Package {MCAtools}

Electricity market structures and electricity supply costs in Sub-Saharan Africa

Description

A cross-country dataset describing electricity sector organization, ownership, network configuration, geographic constraints, and average electricity supply costs in Sub-Saharan Africa.

The dataset combines observed country-level electricity system structures with counterfactual reform scenarios for Cameroon (Cameroon_2018, Cameroon_h1, Cameroon_h2), constructed to assess the potential impact of alternative market designs on electricity supply costs.

Usage

data(electricity_africa)

Format

A data frame with 42 country–system observations and the following variables:

country

Country or system name. Includes observed countries and hypothetical reform scenarios for Cameroon.

iso_code

ISO 3-letter country code or scenario identifier (e.g. CMR_2018, CMR_h1, CMR_h2).

total_cost

Average electricity supply cost, expressed in USD per kWh. For hypothetical Cameroon scenarios, this variable may be missing and treated as an outcome of counterfactual analysis.

vertical_integration

Binary indicator equal to 1 if generation, transmission and distribution are vertically integrated within a single utility, 0 otherwise.

private_in_generation

Indicator for the presence of private sector participation in electricity generation (yes/no).

public_in_generation

Indicator for public ownership or participation in electricity generation (yes/no).

stand_alone_generation

Indicator equal to yes if generation assets operate independently from transmission and distribution.

transmission_bundled_distribution

Indicator equal to 1 if transmission is institutionally bundled with distribution.

transmission_bundled_generation

Indicator equal to 1 if transmission is institutionally bundled with generation.

government_own_transmission

Indicator equal to 1 if transmission assets are government-owned.

multiple_transmission_system

Indicator equal to 1 if multiple transmission operators coexist within the system.

multiple_distributor

Indicator equal to 1 if multiple electricity distribution companies operate in the country.

independent_distributor

Indicator equal to 1 if at least one distribution company operates independently from generation and transmission.

not_interconnected

Indicator equal to 1 if the national electricity system is not interconnected with neighboring countries.

landlocked_country

Indicator equal to 1 if the country is landlocked.

fragmented_island

Indicator equal to 1 for fragmented or small island electricity systems.

openness

Categorical indicator of electricity system openness to regional trade and interconnection, taking values such as I (isolated), E (export-oriented), or I/E (mixed).

Details

Observed data are primarily derived from Trimble et al. (2016) and complementary institutional sources. The dataset is extended with three Cameroon-specific entries: one reflecting the 2018 institutional configuration (Cameroon_2018), and two forward-looking reform scenarios (Cameroon_h1, Cameroon_h2) representing plausible future market designs considered by policymakers.

These counterfactual scenarios are included to explore how alternative organizational structures may affect electricity supply costs.

Source

Trimble, C., Kojima, M., Perez Arroyo, I., and Mohammadzadeh, F. (2016). Financial viability of electricity sectors in Sub-Saharan Africa. World Bank.

Examples

## Load data
data(electricity_africa)

## Load package
library(MCAtools)

## -------------------------------------------------
## 1. Preparation of qualitative data for MCA
## -------------------------------------------------

## Keep only qualitative variables (excluding cost)
df <- electricity_africa[, c("iso_code",
                             "vertical_integration",
                             "private_in_generation",
                             "public_in_generation",
                             "stand_alone_generation",
                             "transmission_bundled_generation",
                             "government_own_transmission",
                             "multiple_transmission_system",
                             "transmission_bundled_distribution",
                             "multiple_distributor",
                             "independent_distributor",
                             "not_interconnected",
                             "landlocked_country",
                             "fragmented_island",
                             "openness"
)]

## Convert to factors
df[] <- lapply(df, as.factor)

## Cameroon reform scenarios treated as supplementary individuals
sup_rows <- which(is.na(electricity_africa$total_cost))

