Persistent Homology and Computational Poverty Dynamics in the West African Monetary Zone

1. Repository Overview

This Zenodo repository contains all supplementary materials associated with the manuscript entitled "Persistent Homology and Computational Poverty Dynamics in the West African Monetary Zone," submitted to Computational Economics. The repository is organized into three principal components: (i) upgraded datasets with multiple imputation strategies; (ii) complete Python replication code implementing the full computational pipeline; and (iii) all figures generated during the analysis at publication resolution (300 DPI). Together, these materials enable full replication of the reported results from raw World Bank Development Indicators through to final figures and tables.

All data are sourced from the World Bank Open Data portal (World Bank Open Data) and are in the public domain. The replication code is released under the MIT License, permitting unrestricted use, modification, and distribution with appropriate attribution. The repository is structured to ensure that any researcher with intermediate Python proficiency can reproduce the complete analysis within approximately 30 minutes on a standard desktop computer.

 

2. Data Files

The data component of this repository consists of a single Excel workbook containing four worksheets. All indicators are drawn from the World Bank World Development Indicators (WDI) database, covering the period 2000 to 2023 for five WAMZ member countries: The Gambia, Ghana, Guinea, Nigeria, and Sierra Leone. The workbook is provided in .xlsx format for universal compatibility.

2.1 File: WAMZ_Poverty_Upgraded_Data.xlsx

This workbook contains the following four worksheets:

Sheet 1: Original_Data: The raw data extracted from the World Bank WDI database without any imputation or modification. This sheet contains 120 rows (5 countries x 24 years) and 11 columns (Country, Code, Year, plus 9 development indicators). Missing values are preserved as blank cells. This sheet serves as the ground truth against which all imputation strategies are compared. Missingness rates range from 0% (5 indicators) to 83.3% (Poverty headcount ratio). Researchers who wish to apply alternative imputation methods should begin with this sheet.

Sheet 2: GroupMean_Imputed: Missing values imputed using country-specific group means. For each indicator and each country, missing observations are replaced by the arithmetic mean of available observations for that indicator-country combination. If all observations for a given indicator-country pair are missing, the global mean across all countries is used. This is the simplest imputation strategy and serves as the baseline for comparison. The sheet contains 120 complete rows with zero missing values.

Sheet 3: MICE_Imputed (Primary Analysis Dataset): Missing values imputed using Multiple Imputation by Chained Equations (MICE) with Bayesian ridge regression. The procedure iteratively models each incomplete variable conditional on all other variables, preserving inter-variable correlations. MICE was implemented via scikit-learn's IterativeImputer with 50 maximum iterations, tolerance 0.001, and random seed 42. Group-mean imputed values from Sheet 2 were used as initialization. This sheet constitutes the primary analysis dataset used for all main results reported in the manuscript. The sheet contains 120 complete rows.

Sheet 4: ForwardFill_Imputed: Missing values imputed using a two-step temporal strategy. Step 1 applies forward-fill and backward-fill within each country's time series (carrying the last observed value forward and the next observed value backward). Step 2 replaces any remaining missing values with country-group means. Step 3 replaces any still-missing values with the global mean. This strategy preserves temporal trends better than simple mean imputation. The sheet contains 120 complete rows.

 

2.2 Variable Definitions and Sources

Indicator	Dimension	WDI Code	Missing %
Life expectancy at birth	Health	SP.DYN.LE00.IN	0.0%
Under-5 mortality rate	Health	SH.DYN.MORT	0.0%
Stunting prevalence	Health	SH.STA.STNT.ZS	70.8%
Adult literacy rate	Education	SE.ADT.LITR.ZS	80.8%
Primary school enrollment	Education	SE.PRM.TENR	50.8%
Access to electricity	Living Standards	EG.ELC.ACCS.ZS	0.0%
Basic sanitation access	Living Standards	SH.STA.BASS.ZS	0.0%
Drinking water access	Living Standards	SH.H2O.BASW.ZS	0.0%
Poverty headcount ratio	Monetary	SI.POV.DDAY	83.3%

 

3. Replication Code

The replication code is provided as a single Python script (replication_code.py) that implements the complete computational pipeline described in Algorithm 1 of the manuscript. The script is self-contained and modular, with clearly defined functions corresponding to each analytical stage. Execution from command line produces all numerical results, tables, and figures reported in the manuscript.

