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All Journal UNP Journal of Statistics and Data Science
Slavina
Universitas Airlangga
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics Social Sciences

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Comparative Analysis of Parametric and Nonparametric Methods in Modeling Under-Five Malnutrition Prevalence Across Indonesia Dita Amelia; Suliyanto; Adelia Putri Andini; Faya Najwatus Silma; Nafla Nara Yonay; Slavina; Dinnara Chairana Aisha
UNP Journal of Statistics and Data Science Vol. 4 No. 3 (2026): UNP Journal of Statistics and Data Science
Publisher : Departemen Statistika Universitas Negeri Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/ujsds/vol4-iss3/554

Abstract

Malnutrition prevalence among children under five in Indonesia varied widely across provinces in 2024, ranging from 8.70% to 37.00%. Addressing this issue supports the global Sustainable Development Goals (SDGs) agenda, particularly SDG 2 (Zero Hunger) and SDG 3 (Good Health and Well-being). While most studies rely on multiple linear regression, its strict assumption of linearity is often violated in practice. This study conducts a comparative analysis between multiple linear regression and nonparametric penalized spline regression to model the effects of professional-assisted deliveries, safe sanitation access, complete basic immunization, and households at risk of stunting across 36 Indonesian provinces. Cross-sectional data for 2024 from the Central Bureau of Statistics (BPS) were analyzed, using MSE, R², and GCV for model comparison. The multiple linear regression model yielded an MSE of 18.812 and an R²  of 53.03%. Conversely, the penalized spline model (second-order polynomial, three knot points, λ = 0.0004) achieved a substantially lower MSE of 2.653 and a higher R² of 92.31%, demonstrating its superior capability in capturing nonlinear patterns. Regarding predictor significance, both models consistently identified safe sanitation, complete basic immunization, and households at risk of stunting as influential factors. However, professional assisted deliveries showed no significant effect in the nonparametric model. These findings confirm that the penalized spline approach provides more accurate estimates and is better suited for modeling provincial level malnutrition determinants.
Comparison of Least Square Spline and Penalized Spline for Modeling Human Development Index Determinants Dita Amelia; Tyo Anugrah Putra; Slavina; Thareq Alexander Manggala Napitupulu; Layyin Gisvira; Nila Khoirun Naili Salam
UNP Journal of Statistics and Data Science Vol. 4 No. 3 (2026): UNP Journal of Statistics and Data Science
Publisher : Departemen Statistika Universitas Negeri Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/ujsds/vol4-iss3/555

Abstract

The Human Development Index (HDI) is a key indicator of national and regional development and supports the achievement of the Sustainable Development Goals (SDGs), particularly Goal 1 (No Poverty) and Goal 4 (Quality Education). However, substantial disparities in HDI remain across Indonesia’s regencies and cities due to complex and nonlinear socioeconomic relationships that cannot always be captured by conventional parametric methods. This study analyzes the determinants of HDI in 514 regencies and cities in Indonesia in 2024 using nonparametric spline regression by comparing Penalized Spline and Least Square Spline estimators. The explanatory variables include mean years of schooling, labor force participation rate, percentage of senior-high-school graduates, and poverty rate. Secondary data from BPS were analyzed through spline basis construction, smoothing parameter selection using Generalized Cross Validation (GCV), parameter estimation, significance testing, and residual diagnostics. The results show that all predictors have nonlinear relationships with HDI. Mean years of schooling and the percentage of senior-high-school graduates positively affect HDI, whereas labor force participation and poverty rate have negative effects. The second-order Penalized Spline model with four knot points achieved the best performance, yielding the lowest GCV (5.388838), the lowest MSE (4.948574), and the highest adjusted R² (86.94%). Residual diagnostics confirmed normality and zero mean but indicated autocorrelation, suggesting spatial dependence. Overall, Penalized Spline regression provides a flexible and accurate approach for modeling HDI determinants and informing evidence-based regional development policy.
Co-Authors Adelia Putri Andini Dinnara Chairana Aisha Dita Amelia Faya Najwatus Silma Layyin Gisvira Nafla Nara Yonay Nila Khoirun Naili Salam Suliyanto Thareq Alexander Manggala Napitupulu Tyo Anugrah Putra