Calcul des indicateurs ODD : IDH, IPM et inégalités

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Introduction

Cette vignette présente le calcul des indicateurs de développement humain conformes aux méthodologies internationales PNUD/OPHI, directement utilisables pour les rapports nationaux sur les ODD.

library(statAfrikR)
library(dplyr)
library(ggplot2)

1. Indice de Développement Humain (IDH)

Calcul national

idh_benin <- calcul_idh(
  esperance_vie   = 61.8,
  annees_scol_moy = 4.5,
  annees_scol_att = 13.1,
  rnb_habitant    = 3360,
  annee           = 2023
)

cat("IDH Bénin 2023 :\n")
cat("  IDH global    :", idh_benin$idh, "\n")
cat("  Santé         :", idh_benin$indice_sante, "\n")
cat("  Éducation     :", idh_benin$indice_education, "\n")
cat("  Revenu        :", idh_benin$indice_revenu, "\n")
cat("  Catégorie     :", idh_benin$categorie, "\n")

Comparaison régionale

pays_afrique <- tibble::tibble(
  pays            = c("Bénin", "Burkina Faso", "Sénégal",
                       "Côte d'Ivoire", "Mali", "Niger",
                       "Togo", "Guinée"),
  esperance_vie   = c(61.8, 61.6, 68.7, 59.1, 59.3, 62.4, 61.5, 58.9),
  annees_scol_moy = c(4.5,  2.0,  3.5,  5.3,  2.4,  2.1,  5.5,  3.1),
  annees_scol_att = c(13.1, 9.3, 14.5, 12.1, 7.5,  9.9, 13.1, 11.2),
  rnb_habitant    = c(3360, 2310, 3690, 5510, 2200, 1340, 2780, 2420)
)

idh_regional <- pays_afrique |>
  dplyr::rowwise() |>
  dplyr::mutate(
    res           = list(calcul_idh(esperance_vie, annees_scol_moy,
                                    annees_scol_att, rnb_habitant)),
    idh           = res$idh,
    indice_sante  = res$indice_sante,
    indice_educ   = res$indice_education,
    indice_revenu = res$indice_revenu,
    categorie     = res$categorie
  ) |>
  dplyr::select(-res) |>
  dplyr::ungroup() |>
  dplyr::arrange(dplyr::desc(idh))

knitr::kable(
  idh_regional[, c("pays", "idh", "categorie",
                    "indice_sante", "indice_educ", "indice_revenu")],
  caption = "IDH — Comparaison régionale Afrique de l'Ouest",
  digits  = 3
)

idh_long <- idh_regional |>
  tidyr::pivot_longer(
    cols      = c(indice_sante, indice_educ, indice_revenu),
    names_to  = "composante",
    values_to = "valeur"
  ) |>
  dplyr::mutate(
    composante = dplyr::recode(composante,
      indice_sante  = "Santé",
      indice_educ   = "Éducation",
      indice_revenu = "Revenu"
    ),
    pays = forcats::fct_reorder(pays, idh)
  )

graphique_barres(
  idh_long,
  var_x      = "pays",
  var_y      = "valeur",
  var_groupe = "composante",
  position   = "stack",
  titre      = "Composantes de l'IDH — Afrique de l'Ouest",
  label_y    = "Valeur de l'indice"
) + ggplot2::coord_flip()

2. Indice de Pauvreté Multidimensionnelle (IPM)

set.seed(2024)
n <- 3000
donnees_menages <- tibble::tibble(
  id_menage       = 1:n,
  region          = sample(c("Nord", "Sud", "Est", "Ouest"), n, replace = TRUE),
  milieu          = sample(c("Urbain", "Rural"), n, replace = TRUE,
                            prob = c(0.35, 0.65)),
  poids           = runif(n, 0.5, 2.5),
  # Dimension Santé
  malnutrition    = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.72, 0.28)),
  mortalite_enf   = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.88, 0.12)),
  # Dimension Éducation
  scol_adulte     = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.62, 0.38)),
  scol_enfants    = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.71, 0.29)),
  # Dimension Niveau de vie
  electricite     = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.52, 0.48)),
  eau_potable     = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.58, 0.42)),
  assainissement  = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.55, 0.45)),
  combustible     = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.60, 0.40)),
  logement        = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.75, 0.25)),
  actifs          = sample(c(0L, 1L), n, replace = TRUE, prob = c(0.68, 0.32))
)

