Multilevel Modeling on Underdispersion Data

Corry Sormin; Niken Rarasati; Gusmanely Z; Hamidreza  Kashefi

doi:10.24036/eksakta/vol23-iss03/297

EKSAKTA: Berkala Ilmiah Bidang MIPA

Open Access

Multilevel Modeling on Underdispersion Data

Corry Sormin ¹

, Niken Rarasati ¹

, Gusmanely Z ¹

, Hamidreza Kashefi ²

¹ Department of Mathematics, Faculty of Science and Technology (FST), Universitas Jambi, Jambi, Indonesia

² Department of Mathematics Education, Farhangian University, Tehran, Iran

Published 2023-09-30

Vol. 24 No. 03 (2023) PAGES 409-415

DOI 10.24036/eksakta/vol23-iss03/297

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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.Â The result shows that number of neonatal death is only affected by number of babies who had Hepatitis B vaccination less than 24 hour

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