Article Per Year (5 Year)
p-Index From 2021 - 2026
0.23
P-Index
This Author published in this journals
All Journal Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika
Fettyana Fettyana
State University of Makassar
Mathematics

Published : 1 Documents Claim Missing Document
Claim Missing Document
Check
Articles

Found 1 Documents
Search

 1 
Principal Component–Truncated Spline Regression Modeling of Population Welfare in South Sulawesi Irwan Thaha; Ayu Rahayu; Nur Fadilah; Fettyana Fettyana
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 9 No. 4 (2026): Volume 9 Nomor 4 Tahun 2026
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v9i4.9790

Abstract

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.
Co-Authors Ayu Rahayu Irwan Thaha Nur Fadilah