A Comparative Study of Penalised, Bayesian, Spatial, and Tree-Based Models for Provincial Poverty in Indonesia: Small Samples and High Collinearity

This paper demonstrates that in the context of Indonesia's provincial poverty analysis with small sample sizes and high collinearity, simple parametrically regularized linear models outperform complex machine learning ensembles in predictive accuracy and consistently identify ICT skills as a key structural driver for poverty reduction.

The Gist

Imagine you are a chef trying to create the perfect soup to feed 34 different villages in Indonesia. You want to know exactly which ingredients (like education, health, or internet skills) make the "poverty soup" taste better or worse.

However, you have a massive problem: You only have 34 bowls of soup to taste, but you have 9 different ingredients to test.

This is the challenge the researchers faced. In statistics, this is called a "small sample" problem. When you have too many ingredients and too few bowls, it's easy to get confused. You might think salt is the secret ingredient, when really it was just the pepper that was acting up. This confusion is called collinearity (when ingredients are so mixed up you can't tell them apart).

Here is what the study found, broken down into simple stories:

1. The "Over-Engineered" vs. The "Simple" Cook

The researchers tested two types of chefs to see who could predict the soup's taste best:

• The "Super-Complex" Chefs (Machine Learning): These are like chefs who use giant, expensive robots (like BART, Random Forest, and XGBoost) to taste the soup. They try to find hidden patterns and secret recipes.
  • The Result: In a small kitchen with only 34 bowls, these robots went crazy. They started memorizing the specific quirks of the 34 bowls instead of learning the general recipe. They "overfit." It's like a student who memorizes the answers to a practice test but fails the real exam because they didn't understand the concepts. The robots made huge mistakes when trying to predict new situations.
• The "Simple & Disciplined" Chefs (Linear Shrinkage): These are chefs who use a simple, strict rulebook (Ridge, LASSO, Elastic Net). They say, "We don't have enough data to be fancy, so let's stick to the basics and ignore the noise."
  • The Result: These chefs won. By being simple and refusing to get distracted by the noise, they gave the most accurate predictions for the villages they hadn't tasted yet.

The Lesson: When you have very little data, a simple, disciplined approach is better than a fancy, complex one.

2. The "Magic Ingredient": ICT Skills

After all the testing, one ingredient stood out as the most reliable predictor of lower poverty: ICT Skills (the ability to use computers and the internet).

• The Analogy: Imagine you are looking at a group of athletes. Some are fast, some are strong, and some are smart. But if you had to pick just one thing that predicts who will win the race, you'd pick "Speed."
• The Finding: In Indonesia, provinces with high ICT skills almost always had lower poverty. But here is the twist: ICT skills aren't just about "using the internet." They are like a report card for a whole package of success. If a province has good internet skills, it usually also has good schools, good hospitals, and good roads.
• The Takeaway: ICT skills are the "canary in the coal mine." If a province has good digital skills, it likely has a strong foundation of development. If it doesn't, it's likely struggling in many other areas too.

3. The "Neighborhood Effect" Myth

The researchers also asked: "Does poverty spread like a virus from one village to its neighbor?" (This is called spatial dependence).

• The Test: They looked at a map and saw that poor villages were often clustered together, like a neighborhood of poor houses.
• The Discovery: Once they accounted for the ingredients (education, health, internet), the "neighborhood effect" disappeared.
• The Analogy: Imagine you see a group of people all wearing red hats. You might think, "Oh, they are all part of the Red Hat Club!" But then you realize they are all wearing red hats because they are all standing next to a red building. The building (the underlying factors like education and jobs) is the real cause, not the club membership (the geography).
• The Takeaway: Poverty clusters together not because poverty "spreads" from neighbor to neighbor, but because neighbors share the same lack of schools, jobs, and internet. Fix the ingredients, and the clustering fixes itself.

Summary: What Should Policymakers Do?

1. Don't get fancy with your math: When you have limited data (like 34 provinces), don't use complex AI models. They will trick you. Use simple, disciplined statistical tools.
2. Focus on Digital Skills: Investing in ICT isn't just about giving people computers; it's a signal that a region is ready for broader development. It's the most stable sign of a healthy economy.
3. Look at the Whole Picture: Don't just look at the map and assume geography is the problem. Look at the ingredients (schools, health, internet). If you improve those, the geography stops being a barrier.

In short: To solve poverty in Indonesia's provinces, don't overcomplicate the math. Focus on the simple truth: regions with better digital skills and a strong foundation of development are the ones that are doing well. Keep it simple, keep it disciplined, and focus on the basics.

Technical Summary

1. Problem Statement

The paper addresses the challenge of identifying structural drivers of poverty in regional datasets characterized by small sample sizes ($n=34$ provinces) and high multidimensional collinearity among predictors.

• The Context: Indonesia exhibits significant provincial disparities in poverty (ranging from 4.53% to 26.80%) and ICT skills.
• The Statistical Hazard: Standard statistical tools (like Ordinary Least Squares - OLS) and complex machine learning (ML) ensembles often fail in this setting.
  • Small $n$: With only 34 observations, complex models risk severe overfitting and high variance.
  • High Collinearity: Predictors such as ICT skills, sanitation, and life expectancy are deeply intertwined. This leads to unstable coefficient estimates, sign reversals, and "false positives" that can misguide public policy.
  • Spatial Bias: Poverty rates are spatially clustered, raising questions about whether geographic proximity represents a distinct spillover effect or merely a proxy for shared socioeconomic factors.

