Pemodelan Faktor yang Mempengaruhi Indeks Demokrasi Indonesia Menggunakan Spline Truncated

Hanny Valida; M. Fariz Fadillah Mardianto; Dita  Amelia; Suliyanto Suliyanto

doi:10.47134/ppm.v3i2.2478

Authors

Hanny Valida Universitas Airlangga
M. Fariz Fadillah Mardianto Universitas Airlangga
Dita Amelia Universitas Airlangga
Suliyanto Universitas Airlangga

DOI:

https://doi.org/10.47134/ppm.v3i2.2478

Keywords:

Indeks Demokrasi Indonesia, Spline Truncated, Regresi Nonparameterik

Abstract

Penelitian ini bertujuan menganalisis faktor-faktor yang memengaruhi Indeks Demokrasi Indonesia (IDI) menggunakan pendekatan regresi spline linier terpotong nonparametrik. Data yang digunakan merupakan data sekunder cross-section dari 34 provinsi di Indonesia pada tahun 2024, dengan variabel prediktor berupa Indeks Pemberdayaan Gender, Indeks Kebebasan Pers, dan Indeks Pembangunan Manusia. Pemilihan model dilakukan menggunakan kriteria Generalized Cross Validation (GCV) untuk menentukan jumlah dan posisi knot yang optimal. Hasil analisis menunjukkan bahwa model terbaik diperoleh dengan tiga titik knot, menghasilkan nilai GCV sebesar 6,79 dan koefisien determinasi (R²) sebesar 89,37 persen. Hasil penelitian menunjukkan adanya hubungan nonlinier antara variabel prediktor dan IDI. Indeks Pemberdayaan Gender memberikan pengaruh positif pada tingkat rendah hingga menengah, namun berubah menjadi negatif pada tingkat yang lebih tinggi. Indeks Kebebasan Pers menunjukkan pengaruh positif pada tingkat rendah tetapi cenderung negatif setelah melewati titik tertentu. Sementara itu, Indeks Pembangunan Manusia memberikan pengaruh positif yang konsisten terhadap IDI. Temuan ini menunjukkan bahwa kualitas demokrasi di Indonesia dipengaruhi oleh dinamika sosial dan institusional yang kompleks.

References

Anisar, A., Sifriyani, S., & Dani, A. (2023). Estimation of A Bi-Response Truncated Spline Nonparametric Regression Model on Life Expectancy and Prevalence of Underweight Children in Indonesia. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 17(4). https://doi.org/10.30598/barekengvol17iss4pp2011-2022 DOI: https://doi.org/10.30598/barekengvol17iss4pp2011-2022

BPS, (2025), [Metode Baru] Indeks Demokrasi Indonesia menurut Provinsi, 2024, https://www,bps,go,id/id/statistics-table/2/MjE1OSMy/-metode-baru-indeks-demokrasi-indonesia-menurut-provinsi,html

Bramante, R., Petrella, G., & Zappa, D. (2013). On the interpretation and estimation of the market model R-square. Electronic Journal of Applied Statistical Analysis, 6(1), 57–66. https://doi.org/10.1285/i20705948v6n1p57

Carolin, W,D,, & Fahmuddin, M, S, (2023), Analisis Regresi Nonparametrik Spline Truncated untuk Menganalisis Faktor-Faktor yang Mempengaruhi Tingkat Pengangguran Terbuka di Provinsi Sulawesi Selatan, VARIANSI: Journal of Statistics and Its Application on Teaching and Research, 5(2), 55–63, https://doi,org/10,35580/vari ansiunm101

Dani, A, T, R,, & Ni’matuzzahroh, L, (2022), Penerapan Keluarga Model Spline Truncated Polinomial pada Regresi Nonparametrik, Inferensi, 5(1), 37, https://doi,org/10,12 962/j27213862,v5i1,12537 DOI: https://doi.org/10.12962/j27213862.v5i1.12537

Economist Intelligence Unit, (2024), Democracy Index 2024, https://www,Eiu,com/n/camp aigns/democracy-index-2024/

Fadly, F,, & Chandra, A, (2024), Human Development To Democracy: An Impact Analysis of Poverty and Income Inequality In Indonesia, Income Inequality In Indonesia, Signifikan: Jurnal Ilmu Ekonomi, 13(2), 231–246, https://doi,org/10,15408/sjie,v13i2,42285

Fajri, H, (2021), Demokrasi Pincang: Analisis Terhadap Indeks Demokrasi Provinsi Sumatera Barat Pasca Reformasi, El-Riyasah, 12, 108–129 DOI: https://doi.org/10.24014/jel.v12i1.13303

Firman (2023), Media Ownership and Democracy Processes In Indonesia, Jurnal Penelitian Politik, 20(1), https://doi,org/10,14203/jpp,v20i1,1446

Graffelman, J., & Van Eeuwijk, F. (2005). Calibration of multivariate scatter plots for exploratory analysis of relations within and between sets of variables in genomic research. Biometrical Journal, 47(6), 863–879. https://doi.org/10.1002/bimj.200510177 DOI: https://doi.org/10.1002/bimj.200510177