## -------------------------------------------------
## 2. Ordinary MCA (lambda = 1)
## -------------------------------------------------

res_ord <- mca_analysis(
  data = df,
  id_ind = "iso_code",
  sup_ind = sup_rows,
  lambda = 1
)

res_ord$eig$percentage[1]



## Extract first dimension (market structure)
dim1 <- res_ord$ind$coord$Dim1

## -------------------------------------------------
## 3. Relationship between market structure and cost
## -------------------------------------------------

analysis_df <- data.frame(
  country = electricity_africa$country[1:39],
  cost = log(electricity_africa$total_cost)[1:39],
  dim1 = scale(dim1)
)

analysis_df <- analysis_df[!is.na(analysis_df$cost), ]

## Quadratic relationship (U-shaped pattern)
model <- lm(cost ~ poly(dim1, 2), data = analysis_df)
summary(model)

## =========================================================
## ROBUSTNESS ANALYSIS OVER THE STABILITY INTERVAL OF lambda
## =========================================================

## -------------------------------------------------
## 4. Selection of phi-divergence parameter lambda
## -------------------------------------------------

lambda_grid <- seq(-2, 2, by = 0.05)

results <- data.frame(
  lambda = lambda_grid,
  inertia1 = NA_real_
)

for (k in seq_along(lambda_grid)) {
  res <- mca_analysis(
    data = df,
    id_ind = "iso_code",
    sup_ind = sup_rows,
    lambda = lambda_grid[k]
  )
  results$inertia1[k] <- res$eig$eigenvalue[1]
}

## Smooth inertia profile to avoid singularities at lambda = 0 and lambda = -1
singular <- abs(results$lambda) < 1e-6 |
  abs(results$lambda + 1) < 1e-6

results$inertia1_clean <- results$inertia1
results$inertia1_clean[singular] <- NA

for (k in seq_along(lambda_grid)) {
  ifelse(
    is.na(results$inertia1_clean[k]),
    results$inertia1_smooth[k] <-
      (results$inertia1_clean[k - 1] + results$inertia1_clean[k + 1]) / 2,
    results$inertia1_smooth[k] <- results$inertia1_clean[k]
  )
}

plot(
  results$lambda,
  results$inertia1_smooth,
  type = "l",
  lwd = 2,
  xlab = "lambda",
  ylab = "Inertie du premier axe",
  main = "Stabilite empirique de l'ACM phi-divergence"
)

abline(v = 1, col = "red", lty = 2)
text(1, max(results$inertia1), "lambda = 1 (chi-square)", pos = 4)

## Optimal lambda and 95% stability interval
lambda_opt <- results$lambda[which.max(results$inertia1_smooth)]

I_max <- max(results$inertia1_smooth, na.rm = TRUE)
lambda_ci <- range(results$lambda[
  results$inertia1_smooth >= 0.95 * I_max
])

lambda_opt
lambda_ci

lambda_min <- -0.335
lambda_max <-  0.095

lambda_grid <- seq(lambda_min, lambda_max, length.out = 25)

## Convert to factors
df[] <- lapply(df, as.factor)

## Container for pooled results
df_U_list <- vector("list", length(lambda_grid))

for (k in seq_along(lambda_grid)) {

  lambda_k <- lambda_grid[k]

  fit <- tryCatch(
    mca_analysis(
      data   = df,
      id_ind = "iso_code",
      sup_ind = sup_rows,
      lambda  = lambda_k
    ),
    error = function(e) NULL
  )

  if (is.null(fit)) next

  ## Active countries only (excluding Cameroon scenarios)
  n_active <- sum(!is.na(electricity_africa$total_cost))

  df_U_list[[k]] <- data.frame(
    country = rownames(fit$ind$coord)[1:n_active],
    dim1    = fit$ind$coord[1:n_active, 1],
    cost    = log(electricity_africa$total_cost[1:n_active]),
    lambda  = rep(lambda_k, n_active)
  )
}

df_U <- do.call(rbind, df_U_list)

