Main Article Content
Abstract
Rainfall is one of the climatic elements in the tropics which is very influential in agriculture, especially in determining the growing season. Thus, proper rainfall modeling is needed to help determine the best time to start cultivating the soil. Rainfall modeling can be done using the Statistical Downscaling (SDS) method. SDS is a statistical model in the field of climatology to analyze the relationship between large-scale and small-scale climate data. This study uses response variables as a small-scale climate data in the form of rainfall and explanatory variables as a large-scale climate data of the General Circulation Model (GCM) output in the form of precipitation. However, the application of SDS modeling is known to cause several problems, including correlated and not stationary response variables, multi-dimensional explanatory variables, multicollinearity, and spatial correlation between grids. Modeling with some of these problems will cause violations of the assumptions of independence and multicollinearity. This research aims to model the rainfall in Indramayu Regency, West Java Province using a combined regression model between the Generalized linear mixed model (GLMM) and Least Absolute Selection and Shrinkage Operator (LASSO) regulation (L1). GLMM was used to deal with the problem of independence and Lasso Regulation (L1) was used to deal with multicollinearity problems or the number of explanatory variables that is greater than the response variable. Several models were formed to find the best model for modeling rainfall. This research used the GLMM-Lasso model with Normal spread compared to the GLMM model with Gamma response (Gamma-GLMM). The results showed that the RMSE and R-square GLMM-Lasso models were smaller than the Gamma-GLMM models. Thus, it can be concluded that GLMM-Lasso model can be used to model statistical downscaling and solve the previously mentioned constraints.
Received February 10, 2021
Revised March 29, 2021
Accepted March 29, 2021
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References
- Krishnamoorthy K. 2006. Handbook of Statistical Distributions with Applications. New York (USA): Chapman Hall/CRC.
- Stephenson DB, Kumar KR, Doblas-Reyes FJ, Royer JF, Chauvin E, Pezzulli S. 1999. Extreme Daily Rainfall Events and Their Impact on Ensemble Forecast of the Indian Monsoon. Monthly Weather Review 127:1954-1966.
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- Sholeh A M. 2015. Pemodelan Linier Sebaran Gamma dan Pareto Terampat dengan Regularisasi L1 pada Statistical Downscaling untuk Pendugaan Curah Hujan Bulanan.
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- Groll A, Tutz, 2012. Variable selection for generalized linear mixed models by L1-penalized estimation. Stat Comput DOI 10.1007/s11222-012-9359-z, Springer Science+Business Media New York 2012.
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- Novkaniza f , Hayati M, Sartono B, Notodiputro KA. 2018. Fused Lasso for Modeling Monthly Rainfall In Indramayu Sub Distric West Java Indonesia, IOP Conference Series: Earth and Environmental Science.
- Stroup W W, 2012, Generalized Linear Mixed Model modern Concepts, Methods and Applications, 1st Edition, CRC Press.
- Tibshirani R. 1996. Regression Shringkage and Selection via the Lasso. R. Stat. Soc. Ser. B. 58(1) 267–288. doi:10.1111/j.1467-9868.2011.00771.x.
- Ranhao S, Baiping Z, Jing T. 2008. A Multivariate Regression Model for Predicting Precipitation in the Daqing Mountains. Mountain Research Development. 23(3): 318-325.
- Wigena AH. 2006. Pemodelan Statistical Downscaling dengan Regresi Projection Pursuit untuk Peramalan Curah Hujan Bulanan. [Disertasi]. Bogor (ID): Institut Pertanian Bogor.
References
Krishnamoorthy K. 2006. Handbook of Statistical Distributions with Applications. New York (USA): Chapman Hall/CRC.
Stephenson DB, Kumar KR, Doblas-Reyes FJ, Royer JF, Chauvin E, Pezzulli S. 1999. Extreme Daily Rainfall Events and Their Impact on Ensemble Forecast of the Indian Monsoon. Monthly Weather Review 127:1954-1966.
Permatasari SM, Dzuraidah A, Soleh AM. 2016. Statistical Downscaling with Gamma Distribution and Elastic Net Regularization (Case Study: Monthly Rainfall 1981-2013 at Indramayu). Proceeding of The 2nd International Conference on Applied Statistics 2016 ISSN: 2579-4361. Indonesia.
Sholeh A M. 2015. Pemodelan Linier Sebaran Gamma dan Pareto Terampat dengan Regularisasi L1 pada Statistical Downscaling untuk Pendugaan Curah Hujan Bulanan.
Gad A M, Kholy R S, 2012, Generalized Linear Mixed Models for Longitudinal Data, International Journal of Probability and Statistics 2012, 1(3): 67-73 DOI:10.5923/j.ijps.20120103.03, Cairo.
Groll A, Tutz, 2012. Variable selection for generalized linear mixed models by L1-penalized estimation. Stat Comput DOI 10.1007/s11222-012-9359-z, Springer Science+Business Media New York 2012.
Jaiswal, R.K., Lohani, A.K., Tiwari, H.L., 2015. Statistical analysis for change detection and trend assessment in climatological parameters. Environ. Proc. 2 (4), 729–749.
Tibshirani, R., Saunders, M., Rosset S, Zhu, J., Knight, K . 2005. Sparsity and Smoothness via The Fused LASSO, Journal Royal Statistical Soc. B, 67, Part 1, pp 91-108.
Muslim A, Hayati M, Sartono B, Notodiputro KA. 2018. A Combined Modeling of Generalized Mixed Model and LASSO Technique for Analyzing Monthly Rainfall Data, IOP Conference Series: Earth and Environmental Science.
Novkaniza f , Hayati M, Sartono B, Notodiputro KA. 2018. Fused Lasso for Modeling Monthly Rainfall In Indramayu Sub Distric West Java Indonesia, IOP Conference Series: Earth and Environmental Science.
Stroup W W, 2012, Generalized Linear Mixed Model modern Concepts, Methods and Applications, 1st Edition, CRC Press.
Tibshirani R. 1996. Regression Shringkage and Selection via the Lasso. R. Stat. Soc. Ser. B. 58(1) 267–288. doi:10.1111/j.1467-9868.2011.00771.x.
Ranhao S, Baiping Z, Jing T. 2008. A Multivariate Regression Model for Predicting Precipitation in the Daqing Mountains. Mountain Research Development. 23(3): 318-325.
Wigena AH. 2006. Pemodelan Statistical Downscaling dengan Regresi Projection Pursuit untuk Peramalan Curah Hujan Bulanan. [Disertasi]. Bogor (ID): Institut Pertanian Bogor.