Handajani, S, S,, Pratiwi, H,, Susanti, Y,, Respatiwulan, R,, Nirwana, M, B,, & Mahmudah, A, (2023), Pemodelan Produksi Padi di Provinsi Jawa Timur dengan Regresi Non Parametrik B-Spline, PYTHAGORAS Jurnal Pendidikan Matematika, 18(2), 159–175, https://doi,org/10,21831/pythagoras,v18i2,67475 DOI: https://doi.org/10.21831/pythagoras.v18i2.67475

Handayani, T,, Sifriyani, S,, & Rian Dani, A, T, (2024), Stunting Prevalence Modeling Using Nonparametric Regression of Quadratic Splines, Jurnal Varian, 7(2), 149–160, https://doi,org/10,30812/varian,v7i2,2916 DOI: https://doi.org/10.30812/varian.v7i2.2916

Harbison, L., & Simmons, K. (2024). Fundamentals of Descriptive Statistics. Journal of Dental Hygiene, 98(5), 51–54. https://www.scopus.com/inward/record.uri?eid=2-s2.0-

85206505899&partnerID=40&md5=2755b42c042ac344c1a50fff0186c20f

Izza, N, (2020), Pemodelan Faktor-faktor yang Mempengaruhi Tingkat Partisipasi Angkatan Kerja Perempuan di Jawa Barat Menggunakan Regresi Nonparametrik Spline Truncated, Inferensi, 3, 21–27, DOI: https://doi.org/10.12962/j27213862.v3i1.6878

Kapelner, Z. (2023). What does it mean to have an equal say? Ethical Theory and Moral Practice. https://doi.org/10.1007/s10677-023-10404-1 DOI: https://doi.org/10.1007/s10677-023-10404-1

Kartapranata, G, Susetyo, A,R,, & Ningsiawati, (2024), Roller Coaster Demokrasi Indonesia, Kompas,Id, https://www,kompas,id/baca/kompas_multimedia/membaca-kehidupan-demokrasi

Moustaid, W., & Erritali, M. (2026). Machine Learning in the Insurance Industry. Lecture Notes in Networks and Systems, 1589 LNNS, 372–386. https://doi.org/10.1007/978-3-032-02312-4_30 DOI: https://doi.org/10.1007/978-3-032-02312-4_30

Ramdani, F,, Tike, A,, & Zelfia, (2024), Kebebasan pers dan etika media (Telaah konsep kebebasan pers dan etika media), Respon: Jurnal Ilmiah Mahasiswa Ilmu Komunikasi, 5(4), 93–102, https://jurnal,ilkom,fs,umi,ac,id/index,php/respon/index DOI: https://doi.org/10.33096/respon.v5i4.273

Romadhona, W,, Syavera, V (2025), Generalized Linear Model Menggunakan Distrbusi Lognormal dan Gamma: Aplikasi Terhadap Indeks Demokrasi Indonesia di Jawa Barat Jurnal Sains Ekonomi dan Edukasi, 2(1), 117–126, https://doi,org/10,62335 DOI: https://doi.org/10.62335/gbezv413

Saifudin, T., Nugraha, G. C., Valida, H., Nahar, M. H., & Fortunata, R. (2025). Modeling Democracy Index In Indonesia With Multivariate Adaptive Regression Spline Approach. Barekeng, 19(4), 2347–2358. https://doi.org/10.30598/barekengvol19iss4p p2347-2358 DOI: https://doi.org/10.30598/barekengvol19iss4pp2347-2358

Sitohang, F. K. S., & Mahmuda, S. (2024). Application Of Truncated Spline Nonparametric Regression For Modeling The Height Of Yeop Chagi Kicks Of Taekwondo Athletes In Samarinda City. Barekeng, 18(2), 657–666. https://doi.org/10.30598/barekengvol18Iss2p p0657-0666 DOI: https://doi.org/10.30598/barekengvol18iss2pp0657-0666

Subono, N, I, (2025), Kepemimpinan Perempuan di Akar Rumput dan Ketahanan Demokrasi: Kajian Pengantar Teoretis, Jurnal Perempuan, 29(3), 259–272, https://doi, org/10,34309/jp,v29i3,1185 DOI: https://doi.org/10.34309/jp.v29i3.1185

Utami, T. W., Haris, M. A., Prahutama, A., & Purnomo, E. A. (2020). Optimal knot selection in spline regression using unbiased risk and generalized cross validation methods. Journal of Physics: Conference Series, 1446(1). https://doi.org/10.1088/1742-6596/1446/1/012049 DOI: https://doi.org/10.1088/1742-6596/1446/1/012049

Wardani, P, K,, Budiantara, I, N,, & Setiawan, S, (2025), Selecting Optimal Knot Points and Oscillation Parameters Using Generalized Cross-validation and Unbiased Risk Method in Nonparametric Regression of Combined Spline Truncated and Fourier Series, KnE Social Sciences, 10(11), 220–234, https://doi,org/10,18502/kss,v10i11,18744 DOI: https://doi.org/10.18502/kss.v10i11.18744

Wrange, P. (2022). SDG 16: Promote Peaceful and Inclusive Societies for Sustainable Development, Provide Access to Justice for All and Build Effective, Accountable and Inclusive Institutions at All Levels. In The Cambridge Handbook of the Sustainable Development Goals and International Law (pp. 399–421). https://doi.org/10.1017/9781108769631.018 DOI: https://doi.org/10.1017/9781108769631.018