## ---------------------------------------------------------
## Normalization of Dim 1 within each lambda
## ---------------------------------------------------------

df_U$dim1_z <- NA_real_

for (l in unique(df_U$lambda)) {
  idx <- df_U$lambda == l
  df_U$dim1_z[idx] <- as.numeric(scale(df_U$dim1[idx]))
}

## Central lambda (previously selected optimal value)
lambda_central <- lambda_opt

df_central <- df_U[
  abs(df_U$lambda - lambda_central) ==
    min(abs(df_U$lambda - lambda_central)),
]

df_central <- df_central[!duplicated(df_central$country), ]

## ---------------------------------------------------------
## Pooled quadratic regression (robustness test)
## ---------------------------------------------------------

curve_fit <- lm(
  cost ~ poly(dim1_z, 2),
  data = df_U
)

summary(curve_fit)

Extract a Symbolic Equation for an MCA Dimension

Description

Generates a symbolic representation of a selected dimension from a Multiple Correspondence Analysis (MCA) result. The equation highlights the modalities that contribute most to the chosen dimension, based on their coordinates and reconstructed contributions.

Usage

generate_mca_equation(
  mca_result,
  dimension = 1,
  top = 5,
  digits = 4
)

Arguments

Details

For the selected dimension, the function extracts modality coordinates from the MCA result. If contribution values are not explicitly available, they are reconstructed as squared coordinates and normalized to sum to 100.

The symbolic equation is formed by retaining the top modalities with the highest absolute contributions. This provides an interpretable approximation of the latent axis in terms of the most influential modalities.

This approach is particularly useful in generalized or phi-divergence-based MCA settings, where classical contribution tables may not always be stored explicitly.

Value

A list with the following components:

Author(s)

Awa Traoré, Assi Lazare N'GUESSAN, MOUSSA Kouamé Richard, Nona Servais KAMDEM SIMO, Muhamad Setyawan Bahari

See Also

mca_analysis for computing MCA results.

Examples

# Example usage:
## Load package
library(MCAtools)

## Load data
data(electricity_africa)

## -------------------------------------------------
## 1. Preparation of qualitative data for MCA
## -------------------------------------------------

## Keep only qualitative variables (excluding cost)
df <- electricity_africa[, c("iso_code",
                             "vertical_integration",
                             "private_in_generation",
                             "public_in_generation",
                             "stand_alone_generation",
                             "transmission_bundled_generation",
                             "government_own_transmission",
                             "multiple_transmission_system",
                             "transmission_bundled_distribution",
                             "multiple_distributor",
                             "independent_distributor",
                             "not_interconnected",
                             "landlocked_country",
                             "fragmented_island",
                             "openness"
)]

## Convert to factors
df[] <- lapply(df, as.factor)

## Cameroon reform scenarios treated as supplementary individuals
sup_rows <- which(is.na(electricity_africa$total_cost))

res_ord <- mca_analysis(
  data = df,
  id_ind = "iso_code",
  sup_ind = sup_rows,
  lambda = 1
)

eq1 <- generate_mca_equation(
  mca_result = res_ord,
  dimension = 1,
  top = 6
)

eq1$equation
eq1$table

Multiple Correspondence Analysis with lambda-divergence and supplementary qualitative variables

Description

Performs a Multiple Correspondence Analysis (MCA) on a data.frame of categorical variables using a general lambda-divergence residuals formulation. The function builds the indicator matrix, computes joint proportions, constructs residuals depending on the 'lambda' parameter, performs a singular value decomposition (SVD) and returns coordinates, contributions, cos2, eta2, v-test for active variables and optionally handles supplementary qualitative and quantitative variables and supplementary individuals.

