Applied fixed effect of Geographically Weighted Panel Regression (GWPR) with M- Estimator approach to estimate sugarcane yield data in East Java
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Abstract
Geographically Weighted Panel Regression (GWPR), a combination of panel regression and geographically weighted regression (GWR), is used to analyze panel data and capture diverse relationship between locations. GWPR was developed on data with panel-fixed effects and applied to modeling data with spatial heterogeneity and time series. One method for estimating parameters in the GWPR is weighted least squares (WLS), which are sensitive to outliers. The present study aimed to use the M- method to estimate GWPR model parameters in data containing outliers using fixed-effect GWPR modeling for the sugar cane yield in East Java of Indonesia from 2019 to 2021. Sugarcane yield data in East Java contained outliers in several areas, including Malang, Blitar, and Ngawi Districts. Because the data contains outliers, a robust method with the M estimator was applied. The results showed that plantation areas significantly affected production in all districts.The R2 of the model was 0.87, showing that GWPR model with M estimation was appropriate in predicting sugarcane yield. Based on the Akaike Information Criterion (AIC) value, the GWPR model with M estimation had better performance than GWPR model alone.
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Keywords
Fixed effect model, Geographically Weighted Panel Regression (GWPR), M estimator, outlier, Weighted Least Square (WLS)
References
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Salvati, N., Tzavidis, N., Pratesi, M. & Chambers, R. (2012). Small area estimation via M-quantile geographically weighted regression. Test, 21, 1-28. DOI 10.1007/s11749-010-0231-1
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VanBuren, J. M., Cavanaugh, J. E., Marshall, T. A., Warren, J. J. & Levy, S. M. (2017). Aic identifies optimal representation of longitudinal dietary variables. Journal of Public Health Dentistry, 77(4), 360-371. https://doi.org/10.1111/jphd.12220
Wang, F. & Lee, C. (2010). An m-estimator for estimating the extended burr type iii parameters with outliers. Communications in Statistics - Theory and Methods, 40(2), 304-322. https://doi.org/10.1080/03610920903411234
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Yu, D. (2010). Exploring Spatiotemporally Varying Regressed Relationships: The Geographically Weighted Panel Regression Analysis. The International Archives of the Photogrammetry. Remote Sensing and Spatial Information Sciences, 38 (2), 134-139
Yu, D., Zhang, Y., Wu, X., Li, D. & Li, G. (2021). The varying effects of accessing high-speed rail system on China’s county development: A geographically weighted panel regression analysis. Land Use Policy, 100, 104935. https://doi.org/10.1016/j.landusepol.2020.104935
Zhang, H. & Mei, C. (2011). Local Least Absolute Deviation Estimation Of Spatially Varying Coefficient Models: Robust Geographically Weighted Regression Approaches. International Journal of Geographical Information Science. 25(9): 1467–1489. https://doi.org/ 10.1080/ 13658816. 2010.528420
Ananda, N. M. S., Suyitno, S. & Siringoringo, M. (2023). Geographically Weighted Panel Regression Modelling of Human Development Index Data in East Kalimantan Province in 2017-2020. Jurnal Matematika, Statistika dan Komputasi, 19(2), 323-341. https://doi.org/10.20956/j.v19i2.23775
Anselin, L. (1988). Spatial econometrics: methods and models (Vol. 4). Springer Science & Business Media.
Bruna, F., & Yu, D. (2016). Geographically weighted panel regression and development accounting for European Regions. In Proceedings of the 6th seminar Jean Paelinck in Spatial Econometrics, pp. 1-20.
Cai, R., Yu, D. & Oppenheimer, M. (2014). Estimating the Spatially Varying Responses of Corn Yields to Weather Variations using Geographically Weighted Panel Regression. Journal of Agricultural and Resource Economics. 39(2): 230–252
Chen, C. (2002). Paper 265-27 Robust regression and outlier detection with the ROBUSTREG procedure. In Proceedings of the Proceedings of the Twenty-Seventh Annual SAS Users Group International Conference.
Cheng, W., Xu, Z., Fan, S., Zhang, P., Xia, J., Wang, H., & Wu, Y. (2022). Effects of variations in the chemical composition of individual rice grains on the eating quality of hybrid indica rice based on near-infrared spectroscopy. Foods, 11(17), 2634. https://doi.org/10.3390/foods11172 634
Clifton, E. V., & Romero-Barrutieta, A. 2006. Institutions versus geography: subnational evidence from the United States.
Danlin , Y., Z. Yaojun, W. Xiwei, L. Ding & L Guangdong. (2021). The varying effects of accessing high-speed rail system on China’s county development: A geographically weighted panel regression analysis. Land Use Policy. 100: 104935. https://doi.org/10.1016/j.landusepol.2020.104935
Directorate General of Estate Crops (2021). Statistical Of National Leading Estate Crops Commodity. Jakarta : Ministry of Agriculture
Erda, G., Indahwati, & Djuraidah, A. (2019). Outlier handling of Robust Geographically and Temporally Weighted Regression. Journal of Physics: Conference Series, 1175(1). DOI 10.1088/1742-6596/1175/1/012041
Fotheringham, A. S., C. Brunsdon & M. Charlton (2002). Geographically Weighted Regression : the Analysis of Spatially Varying Relationship. John Wiley & Sons .England
Gamayanti, N. F., Junaidi, J. & Fadjryani, F. (2023). Analysis Of Spatial Effects On Factors Affecting Rice Production In Central Sulawesi Using Geographically Weighted Panel Regression. BAREKENG: Jurnal Ilmu Matematika dan Terapan, 17(1), 0361-0370.