2. Methodology

The authors employ a rigorous model-comparison framework designed to evaluate predictive performance under strict constraints.

• Data: Cross-sectional data from 2024 for all 34 Indonesian provinces.
  • Outcome: Provincial poverty rate.
  • Predictors ($p=9$): Schooling, Life Expectancy, Unmet Health Needs, Gini Ratio, Sanitation, Water Access, Electricity Access, Unemployment, and ICT Skills.
• Model Portfolio: The study compares 15 distinct specifications across four categories:
  1. Frequentist Linear Models: OLS, Ridge, LASSO, and Elastic Net.
  2. Bayesian Models: Linear regression with Gaussian priors, Bayesian Ridge, Bayesian LASSO, Horseshoe shrinkage, Spike-and-Slab selection, and Beta regression (for bounded outcomes).
  3. Spatial Models: A Bayesian spatial ICAR model (BYM2 specification) accounting for archipelagic geography.
  4. Tree-Based/Non-Linear Ensembles: Bayesian Additive Regression Trees (BART), Random Forest, XGBoost, and Gaussian Process Regression.
• Evaluation Strategy:
  • Strict Leave-One-Out Cross-Validation (LOOCV): Given $n=34$, LOOCV is used to maximize data usage while ensuring out-of-sample validity.
  • Metric: Root Mean Squared Error (RMSE) on the original percentage scale.
  • Validation Rigor: For Bayesian models, PSIS-LOO is used with exact re-fitting for influential observations (Pareto $k > 0.7$). All preprocessing and tuning are performed within each training fold to prevent data leakage.

3. Key Results

A. Predictive Performance (The "Winner")

• Linear Shrinkage Dominance: Simple parametric regularized models (Ridge, Elastic Net, and LASSO) achieved the lowest LOOCV-RMSE (approx. 3.61–3.67), outperforming all other methods.
• Failure of Complex ML: Highly unconstrained algorithms suffered from catastrophic overfitting.
  • BART performed the worst (RMSE = 7.50), nearly double the error of linear shrinkage models.
  • Gaussian Processes also failed to generalize (RMSE = 4.88).
  • Tree Ensembles: Random Forest and XGBoost improved slightly over naive OLS but still underperformed compared to penalized linear models.
• Spatial Redundancy: The spatial ICAR model (RMSE = 4.18) offered no predictive advantage over non-spatial penalized models. Residual spatial dependence vanished after controlling for socioeconomic covariates, suggesting geography acts as a proxy for observed fundamentals rather than a distinct spillover mechanism.

B. Variable Stability and Drivers

• ICT Skills as the Primary Driver: Across all successful regularized frameworks (Frequentist and Bayesian), ICT Skills emerged as the only stable, negative structural predictor of poverty.
  • In the Horseshoe model (M8), the 95% credible interval for ICT skills strictly excluded zero.
  • In Spike-and-Slab selection, ICT skills had a dominant Posterior Inclusion Probability (PIP) of 0.969.
• Instability of Other Variables: Coefficients for schooling, sanitation, and electricity were highly unstable. For instance, the coefficient for "Schooling" flipped from positive in OLS to negative in Ridge regression, a classic symptom of collinearity-induced instability.
• Interpretation: ICT skills likely serve as a composite proxy for a broader bundle of provincial advantages (institutional quality, economic integration, education) rather than acting as an isolated causal lever.

4. Key Contributions

1. Methodological Hierarchy for Micro-Samples: The paper establishes that in small-sample, high-collinearity regional analysis, parametrically regularized linear shrinkage is superior to both naive OLS and complex machine learning. It demonstrates that algorithmic complexity introduces predictive volatility rather than uncovering deeper structure in these contexts.
2. Refining the Role of ICT: It moves beyond the standard view of ICT as just one of many correlates. The study proves ICT is the most robust predictor when statistical noise is aggressively filtered, suggesting it is a summary indicator of overall development readiness.
3. Spatial Diagnostics: It provides empirical evidence that for Indonesian provinces, spatial clustering is largely compositional (explained by covariates) rather than a residual spatial process, arguing against the automatic inclusion of spatial random effects in such models.

5. Significance and Policy Implications

• Policy Reliability: The findings warn policymakers against relying on unpenalized regressions or "black-box" ML models for small regional datasets, as these can produce misleading "false positives" regarding which interventions reduce poverty.
• Integrated Development: The stability of ICT skills suggests that digital inclusion should not be pursued in isolation. Instead, it should be viewed as part of a broader "place-based" development strategy that simultaneously addresses education, health, and infrastructure, as these factors are structurally bundled.
• Blueprint for Regional Science: The paper offers a practical workflow for researchers working with constrained data: regularize aggressively, validate strictly via LOOCV, distinguish raw clustering from residual dependence, and prioritize parsimony over complexity.

Conclusion: The study concludes that for provincial poverty analysis in Indonesia, disciplined linear shrinkage provides the most reliable mathematical foundation for isolating structural priorities, with ICT skills standing out as the most critical, stable indicator of lower poverty.