Usage

mca_analysis(data,
                         id_ind = NULL,
                         sup_ind = NULL, 
                         sup_qual = NULL, 
                         sup_quant = NULL, 
                         lambda = 1, 
                         nonzero = 0.05, 
                         dim1 = 1, dim2 = 2,
                         plottype = "s", 
                         giveplot = TRUE, 
                         mag = 0.8, 
                         acc = 5, 
                         scaleplot = 1.2)

Arguments

Details

This implementation follows these main steps:

1. Build the indicator (dummy) matrix Z from the factor columns of data. The number of columns of Z equals the total number of modalities across variables.

2. Compute the joint proportions matrix P = Z / sum(Z), row and column margins (p_{i.} and p_{.j}), and the independence matrix E = p_{i.} p_{.j}^\top.

3. Compute residuals r_{ij} using the chosen lambda divergence. Three branches are implemented: general lambda (not 0 or -1), lambda == 0 (log-based form with replacement of zeros by nonzero), and lambda == -1 (special formulation). Tiny offsets (e.g. 1e-13) are added to avoid numerical instabilities.

4. Perform singular value decomposition (SVD) of the residual matrix r and compute singular values, principal coordinates for individuals and variables, contributions, cos2, v-test, and eta-squared statistics.

5. If sup_ind is provided, project the corresponding individuals onto the estimated factorial space using the same divergence branch as for active individuals (the branch is re-selected for the supplementary residuals, so the projection is consistent for lambda = 0 and lambda = -1 as well).

6. If sup_qual is provided, compute supplementary coordinates as group means of individual coordinates and compute \eta^2 for each supplementary variable and each dimension.

7. If sup_quant is provided, compute the correlation between each supplementary quantitative variable and the individual coordinates on each dimension.

Note: Input columns of data should be factors. If they are character vectors, convert using data[] <- lapply(data, factor) prior to calling the function.

The arguments dim1, dim2, plottype, giveplot, mag, and scaleplot are accepted for interface compatibility with plot_mca but do not affect the computations of mca_analysis; no plot is produced by this function.

Value

A list with components:

eig

A data.frame of eigenvalues and percentage of explained inertia per dimension and cumulative percentage.

ind

A list with individual results: coord (data.frame of individual coordinates), contrib (contribution percentages for individuals), and cos2 (quality of representation).

var

A list with active-modality results: coord (data.frame of modality coordinates), contrib (contribution percentages of modalities), cos2 (modalities' cos2), v.test (v-test values), and eta2 (eta-squared per active variable and dimension).

var_sup

If sup_qual was provided, a list with coord (a list of data.frames, one per supplementary qualitative variable, giving the group-mean coordinates of its modalities) and eta2 (data.frame of \eta^2 per supplementary variable and dimension). Otherwise NULL.

quanti_sup

If sup_quant was provided, a data.frame of correlations between each supplementary quantitative variable and the individual coordinates, with dimensions as rows. Otherwise NULL.

ind_sup

If sup_ind was provided, a data.frame of the projected coordinates of the supplementary individuals. Otherwise NULL.

Z

The indicator matrix (as a data.frame) used in the analysis.

lambda

The chosen lambda value (numeric), as supplied by the user.

Chi.Squared

Numeric. Rounded Chi-squared statistic used for testing association.

Total.Inertia

Numeric. Rounded total inertia (sum of principal inertias).

P.Value

Numeric. Rounded p-value for the Chi-squared test.

All numeric matrices/data.frames indexed by dimension have column names Dim1, Dim2, ... corresponding to components extracted from the SVD.

Author(s)

Awa Traoré, Assi Lazare N'GUESSAN, MOUSSA Kouamé Richard, Nona Servais KAMDEM SIMO, Muhamad Setyawan Bahari

References

See standard texts on Multiple Correspondence Analysis and phi-divergence approaches for related formulations.

See Also

plot_mca for visualizing MCA results, and generate_mca_equation for extracting a symbolic interpretation of a dimension.

