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Abstract

Infant mortality is an indicator to determine the degree of public health. Infant mortality is death that occurs in the period from birth to before the age of one. The high rate of infant mortality indicates that the quality of public health services is not optimal. The number of infant deaths is an example of count data that follows a Poisson distribution, so it can be analyzed using Poisson Regression. The assumption that must be met when using this method is the equidispersion or variance of the response variable is equal to mean. However, this condition rarely occurs because usually the counted data has a greater variance than the mean or it is called overdispersion. One way to solve this problem is to use the Negative Binomial Regression method. The data used in this study is the case of infant mortality in the city of Padang. First, we model the data using Poisson Regression, then we check the assumption, if there is overdispersion, we handle it by modeling the data with Negative Binomial Regression. The results showed that the equidispersion assumption could not be met so that the data was modeled with Negative Binomial Regression.

Keywords

Overdispersion poisson regression negative binomials

Article Details

How to Cite
1.
Fitri F, Mudia Sari F, Fiskia Gamayanti N, Tri Utami I. Infant Mortality Case: An Application of Negative Binomial Regression in order to Overcome Overdispersion in Poisson Regression. EKSAKTA [Internet]. 2021Sep.30 [cited 2024Nov.21];22(3):200-1. Available from: https://eksakta.ppj.unp.ac.id/index.php/eksakta/article/view/272

References

  1. Sartorius, B. K., & Sartorius, K. (2014). Global infant mortality trends and attributable determinants–an ecological study using data from 192 countries for the period 1990–2011. Population Health Metrics, 12(1), 1-15.
  2. Reidpath, D. D., & Allotey, P. (2003). Infant mortality rate as an indicator of population health. Journal of Epidemiology & Community Health, 57(5), 344-346.
  3. Simeoni, S., Frova, L., & De Curtis, M. (2019). Inequalities in infant mortality in Italy. Italian journal of pediatrics, 45(1), 1-7.
  4. Gonzalez, R. M., & Gilleskie, D. (2017). Infant mortality rate as a measure of a country’s health: a robust method to improve reliability and comparability. Demography, 54(2), 701-720.
  5. Kiross, G. T., Chojenta, C., Barker, D., & Loxton, D. (2020). The effects of health expenditure on infant mortality in sub-Saharan Africa: evidence from panel data analysis. Health economics review, 10(1), 1-9.
  6. Vijay, J., & Patel, K. K. (2020). Risk factors of infant mortality in Bangladesh. Clinical Epidemiology and Global Health, 8(1), 211-214.
  7. Rodriguez, A., Furquim, F., & DesJardins, S. L. (2018). Categorical and limited dependent variable modeling in higher education. In Higher education: Handbook of theory and research (pp. 295-370). Springer, Cham.
  8. Smith, E. K., Lacy, M. G., & Mayer, A. (2019). Performance simulations for categorical mediation: Analyzing khb estimates of mediation in ordinal regression models. The Stata Journal, 19(4), 913-930.
  9. Azen, R., & Walker, C. M. (2021). Categorical data analysis for the behavioral and social sciences. Routledge.
  10. Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to linear regression analysis. John Wiley & Sons.
  11. Hayes, A. F., & Montoya, A. K. (2017). A tutorial on testing, visualizing, and probing an interaction involving a multicategorical variable in linear regression analysis. Communication Methods and Measures, 11(1), 1-30.
  12. Iqbal, W., Tang, Y. M., Chau, K. Y., Irfan, M., & Mohsin, M. (2021). Nexus between air pollution and NCOV-2019 in China: application of negative binomial regression analysis. Process Safety and Environmental Protection, 150, 557-565.
  13. Ardiles, L. G., Tadano, Y. S., Costa, S., Urbina, V., Capucim, M. N., da Silva, I., ... & Martins, L. D. (2018). Negative Binomial regression model for analysis of the relationship between hospitalization and air pollution. Atmospheric Pollution Research, 9(2), 333-341.
  14. Islam, M. A., Kabir, M. R., & Talukder, A. (2020). Triggering factors associated with the utilization of antenatal care visits in Bangladesh: An application of negative binomial regression model. Clinical Epidemiology and Global Health, 8(4), 1297-1301.
  15. Cho, S., Lee, H., Peguero, A. A., & Park, S. M. (2019). Social-ecological correlates of cyberbullying victimization and perpetration among African American youth: Negative binomial and zero-inflated negative binomial analyses. Children and Youth Services Review, 101, 50-60.
  16. Green, J. A. (2021). Too many zeros and/or highly skewed? A tutorial on modelling health behaviour as count data with Poisson and negative binomial regression. Health Psychology and Behavioral Medicine, 9(1), 436-455.
  17. Lee, S. C. (2020). Delta boosting implementation of negative binomial regression in actuarial pricing. Risks, 8(1), 19.
  18. Utoyo, M. I., & Chamidah, N. (2019, March). Modeling of Maternal Mortality and Infant Mortality Cases in East Kalimantan using Poisson Regression Approach Based on Local Linear Estimator. In IOP Conference Series: Earth and Environmental Science (Vol. 243, No. 1, p. 012023). IOP Publishing.1315/243/1/012023.
  19. Dutta, U. P., Gupta, H., Sarkar, A. K., & Sengupta, P. P. (2020). Some determinants of infant mortality rate in SAARC countries: an empirical assessment through panel data analysis. Child Indicators Research, 13, 2093-2116.
  20. Singh, M. P., Bharti, A., Singh, N. K., & Singh, R. D. (2018). Spatial Scan Study for Mortality Under Age 5 year in the EAG States and Assam.
  21. Hancock, J. T., & Khoshgoftaar, T. M. (2020). Survey on categorical data for neural networks. Journal of Big Data, 7(1), 1-41.
  22. Kabir, R. H., & Lee, K. (2020, July). Receding-horizon ergodic exploration planning using optimal transport theory. In 2020 American Control Conference (ACC) (pp. 1447-1452). IEEE.
  23. Braccini, M., Denham, A., O'Neill, M. F., & Lai, E. (2021). Spatial and temporal patterns in catch rates from multispecies shark fisheries in Western Australia. Ocean & Coastal Management, 213, 105883.
  24. Jestel, C., Surmann, H., Stenzel, J., Urbann, O., & Brehler, M. (2021, February). Obtaining Robust Control and Navigation Policies for Multi-robot Navigation via Deep Reinforcement Learning. In 2021 7th International Conference on Automation, Robotics and Applications (ICARA) (pp. 48-54). IEEE.
  25. Loeb, S., Dynarski, S., McFarland, D., Morris, P., Reardon, S., & Reber, S. (2017). Descriptive Analysis in Education: A Guide for Researchers. NCEE 2017-4023. National Center for Education Evaluation and Regional Assistance.
  26. Hastie, T. J., & Pregibon, D. (2017). Generalized linear models. In Statistical models in S (pp. 195-247). Routledge.
  27. Utami, I. U., Setiawan, I., & Daniaty, D. (2021). Modelling the number of HIV/AIDS in Central Sulawesi. In Journal of Physics: Conference Series (Vol. 1763, No. 1, p. 012046). IOP Publishing.
  28. Pratama, W. (2015). Pemetaan dan pemodelan jumlah kasus penyakit tuberculosis (TBC) di provinsi Jawa Barat dengan pendekatan geographically weighted negative binomial regression (GWNBR) (Doctoral dissertation, Institut Technology Sepuluh Nopember).
  29. Martin, B. D., Witten, D., & Willis, A. D. (2020). Modeling microbial abundances and dysbiosis with beta-binomial regression. The annals of applied statistics, 14(1), 94.