Generalized Linear Mixed Model and Lasso Regularization for Statistical Downscaling

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, 2021Revised March 29, 2021Accepted March 29, 2021