Linear Regression with Percentile Lasso and Ridge to Predict Rainfall
The impact of rainfall is usually significant to human life and other living especially an extreme rainfall. It is important to find a method, such as statistical downscaling, which can predict rainfall to anticipate the possible impact. This method develops a linear regression model that relates functionally local scale data as response variable to global scale data as predictor variables in order to predict local scale data.The local scale data are rainfall and the global scale data are precipitation data of General Circulation Model (GCM) output. The characteristics of GCM output are usually multidimensional and multicollinearity which could be the problem in modeling. The addition of least absolute shrinkage and selection operator (lasso) and ridge regularizations into the model can overcome the problem. The coefficient of lasso is determined based on cross validation method. However, according to Roberts and Nowak in 2013, this method usually results in unstable values and the instability is solved using a percentile technique called percentile-lasso. The optimum lasso coefficient is determined based on the values of quantiles Q(0.75), Q(0.90), and Q(0.95). This paper discusses the use of percentile-ridge in statistical downscaling model and this technique is compared to the percentile-lasso. Percentile-ridge (RMSEP=71.11 mm/month; r=0.75) is better than percentile-lasso (RMSEP=72.51 mm/month; r=0.74) in predicting rainfall.