hypergeometric_param_estimate(.x = trunc(x_term), .total = n, .k = n)$parameter_tbl |>
               tidyr::drop_na() |>
               dplyr::slice(1) |>
               dplyr::select(dist_type, m, total) |>
               purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(h, "try-error")) {
      th <- tidy_hypergeometric(
        .n = n,
        .m = trunc(h[[2]]),
        .nn = n - trunc(h[[2]]),
        .k = trunc(h[[2]])
      )
    }

    po <- try(util_poisson_param_estimate(trunc(x_term))$parameter_tbl |>
                dplyr::select(dist_type, lambda) |>
                dplyr::mutate(param_2 = NA) |>
                purrr::set_names("dist_type", "param_1", "param_2"))

    if (!inherits(po, "try-error")) {
      tp <- tidy_poisson(.n = n, .lambda = round(po[[2]], rt))
    }

    comp_tbl <- tidy_combine_distributions(
      tidy_empirical(.x = x_term, .distribution_type = dist_type),
      if (exists("tb") && nrow(tb) > 0) {
        tb
      },
      if (exists("tg") && nrow(tg) > 0) {
        tg
      },
      if (exists("th") && nrow(th) > 0) {
        th
      },
      if (exists("tp") && nrow(tp) > 0) {
        tp
      }
    )
  }

  # Deviance calculations ----
  deviance_tbl <- comp_tbl |>
    dplyr::select(dist_type, x, y) |>
    dplyr::group_by(dist_type, x) |>
    dplyr::mutate(y = stats::median(y)) |>
    dplyr::ungroup() |>
    dplyr::group_by(dist_type) |>
    dplyr::mutate(y = tidy_scale_zero_one_vec(y)) |>
    dplyr::ungroup() |>
    tidyr::pivot_wider(
      id_cols = x,
      names_from = dist_type,
      values_from = y
    ) |>
    dplyr::select(x, Empirical, dplyr::everything()) |>
    dplyr::mutate(
      dplyr::across(
        .cols = -c(x, Empirical),
        .fns = ~ Empirical - .
      )
    ) |>
    tidyr::drop_na() |>
    tidyr::pivot_longer(
      cols = -x
    ) |>
    dplyr::select(-x)

  total_deviance_tbl <- deviance_tbl |>
    dplyr::filter(!name == "Empirical") |>
    dplyr::group_by(name) |>
    dplyr::summarise(total_deviance = sum(value)) |>
    dplyr::ungroup() |>
    dplyr::mutate(total_deviance = abs(total_deviance)) |>
    dplyr::arrange(abs(total_deviance)) |>
    dplyr::rename(
      dist_with_params = name,
      abs_tot_deviance = total_deviance
    )

  # AIC Data ----
  emp_data_tbl <- comp_tbl |>
    dplyr::select(dist_type, x, dy) |>
    dplyr::filter(dist_type == "Empirical")