Harlianingtyas, I. & Hartatie, D. (2021). Modeling of factors affecting the productivity of sugarcane in Jember Regency. In IOP Conference Series: Earth and Environmental Science (Vol. 672, No. 1, p. 012026). IOP Publishing. DOI 10.1088/1755-1315/672/1/012026
Harris, P., Brunsdon, C., Charlton, M., Juggins, S. & Clarke, A. (2014). Multivariate Spatial Outlier Detection Using Robust Geographically Weighted Methods. Mathematical Geosciences. 46(1), 1–31. https://doi.org/10.1007/s11004-013-9491-0
Kimura, K. (2019). Application of a mixed integer nonlinear programming approach to variable selection in logistic regression. Journal of the Operations Research Society of Japan, 62(1), 15-36. https://doi.org/10.15807/jorsj.62.15
Lachenani, A., Bentchikou, M., Boumahdi, M., Hanini, S. & Laidi, M. (2022). Drying process of cement mortar composites reinforced with cellulosic fibres: experiment and mathematical modelling. Kemija U Industriji, (11-12).https://doi.org/10.15255/kui.2022.010
LeSage, J.P. (2004). A Family of Geographically Weighted Regression Models. Advances in Spatial Econometrics: 241-264
Li, C. & S. Managi. (2022). Estimating monthly global ground-level NO2 concentrations using geographically weighted panel regression. Remote Sensing of Environment. 280 : 1-22. https://doi.org/10.1016/j.rse.2022.113152
Ma, Z., Xue, Y. & Hu, G. (2021). Geographically weighted regression analysis for spatial economics data: A Bayesian recourse. International Regional Science Review, 44(5), 582-604.
Musella, G., Castellano, R. & Bruno, E. (2023). Evaluating the spatial heterogeneity of innovation drivers: a comparison between GWR and GWPR. METRON, 1-23. https://doi.org/10.1007/s40300-023-00249-0
Nugroho, W. H., Wardhani, N. W. S., Fernandes, A. A. R. & Solimun, S. (2020). Robust regression analysis study for data with outliers at some significance levels. Mathematics and Statistics, 8(4), 373-381.
Putra, Z., Wijayanto, H. & Aidi, M. N. (2019). Robust Geographically and Temporally Weighted Regression Using S-estimator in Criminal Case in East Java Province. Int J Sci Basic Appl Res [Internet], 48(3), 24-36.
Salvati, N., Tzavidis, N., Pratesi, M. & Chambers, R. (2012). Small area estimation via M-quantile geographically weighted regression. Test, 21, 1-28. DOI 10.1007/s11749-010-0231-1
Shaw, M., Rights, J. D. & Sterba, S. S. (2022). R2mlm: an r package calculating r-squared measures for multilevel models. Behavior Research Methods, 55(4), 1942-1964. https://doi.org/10.3758/s13428-022-01841-4
Subedi, N., Zhang, L. & Zhen, Z. (2018). Bayesian geographically weighted regression and its application for local modeling of relationships between tree variables. iForest-Biogeosciences and Forestry, 11(5), 542.
VanBuren, J. M., Cavanaugh, J. E., Marshall, T. A., Warren, J. J. & Levy, S. M. (2017). Aic identifies optimal representation of longitudinal dietary variables. Journal of Public Health Dentistry, 77(4), 360-371. https://doi.org/10.1111/jphd.12220
Wang, F. & Lee, C. (2010). An m-estimator for estimating the extended burr type iii parameters with outliers. Communications in Statistics - Theory and Methods, 40(2), 304-322. https://doi.org/10.1080/03610920903411234
Wati, D. C. & Utami, H. (2020). Model geographically weighted panel regression (GWPR) dengan fungsi kernel fixed gaussian pada indeks pembangunan manusia di Jawa Timur. Jurnal Matematika Thales, 2(1). https://doi.org/10.22146/jmt.49230
Yu, D. (2010). Exploring Spatiotemporally Varying Regressed Relationships: The Geographically Weighted Panel Regression Analysis. The International Archives of the Photogrammetry. Remote Sensing and Spatial Information Sciences, 38 (2), 134-139
Yu, D., Zhang, Y., Wu, X., Li, D. & Li, G. (2021). The varying effects of accessing high-speed rail system on China’s county development: A geographically weighted panel regression analysis. Land Use Policy, 100, 104935. https://doi.org/10.1016/j.landusepol.2020.104935
Zhang, H. & Mei, C. (2011). Local Least Absolute Deviation Estimation Of Spatially Varying Coefficient Models: Robust Geographically Weighted Regression Approaches. International Journal of Geographical Information Science. 25(9): 1467–1489. https://doi.org/ 10.1080/ 13658816. 2010.528420
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Applied fixed effect of Geographically Weighted Panel Regression (GWPR) with M- Estimator approach to estimate sugarcane yield data in East Java. (2024). Journal of Applied and Natural Science, 16(2), 646-652. https://doi.org/10.31018/jans.v16i2.5443
