Introduction

We present an executable workflow that explains UN EGDI scores from four socioeconomic indicators with no overlap with EGDI sub-components. We use Gradient Boosted Trees (scikit-learn) and validate with temporal cross-validation appropriate for panel data — training on earlier survey years and testing on later ones.

Data and Features

Target: EGDI (UN DESA, 2018/2020/2022). Sample: 52 countries. Features (4, non-overlapping): log(GDP per capita), CPI, urbanization %, government expenditure % GDP. Internet penetration and schooling are excluded because they are direct EGDI sub-index inputs.

Temporal Cross-Validation

Standard k-fold CV is inappropriate for panel data where the same countries appear at multiple timepoints. We use temporal CV — training on earlier years, testing on later years:

The model generalizes consistently across all temporal splits (R² range: 0.862-0.930). Performance improves with more training data (104 vs 52 observations).

Model Comparison

The persistence model is the best forecaster (EGDI scores are highly stable). Our contribution is explanatory: GBT outperforms log(GDP)-only by R² +0.086, demonstrating that CPI, urbanization, and government expenditure add genuine explanatory power. GBT captures non-linearities that OLS misses (R² 0.930 vs 0.856).

Feature Importance

GDP and CPI account for 95% of explanatory power. Government expenditure level matters more than urbanization — institutional quality and fiscal capacity dominate over demographic structure.

Outlier Analysis with Statistical Tests

We compute studentized residuals with t-tests (df=47) to identify statistically significant outliers. The Bonferroni-corrected threshold for 52 tests is t=3.52.

South Korea and Bangladesh are significant at α=0.05. Jordan and Malaysia are marginally significant. Saudi Arabia's positive residual (+0.071) is the 8th largest, with p=0.145 — not statistically significant at conventional thresholds. No outliers survive Bonferroni correction (threshold t=3.52), indicating that while some countries deviate from prediction, no single country is a dramatic outlier given the model's precision.

Honest interpretation: Saudi Arabia does score above its socioeconomic prediction, but the gap is within the model's normal error range. We cannot statistically distinguish this from noise at p=0.05. Claims of Vision 2030's measurable impact on EGDI require a larger sample or a dedicated causal identification strategy.

Implementation

The workflow uses scikit-learn (GradientBoostingRegressor), scipy (t-tests), and matplotlib (charts). Complete source code (~300 lines) is in egdi_model.py:

pip install numpy matplotlib scikit-learn scipy --break-system-packages
python egdi_model.py

Output: console metrics, 3 publication-ready charts, structured JSON.

Related Work

Krishnan et al. (2013, I&M 50(8)) used SEM for e-government maturity factors. Zhao et al. (2014, IT&P 27(1)) found governance quality predicts EGDI. Singh et al. (2020, GIQ 37(3)) used panel regression on 178 countries. Dias (2020, GIQ 37(1)) examined the digital divide with quantile regression. Verkijika & De Wet (2018, EG 14(1)) analyzed EGDI predictors with OLS on 193 countries. We extend this with: (a) non-linear modeling via gradient boosting, (b) deliberate exclusion of circular features, (c) temporal CV appropriate for panel data, and (d) formal outlier significance testing.

Limitations

1. 52 countries. Expanding toward 193 would improve generalizability.
2. Persistence beats for forecasting. This is an explanatory tool.
3. Saudi Arabia not significant. The +0.071 residual does not reach p<0.05.
4. Temporal CV validates projection, not cross-country generalization. The model requires historical data for each country.
5. Negative 5-fold CV. Random CV is inappropriate for this panel structure; temporal CV is the correct approach (all splits positive, R²=0.862-0.930).

References

1. UN DESA, "E-Government Survey 2018," 2018.
2. UN DESA, "E-Government Survey 2020," 2020.
3. UN DESA, "E-Government Survey 2022," 2022.
4. World Bank, "World Development Indicators," 2024.
5. IMF, "World Economic Outlook," Oct 2024.
6. Transparency International, "CPI," 2018-2022.
7. Friedman J.H., "Greedy Function Approximation: A Gradient Boosting Machine," Annals of Statistics 29(5), 2001.
8. Krishnan S. et al., I&M 50(8), 2013.
9. Zhao F. et al., IT&P 27(1), 2014.
10. Singh H. et al., GIQ 37(3), 2020.
11. Dias G.P., GIQ 37(1), 2020.
12. Verkijika S.F. & De Wet L., Electronic Government 14(1), 2018.