Modeling Geographically Weighted Negative Binomial Regression (GWNBR) on Stunting Incidence in Malang Regency: Bahasa Indonesia

Abstract

English

Discrete data on the response variable can be analyzed using poisson regression. The assumption of equidispersion in poisson regression must be fulfilled, but in practice there are many problems of overdispersion. The negative binomial regression model is used to overcome the problem of overdispersion, but this model is global while in some cases each location has different characteristics. Therefore, a method that considers the effects of spatial heterogeneity is needed. If the response variable is discrete data that is overdispersed and includes spatial effects, a model called Geographically Weighted Negative Binomial Regression (GWNBR) is developed. The GWNBR method can be applied in the health sector, such as in stunting. The prevalence of stunting in Malang Regency is still quite high, there is 25.7%. By conducting the GWNBR test, 385 models were obtained, one of them is Tulungrejo Village with factors influencing the incidence of stunting, namely access to permanent healthy latrines, access to posyandu, exclusive breastfeeding, population density and community empowerment. From three weights used, namely the Adaptive Gaussian Kernel, Adaptive Bisquare Kernel and Adaptive Tricube Kernel, the best model was obtained from the Adaptive Bisquare Kernel weighting with the smallest AIC is -211.3763.

Bahasa Indonesia

Data diskrit pada variabel respon dapat dianalisis menggunakan regresi poisson. Asumsi equidispersi dalam regresi poisson harus terpenuhi, namun dalam penerapannya banyak ditemui masalah overdispersi. Model regresi binomial negatif digunakan untuk mengatasi masalah overdispersi, namun model ini bersifat global sedangkan pada beberapa kasus masing-masing lokasi memiliki karakteristik yang berbeda-beda. Oleh karena itu diperlukan metode yang mempertimbangkan efek keheterogenan spasial. Apabila variabel respon berupa data diskrit yang mengalami overdispersi dan menyertakan efek spasialnya maka dilakukan pengembangan model yang disebut Geographically Weighted Negative Binomial Regression (GWNBR). Metode GWNBR dapat diterapkan di bidang kesehatan, seperti pada kejadian stunting. Prevalensi balita stunting di Kabupaten Malang masih tergolong cukup tinggi yaitu sebesar 25.7%. Dengan melakukan uji GWNBR didapatkan 385 model, salah satunya Desa Tulungrejo dengan faktor – faktor yang mempengaruhi kejadian stunting adalah akses jamban sehat permanen, akses posyandu, asi esklusif, kepadatan penduduk dan pemberdayaan masyarakat. Dari ketiga pembobot yang digunakan yaitu Adaptive Gaussian Kernel, Adaptive Bisquare Kernel dan Adaptive Tricube Kernel didapatkan model terbaik dari pembobot Adaptive Bisquare Kernel dengan AIC terkecil sebesar -211.3763.

Keywords

• GWNBR
• Stunting
• Malang Regency