Simulation Study of Bayesian Zero Inflated Poisson Regression

Candra Rezzing Weni Utomo, Achmad Efendi, Ni Wayan S. Wardhani

Abstract


Bayesian merupakan salah satu metode estimasi parameter yang dapat diaplikasikan pada ukuran sampel yang kecil. Zero Inflated Poisson merupakan salah satu metode untuk menganalisis data Poisson yang mengalami overdispersion. Tujuan dari penelitian ini adalah untuk mengevaluasi kinerja analisis Zero Inflated Poisson Regression menggunakan Bayesian. Data yang digunakan adalah jumlah kasus campak di Jawa Timur. Campak merupakan penyakit menular yang berpotensi menjadi wabah di berbagai daerah, termasuk Jawa Timur. Terdapat empat variabel prediktor yang digunakan yaitu Jumlah Penduduk (X1), Persentase Vaksinasi (X2), Persentase Penduduk Miskin (X3), dan Persentase Sanitasi Layak (X4), serta satu variabel respon yaitu Jumlah Kasus Campak. Hasil penelitian ini menunjukkan bahwa estimasi model Zero Inflated Poisson (ZIP) menggunakan Bayesian lebih baik dibandingkan estimasi model Zero Inflated Poisson (ZIP) menggunakan MLE. Hal ini dikarenakan data yang digunakan dalam penelitian memiliki sampel yang kecil sehingga estimasi MLE cenderung kurang baik digunakan dalam estimasi parameter. Pemilihan model terbaik dilakukan dengan menggunakan metode Deviance Information Criteria (DIC). Model terbaik ditunjukkan dengan nilai DIC terkecil pada ukuran sampel 100 dan proporsi nol 0,8.


Keywords


Bayesian; Measles; MLE; Simulation Study;ZIP

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References


[1] Cahyandari, “Pengujian Overdispersi pada Model Regresi Poisson,” EJournal Unisba, vol. Vol. 14 No.2, pp. 69–76, Nov. 2014.

[2] D. Lambert, “Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing,” Technometrics, vol. 34, no. 1, p. 1, Feb. 1992, doi: 10.2307/1269547.

[3] D. A. Pradana and T. E. Lestari, “Estimasi Parameter Regresi Zero-Inflated Negative Binomial Dengan Metode Algoritma Expectation Maximization (EM) (Studi Kasus: Penyakit Difteri di Jawa Barat Tahun 2016),” JKMA, vol. 1, no. 1, p. 18, Jun. 2020, doi: 10.17977/um055v1i12020p18-26.

[4] J. Albert, Bayesian Computation with R. New York, NY: Springer New York, 2009. doi: 10.1007/978-0-387-92298-0.

[5] S. E. Fienberg and A. Rinaldo, “Maximum likelihood estimation in log-linear models,” Ann. Statist., vol. 40, no. 2, Apr. 2012, doi: 10.1214/12-AOS986.

[6] J. S. T. Wong, J. J. Forster, and P. W. F. Smith, “Bayesian mortality forecasting with overdispersion,” Insurance: Mathematics and Economics, vol. 83, pp. 206–221, Nov. 2018, doi: 10.1016/j.insmatheco.2017.09.023.

[7] L. Lu, Y. Fu, P. Chu, and X. Zhang, “A Bayesian Analysis of Zero-Inflated Count Data: An Application to Youth Fitness Survey,” in 2014 Tenth International Conference on Computational Intelligence and Security, Kunming, Yunnan, China: IEEE, Nov. 2014, pp. 699–703. doi: 10.1109/CIS.2014.125.

[8] R. Van De Schoot, D. Kaplan, J. Denissen, J. B. Asendorpf, F. J. Neyer, and M. A. G. Van Aken, “A Gentle Introduction to Bayesian Analysis: Applications to Developmental Research,” Child Development, vol. 85, no. 3, pp. 842–860, May 2014, doi: 10.1111/cdev.12169.

[9] A. Mahfiyah and A. Agoestanto, “Pemodelan multilevel survival dengan Bayesian Markov Chain Monte Carlo pada penyakit DBD,” journal UNNES, vol. Vol 10 No. 2, Desember 2021.

[10] C. X. Feng, “A comparison of zero-inflated and hurdle models for modeling zero-inflated count data,” Feng Journal of Statistical Distributions and Applications, vol. Vol. 8 No. 8, 2021.

[11] H. He, H. Zhang, P. Ye, and W. Tang, “A test of inflated zeros for Poisson regression models,” Stat Methods Med Res, vol. 28, no. 4, pp. 1157–1169, Apr. 2019, doi: 10.1177/0962280217749991.

[12] E. D. Ginting and Sutarman, “Penaksiran Parameter Regresi Poisson Dengan Maximum Likelihood,” Indonesian Journal of Multidiciplinary, vol. Vol 1 No. 6, 2023.

[13] J. M. Hilbe, Modeling Count Data. Cambridge University Press, 2014.

[14] V. Landsman, D. Landsman, C. S. Li, and H. Bang, “Overdispersion models for correlated multinomial data: Applications to blinding assessment,” Statistics in Medicine, vol. 38, no. 25, pp. 4963–4976, Nov. 2019, doi: 10.1002/sim.8344.

[15] J. R. Wilson, “Chi-Square Tests for Overdispersion with Multiparameter Estimates,” Applied Statistics, vol. 38, no. 3, p. 441, 1989, doi: 10.2307/2347732.

[16] J. Haslett, A. C. Parnell, J. Hinde, and R. De Andrade Moral, “Modelling Excess Zeros in Count Data: A New Perspective on Modelling Approaches,” Int Statistical Rev, vol. 90, no. 2, pp. 216–236, Aug. 2022, doi: 10.1111/insr.12479.

[17] F. Famoye and J. S. Preisser, “Marginalized zero-inflated generalized Poisson regression,” Journal of Applied Statistics, vol. 45, no. 7, pp. 1247–1259, May 2018, doi: 10.1080/02664763.2017.1364717.

[18] I. Ntzoufras, A. Katsis, and D. Karlis, “Bayesian Assessment of the Distribution of Insurance Claim Counts Using Reversible Jump MCMC,” North American Actuarial Journal, vol. 9, no. 3, pp. 90–108, Jul. 2005, doi: 10.1080/10920277.2005.10596213.

[19] A. C. Delima, F. Yanuar, and H. Yozza, “Penerapan Metode Regresi Logistik Ordinal Bayesian untuk Menentukan Tingkat Partisipasi Politik Masyarakat Kota Padang,” Jurnal Matematika UNAND, vol. Vol 8 No. 3, pp. 1–8, 2019.

[20] L. Naldi and S. Cazzaniga, “Research Techniques Made Simple: Latent Class Analysis,” Journal of Investigative Dermatology, vol. 140, no. 9, pp. 1676-1680.e1, Sep. 2020, doi: 10.1016/j.jid.2020.05.079.




DOI: https://doi.org/10.18860/cauchy.v10i1.30207

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