The Robust Negative Binomial Regression Model on Under-five Mortality due to Pneumonia in the Province of East Java

Anggun Qur'ani (Mathematics Study Programme, Udayana University, Indonesia)
Chandra Sari Widyaningrum (Master of Mathematics Programme, Universitas Gadjah Mada, Indonesia)
Sa’adatur Rohimiyah (Department of Nursing, Poltekkes Kemenkes Surabaya, Indonesia)

JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI
Vol. 21 No. 1 (2024): SEPTEMBER 2024

Robust Negative Binomial regression model (RNBR) is a modelling method to overcome a problem if there are outliers and overdispersion in the data. Outliers are data points that are significantly different from other data. Outliers have a significant effect on modelling to the resulting model. Furthermore, overdispersion is indicated by the presence of too large values of Pearson statistics. In this study, the RNBR model was used to determine the factors of the toddler immune variable at post neonatal age that significantly influenced the number of under-five deaths caused by pneumonia in East Java Province. Based on the modelling obtained, it shows that the RNBR model provides more robust results in handling outlier and overdispersion problems. This can be seen from the AIC value of the RNBR model is smaller than the AIC of the Poisson regression model. In addition, and which are measures of the influence of outliers on the model, decreased from 1 for the Poisson regression model to around 0.42 for the RNBR model.