Identifikasi Faktor Risiko Kematian Ibu dan Neonatal di Kalimantan Menggunakan Model BPGIGR dengan Algoritma BHHH
DOI:
https://doi.org/10.32493/sm.v7i3.54886Keywords:
BPGIGR, BHHH, Maternal Mortality, Neonatal Mortality, KalimantanAbstract
Poisson regression is widely applied for modeling count data and requires the strict assumption of equidispersion, meaning that the mean and variance of the data must be equal. In practice, this condition is rarely satisfied. To address this issue, the Bivariate Poisson Generalized Inverse Gaussian Regression (BPGIGR) model was developed by combining the Poisson distribution with the Generalized Inverse Gaussian (GIG) distribution to overcome overdisperion in two correlated response variables. This study aims to obtain parameter estimates and corresponding test statistics for the BPGIGR model by incorporating two exposure variables to account to account for differences in population size across analytical units. Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method with the Berndt-Hall-Hall-Hausman (BHHH) algorithm. The BPGIGR model is implemented on maternal and neonatal deaths in Kalimantan in 2024 to identify the significant contributing factors. The results indicate that the model is influenced by the percentages of active posyandu, low birth weight, complete neonatal visits, exclusive breasfeeding, K4 visits, and pregnant women receiving iron tablets with an AICc of 9.719,092.
References
1. Hilbe JM. Modeling Count Data. 2014.
2. Ghitany ME, Karlis D. An EM Algorithm for Multivariate Mixed Poisson. Applied Mathematical Sciences. 2012;6(137):6843–6856.
3. Widiari SM. Penaksiran Parameter dan Statistik Uji dalam Model Regresi Poisson Inverse Gaussian (PIG). 2016.
4. Wijaya SU. Pendugaan Parameter dan Pengujian Hipotesis pada Bivariate Poisson Inverse Gaussian Regression. 2017.
5. Barndorff-Nielsen OE, Blaesild P, Seshadri V. Multivariate distributions with generalized inverse gaussian marginals, and associated poisson mixtures. Canadian Journal of Statistics. 1992;20(2):109–120. doi:10.2307/3315462
6. Jorgensen B. Statistical Properties of the Generalized Inverse Gaussian Distribution. 1982.
7. Nugraha J. Metode Maksimum Likelihood Dalam Model Pemilihan Diskrit. 2017.
8. Tzougas G, Makariou D. The multivariate Poisson–Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters. Risk Management and Insurance Review. 2022;1–17. doi:10.1111/rmir.12224
9. Auliarahmi A, Purhadi P, Andari S. Parameter estimation and hypothesis testing of bivariate poisson generalized inverse gaussian regression model. AIP Conference Proceedings. 2025 Jul 15;3301(1):050005. doi: 10.1063/5.0263244
10. Bozdogan H. Akaike's Information Criterion and Recent Developments in Information Complexity. Journal of Mathematical Psychology. 2000;44:62–91. doi:10.1006/jmps.1999.1277
11. Dinas Kesehatan Provinsi Kalimantan Barat. Profil Kesehatan Provinsi Kalimantan Barat Tahun 2024. 2025.
12. Dinas Kesehatan Provinsi Kalimantan Timur. Profil Kesehatan Provinsi Kalimantan Timur Tahun 2024. 2025.
13. Dinas Kesehatan Provinsi Kalimantan Tengah. Profil Kesehatan Provinsi Kalimantan Tengah Tahun 2024. 2025.
14. Dinas Kesehatan Provinsi Kalimantan Utara. Profil Kesehatan Provinsi Kalimantan Utara Tahun 2024. 2025.
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