Regresi Poisson Invers Gaussian (PIG) untuk Pemodelan Jumlah Kasus Pneumonia pada Balita di Provinsi Jawa Tengah Tahun 2019
Authors: Damayanti CR Mey , Yanti Teti Sofia 
Published: March 2022

Abstract. Poisson regression is a non-linear regression model used on non-negative count or discrete data. Poisson regression is included in the Generalized Linear Model (GLM). In Poisson regression there is an assumption that must be met, that is equidispersion where the value of the variance in the response variable (Y) must be the same as the average value. If in Poisson regression modeling there is an overdispersion or underdispersion and it is ignored, the test will be less accurate because the standard error value will be underestimated. Poisson Inverse Gaussian Regression Model (PIG) can overcome overdispersion data. The Poisson Inverse Gaussian (PIG) distribution is a mixed Poisson distribution. PIG regression is used to model the count data which has a high slope and skews to the right. Maximum likelihood method was used to estimate the parameters in the PIG regression model. Pneumonia is an acute infection that causes inflammation of the lung tissue. The case of pneumonia in children under five is one form of discrete data. The results of the PIG regression model were compared based on the Akaike Information Criterion (AIC) to obtain the best model. From the results of hypothesis testing, it was concluded that the percentage of children under five who had received measles immunization and the percentage of children under five who had received DPT immunization had a significant effect on the of pneumonia cases in children under five. By using the AIC value, the Poisson Inverse Gaussian (PIG) regression model is obtained, that is: .
Abstrak. Regresi poisson merupakan model regresi non-linear yang digunakan pada data cacah atau diskrit non-negatif. Regresi Poisson termasuk kedalam Generalized Linear Model (GLM). Pada regresi Poisson terdapat asumsi yang harus dipenuhi yaitu equidispersi dimana nilai variansi pada variabel respon (Y) harus sama dengan nilai rata-ratanya. Apabila dalam pemodelan regresi Poisson terjadi kasus overdispersi atau underdispersi dan hal tersebut diabaikan maka pengujian akan menjadi kurang akurat karena nilai standard error akan menjadi underestimate. Model Regresi Poisson Invers Gaussian (PIG) dapat mengatasi data overdispersi. Distribusi Poisson Invers Gaussian (PIG) merupakan mixed poisson distribution. Regresi PIG digunakan untuk memodelkan data cacah yang memiliki kemiringan yang tinggi dan menceng ke kanan. Metode maximum likelihood digunakan untuk menaksir parameter pada model regresi PIG.. Pneumonia merupakan infeksi akut yang menyebabkan peradangan pada jaringan paru-paru. Kasus pneumonia pada balita merupakan salah satu bentuk dari data diskrit. Hasil model regresi PIG dibandingkan berdasarkan Akaike Information Criterion (AIC) untuk memperoleh model terbaik. Dari hasil pengujian hipotesis diperoleh kesimpulan bahwa persentase balita yang pernah mendapatkan imunisasi campak dan persentase balita yang pernah mendapatkan imunisasi DPT berpengaruh signifikan terhadap jumlah kasus pneumonia pada balita. Dengan memperhatikan nilai AIC didapatkan model regresi Poisson Invers Gaussian (PIG) yaitu: .