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Abstract

Binomial negative regression is able to handle poisson regression problem with underdispersion assumption. When the data has hierarchy and level that need to be calculated, regression is no longer appropriate to solve this problem, therefore binomial negative regression is used. To solve multilevel binomial negative regression modeling, several steps need to be fulfill: poisson assumption test and underdispersion assumption test, parameter estimation with expectation-maximization algorithm, variance components estimation, feasibility test with likelihood ratio test, significance parameter test with wald test and determining the best model. This research modeled the numbers of neonatal death in district as cluster 1 and small public health center as cluster 2, in the correlation with the number of visit on trimester 1 and 3, number of pregnant mother who have Tetanus Diphtheria vaccination, assumed number of neonatal babies with complication disease, numbers of babies who got Hepatitis B vaccination less than 24 hour, numbers of babies who got BCG vaccination and also number of visit neonatal 1 and 3.  The result shows that number of neonatal death is only affected by number of babies who had Hepatitis B vaccination less than 24 hour

Keywords

Multilevel Modeling Underdispersion

Article Details

How to Cite
1.
Sormin C, Rarasati N, Gusmanely Z, Kashefi H. Multilevel Modeling on Underdispersion Data. EKSAKTA [Internet]. 2023Sep.30 [cited 2024Nov.21];23(03):409-15. Available from: https://eksakta.ppj.unp.ac.id/index.php/eksakta/article/view/297

References

  1. Sormin, C. (2013). Aplikasi Regresi Poisson pada Faktor-Faktor yang Mempengaruhi Banyaknya Pasien Diabetes Mellitus. Skripsi. Tidak diterbitkan. Fakultas Matematika dan Ilmu Pengetahuan Alam. Universitas Negeri Yogyakarta: Yogyakarta.
  2. Dobson, A. J., & Barnett, A. (2008). An Introduction to Generalized Linear Models. CRC press. Boca Raton.
  3. Inan G & Das K. (2017). A Score Test for Testing a Marginalized Zero-Inflated Poisson Regression Model Against a Marginalized Zero-Inflated Negative Binomial Regression. Journal of Agricultural Biological and Environmental Statistics, 23, 113-128.
  4. Almasi, A, dkk. (2015). Multilevel zero-inflated Generalized Poisson regression modelling for dispersed correlated count data. Statistical Methodology, 30, 1-14.
  5. Ismail, N & Jemain, A. A. (2007). Handling overdispersion with Negative Binomial and Generalized Poisson Regression Models. Casualty Actuarial Society Forum, 103-158.
  6. Febritasari P, Wardhani NWS, & Sa’adah U. (2019). Generalized Linier Autoregressive Moving Average (GLARMA) Negative Binomial Regression Models with Metropolis Hasting Algorithm. IOP Conf. Series: Materials Science and Engineering, 546, 1-6.
  7. Hafemeister C & Satija R. (2019). Normalization and Variance Stabilization of Single-cell RNA-seq data using regularized Negative Binomial Regression. Genome Biology, 20, 296-311.
  8. Dadaneh S.Z, Zhou M, & Qian X. (2018). Bayesian Negative Binomial Regression for Differential Expression with Confounding Factors. Bioinformatics, 35, 2346-2359.
  9. Gomes MJTL, Cunto F, & Dilva AR. (2017). Geographically Weighted Negative Binomial Regression Applied to Zonal level safety performance models. Accident Analysis & Prevention, 106, 254-261.
  10. Najaf P, Duddu VR & Pulugurtha SS. (2017). Predictability and interpretability of hybrid link-level crash frequency models for urban arterial compared to cluster-based and general negative binomial regression models. International Journal of Injury Control and Safety Promotion, 25, 3-13.
  11. Hilbe, J. M. (2011). Negative Binomial Regression. Cambridge University Press. New York.
  12. Su Z, Hu H, Tigabu M, Wang G, Zeng A, & Guo F. (2019). Geographically Weighted Negative Binomial Regression Model Predicts Wildfire Occurrence in the Great Xing’an Mountains Better Than Negative Binomial Model. Forests, 10, 377-393.
  13. Zou Y, Ash JE, Park B & Lord D. (2017). Empirical Bayes Estimates of Finite Mixture of Negative Binomial Regression Model and its Application to Highway Safety. Journal of Applied Statistics, 45, 1652-1669.
  14. Sormin, C. (2017). Model Multilevel Regresi Poisson Tergeneralisasi Zero-Inflated. Tesis. Tidak diterbitkan. Fakultas Matematika dan Ilmu Pengetahuan Alam. Universitas Gadjah Mada: Yogyakarta.
  15. Zhao H, Pan Y, Wang C, Guo Y, Yao N, Wang H & Li B. (2021). The Effects of Metal Exposures on Charlson Comorbidity Index Using Zero-Inflated Negative Binomial Regression Model. NHANES 2011-2016 Biological trace element research, 199, 2104-2111.
  16. Sormin, C. & Gusmanely Z (2020). Generalized Poisson Regression Type-II at Jambi City Health Office. Eksakta Berkala Ilmiah Bidang MIPA, 21, 54-58.
  17. Moghimbeigi, A, dkk. (2008). Multilevel zero-inflated negative binomial regression modelling for over-dispersed count data with extra zeros. Journal of Applied Statistics, 35, 1193-1202.
  18. Oztig LI & Askin OE. (2020). Human Mobility and coronavirus disease 2019 (COVID-19): A Negative Binomial Regression Analysis. Public Health (London), 185, 364-367.
  19. Yee, Thomas W. (2020). The VGAM Package for Negative Binomial Regression. Australian & New Zealand journal of statistics, 62, 116-131.
  20. Tohari A, Chamidah N & Fatmawati. (2019). Modeling of HIV and AIDS in Indonesia Using Bivariate Negative Binomial Regression, IOP conference series. Materials Science and Engineering; 546, 52079.
  21. Kim J & Lee W. (2019). On testing the hidden heterogeneity in negative binomial regression models. Metrika, 82, 457-470.
  22. Weng J, Yang D, Qian T & Huang Z. (2018). Combining Zero-inflated Negative Binomial Regression with MLRT Techniques: An Approach to Evaluating Shipping Accident Casualties. Ocean Engineering, 166, 135-144.
  23. Ardiles, L.G. et. Al (2018). Negative Binomial Regression Model for Analysis of the Relationship Between Hospitalization and Air Pollution. Atmospheric Pollution Research, 9, 333-341.
  24. Liu C, Zhao M & Sharma A. (2018). Multivariate Random Parameters Zero-Inflated Negative Binomial Regression for Analyzing Urban Midblock Crashes. Analytic Methods in Accident Research, 17, 32-46.