3.1 File: replication_code.py

The script contains eight modular functions:

load_and_impute(filepath) Loads the raw Excel file, applies group-mean imputation as initialization, and then applies MICE imputation using scikit-learn's IterativeImputer with Bayesian ridge regression. Returns the fully imputed DataFrame.

compute_persistence(X, scale=0.9) Computes persistent homology using the Vietoris-Rips filtration via the GUDHI library. Calculates pairwise Euclidean distances, sets epsilon_max to the specified percentile of distances (default 90th), constructs the Rips complex, builds the simplex tree, and computes persistence diagrams in dimensions H0, H1, and H2. Returns normalized persistence diagrams, the maximum edge length, and the simplex tree.

build_mapper(X, labels, ...) Constructs the Mapper graph using PCA as the lens function, 10 cover intervals with 30% overlap, and DBSCAN clustering. Returns nodes, edges, the NetworkX graph object, and a dictionary of graph-theoretic metrics (nodes, edges, components, density, modularity, clustering, betweenness).

wasserstein_distance_diag(diag1, diag2) Computes an approximate 2-Wasserstein distance between two persistence diagrams using greedy point matching with projection-to-diagonal for unmatched points.

compute_tci(diag_a, diag_b) Computes the Topological Convergence Index (TCI) between two persistence diagrams via the Wasserstein distance approximation.

bootstrap_inference(X, B=500, scale=0.9) Performs bootstrap resampling with replacement (B=500 by default) to construct percentile-based confidence intervals for maximum persistence values and significant feature counts. Returns mean, standard deviation, 95% CI, and detection rate for H1 features.

ml_benchmarking(X, labels) Benchmarks TDA against PCA, k-means (k=3,4,5), t-SNE, and UMAP, reporting explained variance ratios and silhouette scores.

markov_analysis(X, years) Implements Markov transition analysis by clustering observations into 3 deprivation states, computing per-country transition matrices, and calculating pooled steady-state distributions.

sensitivity_analysis(X) Systematically varies filtration scales (85th, 90th, 95th percentiles) and noise thresholds (0.03 to 0.07) to produce a sensitivity heatmap.

 

3.2 Software Requirements

The replication code requires Python 3.11 or higher and the following packages:

•  pandas >= 2.0.0 (data manipulation and Excel I/O)

•  numpy >= 1.24.0 (numerical operations)

•  matplotlib >= 3.7.0 (figure generation)

•  seaborn >= 0.12.0 (statistical visualization)

•  scipy >= 1.10.0 (distance computations)

•  scikit-learn >= 1.3.0 (standardization, PCA, clustering, MICE imputation, t-SNE)

•  gudhi >= 3.8.0 (persistent homology computation via Vietoris-Rips)

•  networkx >= 3.1 (graph-theoretic metrics for Mapper analysis)

•  umap-learn >= 0.5.3 (UMAP dimensionality reduction for benchmarking)

Installation command: pip install pandas numpy matplotlib seaborn scipy scikit-learn gudhi networkx umap-learn

Expected runtime: approximately 30 minutes on a standard desktop computer (Intel Core i5 or equivalent) for the full analysis including B=500 bootstrap resamples. The bootstrap component accounts for the majority of runtime (approximately 25 minutes). All other computations complete within 5 minutes.

 

4. Figures

All figures are provided as high-resolution PNG files at 300 DPI, suitable for direct inclusion in academic publications. Each figure corresponds to a specific analytical component described in the manuscript. Figures are numbered sequentially to match their order of appearance in the manuscript.

Figure 1: fig1_persistence.png - Persistence diagram for the combined WAMZ deprivation space (MICE imputation, n=120, 9 indicators). Blue circles denote H0 features (connected components); red triangles denote H1 features (1-cycles). The dashed diagonal represents zero persistence; dotted lines mark the noise threshold tau=0.05. Dimensions: 2400x2100 pixels.

Figure 2: fig2_barcodes.png - Persistence barcodes for the combined WAMZ space (MICE). Top panel: H0 components (119 finite features). Bottom panel: H1 cycles (21 finite features, 3 significant at tau>0.05). Each horizontal bar represents the lifespan of a topological feature across the filtration scale. Dimensions: 3600x2100 pixels.

Figure 3: fig3_country_barcodes.png - H0 persistence barcodes by individual country using 5 core indicators with complete data (no imputation). Five subplots show The Gambia, Ghana, Guinea, Nigeria, and Sierra Leone. The sixth panel is disabled. No H1 features are detected at the individual country level due to data sparsity (24 points in 5 dimensions). Dimensions: 4500x2700 pixels.

