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

📅 2026-04-07
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This study addresses the challenges of analyzing provincial poverty in Indonesia, where a small sample size (n = 34) and high-dimensional multicollinearity undermine the stability of conventional regression models. To tackle this, the authors develop a systematic comparative framework evaluating several regularization and machine learning approaches—including ridge regression, LASSO, elastic net, Bayesian shrinkage priors, spatial ICAR, and Bayesian additive regression trees (BART)—in terms of predictive performance and robustness. The results demonstrate that parametric linear shrinkage methods, particularly ridge regression, yield the most accurate and stable predictions, whereas more complex ensemble models tend to overfit. Notably, ICT skills emerge as a consistently significant negative predictor of poverty across all well-performing models, highlighting their potential as a strategic priority for development policy. This work offers a reliable modeling paradigm and empirical foundation for evidence-based policymaking in data-scarce settings.

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📝 Abstract
Identifying the structural drivers of poverty in regional datasets is frequently hindered by small sample sizes and high multidimensional collinearity, which can result in unstable and misleading policy advice. This paper evaluates the provincial causes of poverty in Indonesia by addressing these specific statistical hazards. We employ a rigorous model-comparison framework designed for small samples ($n=34$) with high collinearity, comparing standard linear models with frequentist penalisation, Bayesian shrinkage priors, an adjusted spatial intrinsic conditionally autoregressive (ICAR) model, and complex machine learning ensembles. To ensure a robust evaluation, we measure predictive performance using strict Leave-One-Out Cross-Validation (LOOCV). The results demonstrate that algorithmic complexity is inherently risky in regional datasets: simple linear shrinkage models (Ridge, Elastic Net, LASSO) achieve the superior out-of-sample prediction, whereas complex ensembles like BART suffer from severe overfitting. Across all successful regularised models, ICT skills consistently emerge as the most stable proxy for lower provincial poverty. The primary contribution of this paper is demonstrating that, in data-constrained regional analysis, parametrically regularised linear shrinkage provides a more reliable mathematical foundation for isolating structural development priorities, such as ICT, than either naive OLS or unconstrained machine learning.
Problem

Research questions and friction points this paper is trying to address.

small samples
high collinearity
poverty drivers
regional analysis
structural development
Innovation

Methods, ideas, or system contributions that make the work stand out.

regularized linear models
small sample inference
high collinearity
Leave-One-Out Cross-Validation
model comparison
💼 Related Jobs
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A
A. H. Jamaluddin
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, Serdang, Malaysia; Statistical Data Science Group, Faculty of Science, Universiti Putra Malaysia, Serdang, Malaysia
A
A. T. R. Dani
Doctoral Study Programme MIPA, Faculty of Science and Technology, Airlangga University, Surabaya 60115, Indonesia; Statistics Study Programme, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Mulawarman University, Samarinda 75123, Indonesia
N
N. I. Mahat
Research Management Centre, Universiti Utara Malaysia, Sintok Kedah, 06010, Malaysia
V
V. Ratnasari
Department of Statistics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, Surabaya 60111, Indonesia
S
S. S. M. Fauzi
Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Perlis, Arau Campus, Perlis, Malaysia; Information System Study Program, Faculty of Science and Technology, Universitas Airlangga, Surabaya, Indonesia