  # aic_tbl <- comp_tbl |>
  #   dplyr::filter(!dist_type == "Empirical") |>
  #   dplyr::select(dist_type, dy) |>
  #   tidyr::nest(data = dy) |>
  #   dplyr::mutate(
  #     lm_model = purrr::map(
  #       data,
  #       function(df) stats::lm(dy ~ emp_data_tbl$dy, data = df)
  #     )
  #   ) |>
  #   dplyr::mutate(aic_value = purrr::map(lm_model, stats::AIC)) |>
  #   dplyr::mutate(aic_value = unlist(aic_value)) |>
  #   dplyr::mutate(abs_aic = abs(aic_value)) |>
  #   dplyr::arrange(abs_aic) |>
  #   dplyr::select(dist_type, aic_value, abs_aic)
  aic_tbl <- comp_tbl |>
    dplyr::select(dist_type, y) |>
    dplyr::filter(!stringr::str_detect(dist_type, "Empirical")) |>
    tidyr::nest(data = y) |>
    dplyr::mutate(aic_value = dplyr::case_when(
      # Beta
      stringr::str_detect(dist_type, "Beta") ~ tryCatch(
        util_beta_aic(x_term),
        error = function(e) NA_real_
      ),
      # Cauchy
      stringr::str_detect(dist_type, "Cauchy") ~ tryCatch(
        util_cauchy_aic(x_term),
        error = function(e) NA_real_
      ),
      # Chi-Squared
      stringr::str_detect(dist_type, "Chisquare") ~ tryCatch(
        util_chisquare_aic(x_term),
        error = function(e) NA_real_
      ),
      # Exponential
      stringr::str_detect(dist_type, "Exponential") ~ tryCatch(
        util_exponential_aic(x_term),
        error = function(e) NA_real_
      ),
      # Gamma
      stringr::str_detect(dist_type, "Gamma") ~ tryCatch(
        util_gamma_aic(x_term),
        error = function(e) NA_real_
      ),
      # Logistic
      stringr::str_detect(dist_type, "Logistic") ~ tryCatch(
        util_logistic_aic(x_term),
        error = function(e) NA_real_
      ),
      # Lognormal
      stringr::str_detect(dist_type, "Lognormal") ~ tryCatch(
        util_lognormal_aic(x_term),
        error = function(e) NA_real_
      ),
      # Normal
      stringr::str_detect(dist_type, "Gaussian") ~ tryCatch(
        util_normal_aic(x_term),
        error = function(e) NA_real_
      ),
      # Pareto
      stringr::str_detect(dist_type, "Pareto") ~ tryCatch(
        util_pareto_aic(x_term),
        error = function(e) NA_real_
      ),
      # Uniform
      stringr::str_detect(dist_type, "Uniform") ~ tryCatch(
        util_uniform_aic(x_term),
        error = function(e) NA_real_
      ),
      # Weibull
      stringr::str_detect(dist_type, "Weibull") ~ tryCatch(
        util_weibull_aic(x_term),
        error = function(e) NA_real_
      ),
      # Binomcial
      stringr::str_detect(dist_type, "Binomial") ~ tryCatch(
        util_binomial_aic(x_term),
        error = function(e) NA_real_
      ),
      # Geometric
      stringr::str_detect(dist_type, "Geometric") ~ tryCatch(
        util_geometric_aic(x_term),
        error = function(e) NA_real_
      ),
      # Hypergeometric
      stringr::str_detect(dist_type, "Hypergeometric") ~ tryCatch(
        util_hypergeometric_aic(x_term),
        error = function(e) NA_real_
      ),
      # Poisson
      stringr::str_detect(dist_type, "Poisson") ~ tryCatch(
        util_poisson_aic(x_term),
        error = function(e) NA_real_
      ),
      TRUE ~ NA_real_
    )) |>
    dplyr::select(-data) |>
    dplyr::mutate(abs_aic = abs(aic_value))

  ks_tbl <- comp_tbl |>
    dplyr::filter(dist_type != "Empirical") |>
    dplyr::select(dist_type, dy) |>
    tidyr::nest(data = dy) |>
    dplyr::mutate(
      ks = purrr::map(
        .x = data,
        .f = ~ ks.test(
          x = .x$dy,
          y = emp_data_tbl$dy,
          alternative = "two.sided",
          simulate.p.value = TRUE
        )
      ),
      tidy_ks = purrr::map(ks, broom::tidy)
    ) |>
    tidyr::unnest(cols = tidy_ks) |>
    dplyr::select(-c(data, ks)) |>
    dplyr::mutate(dist_char = as.character(dist_type)) |>
    purrr::set_names(
      "dist_type", "ks_statistic", "ks_pvalue", "ks_method", "alternative",
      "dist_char"
    )

  multi_metric_tbl <- total_deviance_tbl |>
    dplyr::mutate(dist_with_params = as.factor(dist_with_params)) |>
    dplyr::inner_join(aic_tbl, by = c("dist_with_params" = "dist_type")) |>
    dplyr::inner_join(ks_tbl, by = c("dist_with_params" = "dist_char")) |>
    dplyr::select(dist_type, dplyr::everything(), -dist_with_params) |>
    dplyr::mutate(dist_type = as.factor(dist_type))

  # Return ----
  output <- list(
    comparison_tbl         = comp_tbl,
    deviance_tbl           = deviance_tbl,
    total_deviance_tbl     = total_deviance_tbl,
    aic_tbl                = aic_tbl,
    kolmogorov_smirnov_tbl = ks_tbl,
    multi_metric_tbl       = multi_metric_tbl
  )

  # Attributes ----
  attr(deviance_tbl, ".tibble_type") <- "deviance_comparison_tbl"
  attr(total_deviance_tbl, ".tibble_type") <- "deviance_results_tbl"
  attr(aic_tbl, ".tibble_type") <- "aic_tbl"
  attr(comp_tbl, ".tibble_type") <- "comparison_tbl"
  attr(ks_tbl, ".tibble_type") <- "kolmogorov_smirnov_tbl"
  attr(multi_metric_tbl, ".tibble_type") <- "full_metric_tbl"
  attr(output, ".x") <- x_term
  attr(output, ".n") <- n

  # Return ----
  return(invisible(output))
}