ZERO-INFLATED NEGATIVE BINOMIAL MODELING IN INFANT DEATH CASE DUE TO PNEUMONIA IN EAST JAVA PROVINCE

  • Cindy Cahyaning Astuti Information Technology of Education, Faculty of Psychology and Educational Sciences, University of Muhammadiyah Sidoarjo, Indonesia
  • Agnes Ona Bliti Puka Mathematics Education Department, Faculty of Teacher Training and Education, Larantuka Institute of Teacher Training and Technology, Indonesia
  • Akbar Wiguna Information Technology of Education, Faculty of Psychology and Educational Sciences, University of Muhammadiyah Sidoarjo, Indonesia
DOI: https://doi.org/10.30598/barekengvol17iss4pp1835-1844
Keywords: Pneumonia, ZINB, East Java, SDGs

Abstract

Pneumonia is an acute infectious disease of the respiratory tract and an infection caused by a virus, bacteria or fungus that attacks the lung tissue. Several cases of pneumonia have resulted in deaths that occurred in toddlers aged 12-59 months. Based on official health in profile data, East Java's health in 2021 has a zero number of deaths under five aged 12-59 months due to pneumonia. Modeling data with many response variables is zero and there is overdispersion can be done using Zero Inflated Negative Binomial (ZINB) regression. This study aims to model the number of infant deaths aged 12-59 months due to pneumonia in East Java Province based on seven factors that are considered to influence the number of deaths in infants due to pneumonia. From this model, it can be seen that the factors that significantly influence the death of infants aged 12-59 months due to pneumonia in East Java Province using Zero Inflated Negative Binomial (ZINB) regression. The results of testing the parameters of the ZINB regression model show that the predictor variables that have a partial significant effect on the negative binomial model in East Java are the percentage of infants who received complete basic immunization, the percentage of coverage of under-five health services, the percentage of under-five children with malnutrition, the percentage of LBW (low birth weight babies). Selection of the best model is obtained by using the Bayesian Information Criterion (BIC) of 101,587.

Downloads

Download data is not yet available.

References

J. Fox, Applied Regression Analysis and Generalized Linear Models, vol. 3rd Edition. Sage Publication, Inc, 2016.

H. Permadi and S. D. Maulidah, “Zero Inflated Poisson Regression Analysis on IMB Ownership in Sidoarjo Regency 2019,” in Journal of Physics: Conference Series, IOP Publishing Ltd, May 2021. doi: 10.1088/1742-6596/1872/1/012030.

H. Campbell, “The Consequences of Checking for Zero-Inflation and Overdispersion in The Analysis of Count Data,” Methods Ecol Evol, vol. 12, no. 4, pp. 665–680, Apr. 2021, doi: 10.1111/2041-210X.13559.

F. Famoye and J. S. Preisser, “Marginalized zero-inflated generalized Poisson regression,” J Appl Stat, vol. 45, no. 7, pp. 1247–1259, May 2018, doi: 10.1080/02664763.2017.1364717.

P. Saengthong, W. Bodhisuwan, and A. Thongteeraparp, “The Zero Inflated Negative Binomial Crack distribution: Some Properties and Parameter Estimation,” 2015. [Online]. Available: http://www.sjst.psu.ac.th

C. C. Astuti and A. D. Mulyanto, “Estimation Parameters And Modelling Zero Inflated Negative Binomial,” CAUCHY: Jurnal Matematika Murni dan Aplikasi, vol. 4, no. 3, pp. 115–119, Nov. 2016, doi: 10.18860/ca.v4i3.3656.

K. J. Hong and J. Kim, “Risk Factors Preventing Immediate Fall Detection: A Study Using Zero-Inflated Negative Binomial Regression,” Asian Nurs Res (Korean Soc Nurs Sci), vol. 15, no. 4, pp. 272–277, Oct. 2021, doi: 10.1016/j.anr.2021.09.001.

N. Achmad, M. R. F. Payu, and Y. Rahim, “Pemodelan Pneumonia Berat Menggunakan Regresi Zero Inflated Negative Binomial di Gorontalo,” Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi, vol. 10, no. 1, pp. 45–53, May 2022, doi: 10.34312/euler.v10i1.13990.

J. Kruppa and L. Hothorn, “A Comparison Study on Modeling of Clustered and Overdispersed Count Data for Multiple Comparisons,” Journal of Applied Statistics. Taylor and Francis Ltd., pp. 1–13, 2020. doi: 10.1080/02664763.2020.1788518.

Y. Tiara, M. N. Aidi, E. Erfiani, and R. Rachmawati, “Overdispersion Handling In Poisson Regression Model By Applying Negative Binomial Regression,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 17, no. 1, pp. 0417–0426, Apr. 2023, doi: 10.30598/barekengvol17iss1pp0417-0426.

J. Stachurski, A Primer in Econometric Theory. London, England: MIT Press, 2017.

T. Kyriazos and M. Poga, “Dealing with Multicollinearity in Factor Analysis: The Problem, Detections, and Solutions,” Open J Stat, vol. 13, no. 03, pp. 404–424, 2023, doi: 10.4236/ojs.2023.133020.

H. Zamani and N. Ismail, “Functional Form for the Zero Inflated Generalized Poisson Regression Model,” Commun Stat Theory Methods, vol. 43, no. 3, pp. 515–529, Feb. 2014, doi: 10.1080/03610926.2012.665553.

Y. Gençtürk and A. Yiğiter, “Modelling Claim Number Using a New Mixture Model: Negative Binomial Gamma Distribution,” J Stat Comput Simul, vol. 86, no. 10, pp. 1829–1839, Jul. 2016, doi: 10.1080/00949655.2015.1085987.

P. Roback and J. Legler, “Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R,” 2021.

Published
2023-12-18
How to Cite
[1]
C. Astuti, A. Puka, and A. Wiguna, “ZERO-INFLATED NEGATIVE BINOMIAL MODELING IN INFANT DEATH CASE DUE TO PNEUMONIA IN EAST JAVA PROVINCE”, BAREKENG: J. Math. & App., vol. 17, no. 4, pp. 1835-1844, Dec. 2023.
Issue
Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Section
Articles

Copyright (c) 2023 Cindy Cahyaning Astuti, Agnes Ona Bliti Puka, Akbar Wiguna

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Authors who publish with this Journal agree to the following terms:

  1. Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
  2. Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
  3. Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.