DOI : https://doi.org/10.18517/ijaseit.11.6.14217

Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Model and Its Application

- Purhadi (1), - Ermawati (2), Rossy Noviyana (3), - Sutikno (4)
(1) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
(2) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
(3) Department of Statistics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
(4) Department of Mathematics, Universitas Islam Negeri Alauddin Makassar, 92118, Indonesia
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How to cite (IJASEIT) :
Purhadi, -, et al. “Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Model and Its Application”. International Journal on Advanced Science, Engineering and Information Technology, vol. 11, no. 6, Dec. 2021, pp. 2407-15, doi:10.18517/ijaseit.11.6.14217.
Citation Format :
This study developed a Bivariate Zero-Inflated Poisson Inverse Gaussian Regression (BZIPIGR) model to presents the form of BZIPIGR parameter estimation and modeling of the number of HIV and AIDS cases in each sub-district in Trenggalek and Ponorogo regencies to determine the factors that have a significant effect. This model can be used on data that have overdispersion cases caused by extra zeros in the response variables. The parameter estimation of the BZIPIGR model uses the Maximum Likelihood Estimation (MLE). The first derivative of the BZIPIGR model has obtained not closed form, therefor it has continued with the Berndt Hall Hall Hausman (BHHH) iteration to obtain the maximum likelihood estimators, while the hypothesis testing of the BZIPIGR model is derived using Maximum Likelihood Ratio Test (MLRT) approach. Based on the AICc value obtained, the BZIPIGR model is a feasible model to be applied to data on the number of HIV and AIDS cases in Trenggalek and Ponorogo Districts, East Java Province. The variable that had a significant effect on the increase in the number of HIV and AIDS cases was the percentage of the population with low education (SMA). The variables that had a significant effect on reducing the number of HIV and AIDS cases were the percentage of the population aged 25-29 years, the percentage of reproductive-age couples using condoms, the percentage of health educations activities about HIV and AIDS, and the percentage of community health insurance (Jamkesmas).

R. Fitriani, L. N. Chrisdiana, and A. Efendi, “Simulation on the Zero Inflated Negative Binomial (ZINB) to Model Overdispersed, Poisson Distributed Data,” IOP Conf. Ser. Mater. Sci. Eng., vol. 546, no. 5, 2019, doi: 10.1088/1757-899X/546/5/052025.

R. D. Kusuma and Y. Purwono, “Zero-Inflated Poisson Regression Analysis On Frequency Of Health Insurance Claim PT. XYZ,” in Proceedings of the 12th International Conference on Business and Management Research (ICBMR 2018), 2019, vol. 72, no. Icbmr 2018, pp. 321-325, doi: 10.2991/icbmr-18.2019.52.

D. Karlis and E. Xekalaki, “Mixed Poisson distributions,” Int. Stat. Rev., vol. 73, no. 1, pp. 35-58, 2005, doi: 10.1111/j.1751-5823.2005.tb00250.x.

Purhadi, Sutikno, S. M. Berliana, and D. I. Setiawan, “Geographically weighted bivariate generalized Poisson regression: application to infant and maternal mortality data,” Lett. Spat. Resour. Sci., vol. 14, no. 1, pp. 79-99, 2021, doi: 10.1007/s12076-021-00266-5.

L. Amaliana, U. Sa’Adah, and N. W. Surya Wardhani, “Modeling Tetanus Neonatorum case using the regression of negative binomial and zero-inflated negative binomial,” J. Phys. Conf. Ser., vol. 943, no. 1, 2018, doi: 10.1088/1742-6596/943/1/012051.

S. Mardalena, Purhadi, J. T. D. Purnomo, and D. D. Prastyo, “Bivariate Poisson Inverse Gaussian Regression Model with Exposure Variable: Infant and Maternal Death Case Study,” J. Phys. Conf. Ser., vol. 1752, no. 1, 2021, doi: 10.1088/1742-6596/1752/1/012016.

X. F. Huang, G. L. Tian, C. Zhang, and X. Jiang, “Type I multivariate zero-inflated generalized Poisson distribution with applications,” Stat. Interface, vol. 10, no. 2, pp. 291-311, 2017, doi: 10.4310/SII.2017.v10.n2.a12.