# Définition des dimensions IPM standard OPHI
indicateurs_ipm <- list(
  sante      = c("malnutrition", "mortalite_enf"),
  education  = c("scol_adulte", "scol_enfants"),
  niveau_vie = c("electricite", "eau_potable", "assainissement",
                  "combustible", "logement", "actifs")
)

resultat_ipm <- calcul_ipm(
  donnees_menages,
  var_nutrition      = 'malnutrition',
  var_mortalite_inf  = 'mortalite_enf',
  var_scolarisation  = 'scol_enfants',
  var_annees_scol    = 'scol_adulte',
  var_electricite    = 'electricite',
  var_eau            = 'eau_potable',
  var_assainissement = 'assainissement',
  var_combustible    = 'combustible',
  var_logement       = 'logement',
  var_actifs         = 'actifs',
  poids   = 'poids',
  seuil_k = 1/3
)

IPM par région

donnees_enrichies <- resultat_ipm$donnees_enrichies

ipm_region <- donnees_enrichies |>
  dplyr::group_by(region) |>
  dplyr::summarise(
    n_menages        = dplyr::n(),
    taux_pauvrete_md = round(mean(.est_pauvre_multi) * 100, 1),
    score_moyen      = round(mean(.score_privation), 3),
    .groups          = "drop"
  ) |>
  dplyr::arrange(dplyr::desc(taux_pauvrete_md))

knitr::kable(
  ipm_region,
  caption = "Pauvreté multidimensionnelle par région",
  col.names = c("Région", "Ménages", "Taux pauvreté (%)", "Score moyen")
)

3. Inégalités

set.seed(2024)
donnees_revenus <- tibble::tibble(
  menage         = 1:2000,
  milieu         = sample(c("Urbain", "Rural"), 2000, replace = TRUE,
                           prob = c(0.4, 0.6)),
  quintile       = sample(1:5, 2000, replace = TRUE),
  depense_totale = exp(rnorm(2000, log(500000), 0.8)),
  poids          = runif(2000, 0.5, 2.0)
)

inegalites <- decomposer_inegalite(
  donnees_revenus,
  var_revenu = "depense_totale",
  var_groupe = "milieu",
  poids = "poids"
)

knitr::kable(
  inegalites$decomposition,
  caption = "Décomposition des inégalités par milieu",
  digits  = 3
)

# Construction manuelle de la courbe de Lorenz
x_sorted <- sort(donnees_revenus$depense_totale)
n         <- length(x_sorted)
lorenz_df <- tibble::tibble(
  pop_cumulee = c(0, seq_len(n) / n),
  rev_cumulee = c(0, cumsum(x_sorted) / sum(x_sorted))
)

ggplot2::ggplot(lorenz_df, ggplot2::aes(pop_cumulee, rev_cumulee)) +
  ggplot2::geom_line(color = "#1B6CA8", linewidth = 1.2) +
  ggplot2::geom_abline(intercept = 0, slope = 1,
                        linetype = "dashed", color = "#888888") +
  ggplot2::annotate("text", x = 0.7, y = 0.35,
                     label = paste0("Gini = ", inegalites$gini),
                     color = "#1B6CA8", fontface = "bold", size = 4) +
  ggplot2::labs(
    title = "Courbe de Lorenz — Dépenses des ménages",
    x     = "Part cumulée de la population",
    y     = "Part cumulée des dépenses"
  ) +
  theme_ins()

Synthèse

tibble::tibble(
  Indicateur = c("IDH Bénin 2023", "IPM (H × A)", "Incidence (H)",
                  "Intensité (A)", "Gini"),
  Valeur = c(
    idh_benin$idh,
    resultat_ipm$ipm,
    round(resultat_ipm$H, 3),
    round(resultat_ipm$A, 3),
    inegalites$gini
  ),
  Interpretation = c(
    idh_benin$categorie,
    paste0(round(resultat_ipm$ipm * 100, 1), "% de pauvreté multidim."),
    paste0(round(resultat_ipm$H * 100, 1), "% de ménages pauvres"),
    paste0(round(resultat_ipm$A * 100, 1), "% de privations en moyenne"),
    dplyr::case_when(
      inegalites$gini < 0.3 ~ "Inégalités faibles",
      inegalites$gini < 0.4 ~ "Inégalités modérées",
      TRUE                  ~ "Inégalités élevées"
    )
  )
) |>
knitr::kable(caption = "Tableau de bord des indicateurs ODD")

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