Principal Component–Truncated Spline Regression Modeling of Population Welfare in South Sulawesi
DOI:
https://doi.org/10.30605/proximal.v9i4.9790Keywords:
Population Welfare, Principal Component Analysis, Truncated Spline, Nonparametric Regression, South SulawesiAbstract
Population welfare modeling with socioeconomic predictors faces two problems: multicollinearity and an unknown functional form. This study combines Principal Component Analysis (PCA) with nonparametric truncated spline regression to model the Human Development Index (HDI), used as a proxy for the human development dimension of population welfare, across the 24 regencies/cities of South Sulawesi in 2024, using six predictors: population density, number of poor people, labor force size, real per-capita expenditure, life expectancy, and mean years of schooling. The KMO measure (0.591) and Bartlett's test (χ² = 97.72; p < .001) supported dimension reduction, and two components with eigenvalues > 1 were retained (78.83% of variance). The polynomial order (m = 1, 2, 3), number of knots per component (r = 1, 2, 3), and knot locations were selected jointly by minimizing Generalized Cross-Validation (GCV), with knots searched exhaustively within the 15th–85th percentile range of each component. The optimal model, a linear truncated spline with two knots per component (GCV = 0.453), achieved R² = 0.9836 and AIC = 46.54, outperforming linear principal component regression (R² = 0.9571; AIC = 61.59); its leave-one-out cross-validated R² was 0.9625. The first component, a development-scale dimension, has an increasing effect over three segments (slopes 1.80, 4.22, and 1.43); the second, contrasting poverty–labor pressure with human-capital quality, decreases overall with a local slope change between two closely spaced knots. The estimated knots group regencies/cities into segments with different marginal associations with the HDI, offering an empirical basis for prioritizing regional development.References
Badan Pusat Statistik. (2025). Indeks Pembangunan Manusia 2024 [Human Development Index 2024]. Badan Pusat Statistik Republik Indonesia. https://www.bps.go.id/id/publication/2025/05/15/dd9a3ce7dfae1c733e46338f/indeks-pembangunan-manusia-2024.html
Badan Pusat Statistik Provinsi Sulawesi Selatan. (2025). Provinsi Sulawesi Selatan dalam angka 2025 [South Sulawesi Province in figures 2025]. Badan Pusat Statistik Provinsi Sulawesi Selatan. https://sulsel.bps.go.id/en/publication/2025/02/28/a7beacd81481497cecb44084/provinsi-sulawesi-selatan-dalam-angka-2025.html
Ell Goldameir, N., Djuraidah, A., & Wigena, A. H. (2015). Quantile spline regression on statistical downscaling model to predict extreme rainfall in Indramayu. Applied Mathematical Sciences, 9(126), 6263–6272. https://doi.org/10.12988/ams.2015.57502
Islamiyanti, A., Statistika, D., Matematika, F., & Alam, P. (2019). Regresi Spline Polynomial Truncated Biprediktor untuk Identifikasi Perubahan Jumlah Trombosit Pasien Demam Berdarah Dengue. 7(2), 97–112.
Islamiyati, A., Fatmawati, & Chamidah, N. (2017). Fungsi Goodness of Fit dalam Kriteria Penalized Spline pada Estimasi Regresi Nonparametrik Birespon untuk Data Longitudinal. Seminar Nasional Matematika Dan Aaplikasinya, 2007, 216–221.
Islamiyati, A., Kalondeng, A., Sunusi, N., Zakir, M., & Kamal, A. (2022). Journal of King Saud University – Science Biresponse nonparametric regression model in principal component analysis with truncated spline estimator. Journal of King Saud University - Science, 34(3), 101892. https://doi.org/10.1016/j.jksus.2022.101892
Islamiyati, A., Sahriman, S., & Massalesse, J. (2023). Model Regresi Kuantil Spline Orde Dua Dalam Menganalisis Perubahan Trombosit Pasien Demam Berdarah. 5(1), 38–45.
Latief, A. N., Islamiyati, A., Sunusi, N., & Kuswanto, H. (2022). The Implementation of Hierarchical Linear Spline Regression Model to The Implementation of Hierarchical Linear Spline Regression Model to Maternal Mortality Rate Data in Indonesia. December. https://doi.org/10.47119/IJRP10011311120214161
Lestari, B., Fatmawati, Budiantara, I. N., & Chamidah, N. (2018). Estimation of Regression Function in Multi-Response Nonparametric Regression Model Using Smoothing Spline and Kernel Estimators. Journal of Physics: Conference Series, 1097(1). https://doi.org/10.1088/1742-6596/1097/1/012091
Pratama, Y. M., Fernandes, A. A. R., Wardhani, N. W. S., & Hamdan, R. (2024). Nonparametric Smoothing Spline Approach in Examining Investor Interest Factors. JTAM (Jurnal Teori Dan Aplikasi Matematika), 8(2), 425. https://doi.org/10.31764/jtam.v8i2.20192
Tenggara, N., Hidayati, L., Budiantara, I. N., & Chamidah, N. (2020). Bi-Response Semiparametric Regression Model based on Spline Truncated for Estimating Computer based National Exam in West. ICMIs 2018, 357–361. https://doi.org/10.5220/0008521903570361
Utami, T. W., Chamidah, N., Saifudin, T., Lestari, B., & Aydin, D. (2025). Estimation of Biresponse Semiparametric Regression Model for Longitudinal Data Using Local Polynomial Kernel Estimator. 1–22. https://doi.org/https://doi.org/10.3390/sym17030392
Yulianti, A. S., Islamiyati, A., & Herdiani, E. T. (2024). The Principal Component Linear Spline Quantile Regression Model in Statistical Downscaling for Rainfall Data. 35(2), 159–166.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Irwan Thaha, Ayu Rahayu, Nur Fadilah, Fettyana Fettyana
This work is licensed under a Creative Commons Attribution 4.0 International License.
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
License and Copyright Agreement
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