M. S. Nur, Purhadi, and A. Choiruddin, “Parameter Estimation and Hypothesis Testing of Geographically Weighted Bivariate Zero Inflated Poisson Inverse Gaussian Regression Models,” IOP Conf. Ser. Mater. Sci. Eng., vol. 1115, no. 1, p. 012043, 2021, doi: 10.1088/1757-899x/1115/1/012043.

J. M. Hilbe, Cambridge Books Online, vol. 48, no. 04. 2010.

Q. Aini, Purhadi, and Irhamah, “Bivariate zero inflated generalized Poisson regression model in the number of pregnant maternal mortality and the number of postpartum maternal mortality in the Central Java Province in 2017,” J. Phys. Conf. Ser., vol. 1511, no. 1, 2020, doi: 10.1088/1742-6596/1511/1/012055.

Dinas kesehatan Provinsi Jawa Timur, Profil Kesehatan Provinsi Jawa Timur Tahun 2018. Jawa Timur, Indonesia: Dinas Kesehatan Provinsi Jawa Timur, 2019.

Kementerian Kesehatan Republik Indonesia, “Infodatin (Situasi HIV dan AIDS di Indonesia),” Pusdatin, 2020, [Online]. Available: https://pusdatin.kemkes.go.id/resources/download/pusdatin/infodatin/infodatin-2020-HIV.pdf.

I. Purnamasari and I. N. Latra, “Parameter Estimation and Statistical Test in Modeling Geographically Weighted Poisson Inverse Gaussian Regression,” in International Conference Research:Implementation and Education of Mathematics and Science, 2016, no. May, pp. 16-17.

S. Mardalena, P. Purhadi, J. D. T. Purnomo, and D. D. Prastyo, “Parameter Estimation and Hypothesis Testing of Multivariate Poisson Inverse Gaussian Regression,” Symmetry (Basel)., vol. 12, no. 10, p. 1738, Oct. 2020, doi: 10.3390/sym12101738.

J. Amalia, Purhadi, and B. W. Otok, “Application of geographically weighted bivariate poisson inverse Gaussian regression,” AIP Conf. Proc., vol. 2268, no. September 2020, doi: 10.1063/5.0017393.

J. Pangulimang, “Parameter Estimation and Hypothesis Testing Geographically Weighted Bivariate Zero-Inflated Poisson,” in International Conference Research:Implementation and Education of Mathematics and Science, 2016, no. May, pp. 16-17, [Online]. Available: http://seminar.uny.ac.id/icriems/sites/seminar.uny.ac.id.icriems/files/prosiding/M-12.pdf.

S. M. Berliana, Purhadi, Sutikno, and S. P. Rahayu, “Parameter estimation and hypothesis testing of geographically weighted multivariate generalized poisson regression,” Mathematics, vol. 8, no. 9, pp. 1-14, 2020, doi: 10.3390/math8091523.

J. N. Goní§alves and W. Barreto-Souza, “Flexible regression models for counts with high-inflation of zeros,” Metron, vol. 78, no. 1, pp. 71-95, 2020, doi: 10.1007/s40300-020-00163-9.

H. Cho, T. Porras, D. Baik, M. Beauchemin, and R. Schnall, “Understanding the predisposing, enabling, and reinforcing factors influencing the use of a mobile-based HIV management app: A real-world usability evaluation,” Int. J. Med. Inform., vol. 117, pp. 88-95, 2018, doi: 10.1016/j.ijmedinf.2018.06.007.

S. U. Wijaya, Pendugaan Parameter dan Pengujian Hipotesis pada Bivariate Poisson Inverse Gaussian Regression (Studi Kasus: Jumlah Kasus Baru HIV dan AIDS di Kabupaten Trenggalek dan Ponorogo Tahun 2012). Indonesia: Repository ITS, 2017.

S. M. Berliana, Purhadi, Sutikno, and S. P. Rahayu, “Multivariate generalized Poisson regression model with exposure and correlation as a function of covariates: Parameter estimation and hypothesis testing,” AIP Conf. Proc., vol. 2192, 2019, doi: 10.1063/1.5139171.

N. Shrestha, “Detecting Multicollinearity in Regression Analysis,” Am. J. Appl. Math. Stat., vol. 8, no. 2, pp. 39-42, 2020, doi: 10.12691/ajams-8-2-1.

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