ANALYTICAL APPROACH OF GENERALIZED LINEAR MODELS FOR HANDLING OVERDISPERSION IN POVERTY DATA OF INDONESIA

Abstrak

Poverty is one of the complex phenomena that occurs in Indonesia. Various socio-economic variables in Indonesia influence poverty, which we can mathematically model using the Generalized Linear Model (GLM) framework. In this study, we modeled data on the number of poor people per province in 2023 taken from the Badan Pusat Statistik of Indonesia website. The response variable in this study was initially assumed to exhibit equidispersion, where the variance equals the mean. However, the observed variance exceeded the mean, indicating overdispersion. Consequently, Negative Binomial Regression, an extension of the GLM that introduces an additional dispersion parameter, was applied to account for this overdispersion. This approach accommodates overdispersed count data by incorporating a gamma-distributed latent variable. The aim of this study is to determine the best model using Negative Binomial Regression in handling overdispersion in Indonesia's poverty data. This model was chosen for its robustness in capturing increased data variability, enabling the identification of factors that influence poverty. The results of this study offer a mathematically rigorous approach to better understand the underlying dynamics of poverty across provinces in Indonesia.