KAJIAN SIMULASI OVERDISPERSI PADA REGRESI POISSON DAN BINOMIAL NEGATIF TERBOBOTI GEOGRAFIS UNTUK DATA BALITA GIZI BURUK
Keywords:geographically weighted poisson regression, geographically weighted negative binomial regression, overdispersion
One type of geographically weighted regression (GWR) that can be used to explain the relationship between the response variables in the form of count data and explanatory variables is the geographically weighted Poisson regression (GWPR). In the GWPR, there is an assumption that should be fulfilled called equidispersion, a condition where the variance equals the mean. If that condition is ignored, overdispersion will occur. Overdispersion is a condition when the variance is greater than the mean. The use of GWPR analysis in an overdispersion situation will produce a smaller standard error than it should be (underestimate). This may produce a significant test result leading to the rejection of the null hypothesis. One of the classic approaches commonly used to handle overdispersion in GWR is geographically weighted negative binomial regression (GWNBR). GWNBR is derived from a mixture of Poisson and Gamma distributions which is similar to the negative binomial distribution. Simulation data and real data were used in this study. The results showed that the application of GWPR on overdispersion data could increase the number of rejections of H0 or the number of p-values. The application of GWNBR on the East Java malnutrition toddler data in 2017 showed that the GWNBR model is better than GWPR based on the comparison of AIC, Pseudo R2, and RMSE.
Agresti, A. (2003). Categorical data analysis (Vol. 482). New York (US): John Wiley & Sons.
da Silva, A. R., & Rodrigues, T. C. V. (2014). Geographically weighted negative binomial regressionâ€”incorporating overdispersion. Statistics and Computing, 24(5): 769â€“783.
Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2003). Geographically weighted regression: the analysis of spatially varying relationships. Chichester (UK): John Wiley & Sons.
Liu, J., Zhao, Y., Yang, Y., Xu, S., Zhang, F., Zhang, X., â€¦ Qiu, A. (2017). A mixed geographically and temporally weighted regression: Exploring spatial-temporal variations from global and local perspectives. Entropy, 19(2)(53): 1â€“20. https://doi.org/10.3390/e19020053
McCullagh, P., & Nelder, J. A. (1989). Generalized Linear Models. Second edition. London (UK): CRC Monographs on Statistics & Applied Probability.
Miranti, Z., & Purhadi. (2016). Pemetaan Jumlah Balita Gizi Buruk di Kota Surabaya dengan GWNBR dan Flexibly Shaped Spatial Scan Statistic. Jurnal Sains Dan Seni ITS, 5(2): D247â€“D252. https://doi.org/10.12962/j23373520.v5i2.16567
Nakaya, T., Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2005). Geographically weighted Poisson regression for disease association mapping. Statistics in Medicine, 24(17): 2695â€“2717.
Sofia, A. (2018). Regresi Poisson Dan Spasial Otoregresif Poisson Dalam Menduga Faktor-Faktor Kasus Gizi Buruk Balita di Pulau Jawa [Thesis]. Bogor (ID): Institut Pertanian Bogor.