Pemodelan Semiparametric Geographically Weighted Regression Pada Kasus Pneumonia Balita Provinsi Jawa Tengah

Abstract

Geographical and inter-regional differences have contributed to the diversity of child pneumonia cases in Central Java, so a spatial regression modelling is formed that is called Geographically Weighted Regression (GWR). GWR is a development of linear regression by involving diverse factors geographical location, so that local parameters are produced. Sometimes, there are non-local GWR parameters. To overcome some non-local parameters, Semiparametric Geographically Weighted Regression (SGWR) is formed to develop a GWR model with local and global influences simultaneously. SGWR Model is used to estimate the model of percentage of children with pneumonia in Central Java with population density, average temperature, percentage of children with severe malnutrition, percentage of children with under the red line weight, percentage of households behave in clean and healthy lives, and percentage of children who measles immunized. SGWR models on percentage of children with pneumonia in Central Java produce locally significant variables that is population density, average temperature, and percentage of households behave in clean and healthy lives. Variable that globally significant is percentage of children with severe malnutrition. Based on Akaike Information Criterion (AIC), SGWR is a better model to analize percentage of children with pneumonia in Central Java because of smallest AIC. Keywords: Akaike Information Criterion, Geographically Weighted Regression, Semiparametric Geographically Weighted Regression

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“…Artinya varians dalam model regresi tidak selalu sama, tetapi berubah berdasarkan tempat pengamatan dilakukan. Uji Breusch-Pagan dapat digunakan untuk memeriksa heterogenitas spasial pada persamaan (2.10) [11].…”

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“…𝑢 𝑖 , 𝑣 𝑖 ) + ∑ 𝛽 𝑘 (𝑢 𝑖 , 𝑣 𝑖 )𝑋 𝑖𝑡𝑘 + 𝜀 𝑖𝑡 𝑝 𝑘=1 .................................................................................... (2) dengan 𝑦 𝑖𝑡= variabel dependen pada lokasi i dan periode ke-t 𝛽 𝑘 (𝑢 𝑖 , 𝑣 𝑖 ) = koefisien regresi variabel independen lokasi i (𝑢 𝑖 , 𝑣 𝑖 ) = koordinat lokasi geografis dari lokasi i 𝑋 𝑖𝑡𝑘 = variabel independen ke-k dari lokasi i dan periode ke-t 𝜀 𝑖𝑡 = error dari lokasi i dan periode ke-tAdapun tahapan analisis inferensia dengan GWPR adalah sebagai berikut(Chotimah et al, 2019;Meutuah, 2017;Bruna & Yu, 2016): 1) Membangun model regresi panel sebagai model regresi global Pemilihan model global terbaik dilakukan dengan uji Chow dan uji Hausman dilakukan pada masingmasing level winsorize dan model terbaik yang terpilih yaitu model Fixed Effect Model.2) Menguji asumsi residual model regresi globalPengujian asumsi klasik dilakukan untuk menunjukkan bahwa model telah valid dan memenuhi syarat penduga yang BLUE (Best Linear Unbiased Estimator). Pengujian asumsi klasik yang dilakukan meliputi uji asumsi normalitas residual, uji multikolinearitas, uji autokorelasi, dan uji heteroskedastisitas.3) Melakukan pengujian heterogenitas spasialPengujian heterogenitas spasial pada data penelitian ini menggunakan uji Breusch-Pagan.…”