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Abstract
The number of infant mortality cases is data in the form of counts which is modeled by Poisson regression. There is an assumption that needs to be met, namely equidispersion. Equidispersion is a condition in which the mean and variance of the variables are the same, but in practice this assumption is often not met. There are two possible events, namely overdispersion and underdispersion. The Generalized Poisson Regression (GPR) model is one solution to solve this problem. In estimating the GPR parameter, the Maximum Likelihood Estimation (MLE) method is used, but the derivation of the log-likelihood function does not always produce explicit results, so the Newton-Raphson iteration method is used. Poisson regression analysis conducted on the number of infant mortality cases in West Java showed that the model had overdispersion as seen from the value of the dispersion parameter which was more than zero, so the GPR model was used. Parameter significance test was carried out on three factors, namely the poverty gap index , the percentage of low birth weight infants , and the percentage of exclusive breastfeeding for infants the results obtained that all factors affected the number of infant mortality cases in West Java.
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References
- Rashwan, N. A., & Kamel, M. M. (2011). Using generalized Poisson log linear regression models in analyzing two-way contingency tables. Applied Mathematical Sciences, 5(5), 213-222.
- Purhadi, Sutikno, Berliana, S. M., & Setiawan, D. I. (2021). Geographically weighted bivariate generalized Poisson regression: application to infant and maternal mortality data. Letters in Spatial and Resource Sciences, 14, 79-99.
- Gao, G., Wang, H., & Wüthrich, M. V. (2022). Boosting Poisson regression models with telematics car driving data. Machine Learning, 1-30.
- Famoye, F., Wulu, J. T., & Singh, K. P. (2004). On the generalized Poisson regression model with an application to accident data. Journal of Data Science, 2(3), 287-295.
- Lukman, A. F., Adewuyi, E., Månsson, K., & Kibria, B. M. (2021). A new estimator for the multicollinear Poisson regression model: simulation and application. Scientific Reports, 11(1), 1-11.
- Amin, M., Akram, M. N., & Amanullah, M. (2022). On the James-Stein estimator for the Poisson regression model. Communications in Statistics-Simulation and Computation, 51(10), 5596-5608.
- Motta, V. (2019). Estimating Poisson pseudo-maximum-likelihood rather than log-linear model of a log-transformed dependent variable. RAUSP Management Journal, 54, 508-518.
- Ogallo, W., Wanyana, I., Tadesse, G. A., Wanjiru, C., Akinwande, V., Kabwama, S., ... & Walcott-Bryant, A. (2023). Quantifying the impact of COVID-19 on essential health services: a comparison of interrupted time series analysis using Prophet and Poisson regression models. Journal of the American Medical Informatics Association, 30(4), 634-642.
- Zubedi, F., Aliu, M. A., Rahim, Y., & Oroh, F. A. (2021). Analisis Faktor-Faktor Yang Mempengaruhi Stunting Pada Balita Di Kota Gorontalo Menggunakan Regresi Binomial Negatif. JAMBURA Journal of probability and statistics, 2(1), 48-55.
- Aulele, S. N., Lewaherilla, N., & Matdoan, M. Y. (2022). Pendekatan Geographically Weighted Poisson Regression Dengan Pembobot Fungsi Kernel Gauss Untuk Menganalisis Jumlah Kematian Bayi Di Provinsi Maluku. Jurnal Aplikasi Statistika & Komputasi Statistik, 14(2), 67-80.
- Jao, N., Islamiyati, A., & Sunusi, N. (2022). Pemodelan Regresi Nonparametrik Spline Poisson pada Tingkat Kematian Bayi di Sulawesi Selatan. Estimasi: Journal of Statistics and Its Application, 14-22.
- Majore, M., Salaki, D. T., & Prang, J. D. (2020). Penerapan Regresi Binomial Negatif Dalam Mengatasi Overdispersi Regresi Poisson Pada Kasus Jumlah Kematian Ibu. d'CARTESIAN: Jurnal Matematika dan Aplikasi, 133-139.
- Aminullah, A. A. H., & Purhadi, P. (2020). Pemodelan untuk Jumlah Kasus Kematian Bayi dan Ibu di Jawa Timur Menggunakan Bivariate Generalized Poisson Regression. Jurnal Sains dan Seni ITS, 8(2), D72-D78.
- Setyawan, Y., Suryowati, K., & Octaviana, D. (2022). Application of Negative Binomial Regression Analysis to Overcome the Overdispersion of Poisson Regression Model for Malnutrition Cases in Indonesia. Parameter: Journal of Statistics, 2(2), 1-9.
- Wasilaine, T. L., Talakua, M. W., & Lesnussa, Y. A. (2014). Model Regresi Ridge Untuk Mengatasi Model Regresi Linier Berganda Yang Mengandung Multikolinieritas. BAREKENG: Jurnal Ilmu Matematika dan Terapan, 8(1), 31-37.
- Herawati, N., Nisa, K., Setiawan, E., Nusyirwan, N., & Tiryono, T. (2018). Regularized multiple regression methods to deal with severe multicollinearity. International Journal of Statistics and Applications, 8(4), 167-172.
- Winkelmann, R. (2008). Econometric analysis of count data. Springer Science & Business Media.
- Sundari, I. (2012). Regresi poisson dan penerapannya untuk memodelkan hubungan usia dan perilaku merokok terhadap jumlah kematian penderita penyakit kanker paru-paru. Jurnal Matematika UNAND, 1(1), 71-76.
- Bauer, T., Göhlmann, S., & Sinning, M. (2007). Gender differences in smoking behavior. Health Economics, 16(9), 895-909.
- Cahyandari, R. (2014). Pengujian Overdispersi pada Model Regresi Poisson (Studi Kasus: Laka Lantas Mobil Penumpang di Provinsi Jawa Barat). Statistika, 14(2), 69-76.
- Saputro, D. R. S., Susanti, A., & Pratiwi, N. B. I. (2021). The handling of overdispersion on Poisson regression model with the generalized Poisson regression model. In AIP Conference Proceedings (Vol. 2326, No. 1, p. 020026). AIP Publishing LLC.
- Ruliana, R., Hendikawati, P., & Agoestanto, A. (2016). Pemodelan Generalized Poisson Regression (GPR) untuk Mengatasi Pelanggaran Equidispersi pada Regresi Poisson Kasus Campak di Kota Semarang Tahun 2013. Unnes Journal of Mathematics, 5(1), 39-46.
- Sandjadirja, L. M., Aidi, M. N., & Rizki, A. (2019). Penanganan Overdispersi pada Regresi Poisson dengan Regresi Binomial Negatif pada Kasus Kemiskinan di Indonesia. Xplore: Journal of Statistics, 8(1).
- Schober, P., & Vetter, T. R. (2021). Count data in medical research: Poisson regression and negative binomial regression. Anesthesia & Analgesia, 132(5), 1378-1379.
- Cantoni, E., & Zedini, A. (2011). A robust version of the hurdlemodel. Journal of Statistical Planning and Inference, 141(3), 1214-1223.
- Feng, C. X. (2021). A comparison of zero-inflated and hurdle models for modeling zero-inflated count data. Journal of statistical distributions and applications, 8(1), 8.
- D’Este, M., Ganga, A., Elia, M., Lovreglio, R., Giannico, V., Spano, G., ... & Sanesi, G. (2020). Modeling fire ignition probability and frequency using Hurdle models: A cross-regional study in Southern Europe. Ecological Processes, 9, 1-14.