Figure 4: fig4_mapper.png - Mapper graph for WAMZ deprivation regimes (MICE imputation). Nodes represent clusters of country-year observations; edges connect overlapping clusters. Node color indicates dominant country (The Gambia=blue, Ghana=orange, Guinea=green, Nigeria=red, Sierra Leone=purple); node size reflects cluster membership count. PCA lens reveals deprivation progression vertically. Four connected components are visible. Dimensions: 4200x3000 pixels.

Figure 5: fig5_ml_benchmarking.png - Machine learning benchmarking comparison. Six panels show PCA, t-SNE, UMAP, and K-Means clustering (k=3,4,5) on WAMZ deprivation data. Country colors distinguish the five nations. Demonstrates that TDA captures structures these methods do not directly quantify. Dimensions: 5400x3300 pixels.

Figure 6: fig6_markov_transitions.png - Markov transition heatmaps for 3 deprivation states. Five per-country panels (The Gambia, Ghana, Guinea, Nigeria, Sierra Leone) plus pooled WAMZ. States 0, 1, 2 represent low, medium, and high deprivation. Color intensity indicates transition probability. State 2 is absorbing for 4 of 5 countries. Dimensions: 4500x3000 pixels.

Figure 7: fig7_persistence_landscapes.png - Persistence landscapes lambda_1, lambda_2, lambda_3 for H0 (blue, top row) and H1 (red, bottom row) with MICE imputation. Landscape functions provide stable vector representations of persistence diagrams. Dimensions: 4500x2400 pixels.

Figure 8: fig8_sensitivity.png - Sensitivity heatmap showing counts of significant H1 features across 15 parameter combinations: 3 filtration scales (85th, 90th, 95th percentile) x 5 noise thresholds (0.03, 0.04, 0.05, 0.06, 0.07). Results are stable with 2-4 significant features across all specifications. Dimensions: 2400x1800 pixels.

Figure 9: fig9_temporal.png - Temporal topology evolution across three periods: Early (2000-2007), Middle (2008-2015), Late (2016-2023). Three-panel bar chart showing H0 maximum persistence, H1 maximum persistence, and H1 significant feature count per period. The middle period shows transient cyclical structure. Dimensions: 3000x1500 pixels.

Figure 10: fig10_bootstrap.png - Bootstrap distributions (MICE, B=500). Left: H0 maximum persistence histogram with 95% CI [0.6372, 0.7248]. Right: H1 significant feature count histogram with 95% CI [1, 4] and 94% detection rate. Red dashed lines mark confidence interval boundaries. Dimensions: 3600x1350 pixels.

 

5. Replication Workflow

To replicate the complete analysis from raw data to final figures, follow these steps:

Step 1: Download the raw data: Download WAMZ_Poverty_TDA_Data.xlsx from the World Bank Open Data portal (World Bank Open Data) or use the provided upgraded data file WAMZ_Poverty_Upgraded_Data.xlsx.

Step 2: Install dependencies: Run: pip install pandas numpy matplotlib seaborn scipy scikit-learn gudhi networkx umap-learn

Step 3: Execute the replication script: Place replication_code.py and the data file in the same directory. Run: python replication_code.py. The script executes all eight analytical functions in sequence and prints results to console.

Step 4: Verify outputs: The script outputs all numerical results reported in the manuscript (persistence statistics, TCI matrix, bootstrap CIs, ML benchmarks, Markov matrices, sensitivity heatmap). Cross-reference with Tables 5-15 in the manuscript.

Step 5: Generate figures: Figures are saved to the figures/ subdirectory. The script produces all 10 figures at 300 DPI resolution. Cross-reference with Figures 1-10 in the manuscript.

 

6. Citation and Licensing

When using these materials, please cite the associated manuscript:

Opue, J. A. (2026). Persistent Homology and Computational Poverty Dynamics in the West African Monetary Zone. Computational Economics, forthcoming.

Data: World Bank World Development Indicators, publicly available at World Bank Open Data. World Bank (2024). World Development Indicators. World Bank Group, Washington, DC.

Code license: MIT License. You are free to use, modify, and distribute the replication code with appropriate attribution to the original author.

Data license: CC0 (public domain). The World Bank Open Data portal provides these indicators free of charge for research, commercial, and non-commercial purposes.

 

7. Contact and Support

For questions regarding the data, replication code, or figures, please contact:

•  Author: Job Agba Opue (job.opue@covenantuniversity.edu.ng)

•  Institution: Department of Economics and Development Studies, Covenant University, Ota, Nigeria

•  GitHub repository: github.com

Bug reports and feature requests should be submitted via the GitHub repository issue tracker. The author commits to responding to all replication-related inquiries within 14 days.