Examples

## Load data
  data(electricity_africa)

## Load package
library(MCAtools)

## -------------------------------------------------
## 1. Preparation of qualitative data for MCA
## -------------------------------------------------

## Keep only qualitative variables (excluding cost)
df <- electricity_africa[, c("iso_code",
                             "vertical_integration",
                             "private_in_generation",
                             "public_in_generation",
                             "stand_alone_generation",
                             "transmission_bundled_generation",
                             "government_own_transmission",
                             "multiple_transmission_system",
                             "transmission_bundled_distribution",
                             "multiple_distributor",
                             "independent_distributor",
                             "not_interconnected",
                             "landlocked_country",
                             "fragmented_island",
                             "openness"
)]

## Convert to factors
df[] <- lapply(df, as.factor)

## Cameroon reform scenarios treated as supplementary individuals
sup_rows <- which(is.na(electricity_africa$total_cost))


## -------------------------------------------------
## 2.Ordinnary MCA (lambda = 1)
## -------------------------------------------------

res_ord <- mca_analysis(
  data = df,
  id_ind = "iso_code",
  sup_ind = sup_rows,
  lambda = 1
)

res_ord$eig$percentage[1]

Plot Multiple Correspondence Analysis Results

Description

Produces 2D scatterplots from an MCA result object created by mca_analysis, displaying individuals and/or variable modalities on selected principal dimensions. The function provides several plot types (individuals, variables, or both) and allows customization of scaling and label size.

Usage

plot_mca(custom_result, plot_type = "both", scaleplot = 1.0,
         dims = c(1, 2), mag = 1.0, plottype = "s",
         label_ind = TRUE, label_var = TRUE, legend_pos = "topright")

Arguments

Details

The function extracts the coordinates of individuals and variable modalities for the selected dimensions and generates a biplot-like figure:

• Individuals (rows) are represented by blue '+' symbols.

• Variable modalities (columns) are represented by red '*' symbols.

Labels are automatically annotated beside their respective points.

The axes labels indicate the dimension number and its percentage of explained inertia (from custom_result$eig). A subtitle shows the cumulative percentage of total inertia explained by the displayed dimensions. Horizontal and vertical reference lines are drawn at zero.

If plot_type = "ind", only individuals are shown; if plot_type = "var", only variables are shown.

Value

This function returns no value. It is used for its graphical output (a base R plot). The function produces a 2D plot of MCA results using the provided object.

Author(s)

Awa Traoré, Assi Lazare N'GUESSAN, MOUSSA Kouamé Richard, Nona Servais KAMDEM SIMO, Muhamad Setyawan Bahari

See Also

mca_analysis for generating the MCA result used as input.

Examples

library(MCAtools)

## -------------------------------------------------
## 1. Preparation of qualitative data for MCA
## -------------------------------------------------

## Keep only qualitative variables (excluding cost)
df <- electricity_africa[, c("iso_code",
                             "vertical_integration",
                             "private_in_generation",
                             "public_in_generation",
                             "stand_alone_generation",
                             "transmission_bundled_generation",
                             "government_own_transmission",
                             "multiple_transmission_system",
                             "transmission_bundled_distribution",
                             "multiple_distributor",
                             "independent_distributor",
                             "not_interconnected",
                             "landlocked_country",
                             "fragmented_island",
                             "openness"
)]

## Convert to factors
df[] <- lapply(df, as.factor)

## Cameroon reform scenarios treated as supplementary individuals
sup_rows <- which(is.na(electricity_africa$total_cost))

res_ord <- mca_analysis(
  data = df,
  id_ind = "iso_code",
  sup_ind = sup_rows,
  lambda = 1
)

# Plot individuals and variables together
plot_mca(
  res_ord,
  plot_type = "both",
  dims = c(1, 2),
  mag = 0.8
)

# Plot individuals only
plot_mca(
  res_ord,
  plot_type = "ind",
  dims = c(1, 2),
  mag = 0.8
)

# Plot variable modalities only
plot_mca(
  res_ord,
  plot_type = "var",
  dims = c(1, 2),
  mag = 0.8
)