Gamma Response Regression with Percentile Lasso and Ridge to Estimate Extreme Rainfall

  • Ichsan Ali Bogor Agriculture University, Bogor, Indonesia.
  • Anik Djuraidah Bogor Agricultural University, Bogor, Indonesia.
  • Agus Mohamad Soleh Bogor Agricultural University, Bogor, Indonesia.


An extreme rainfall can cause flood or drought and so it is necessary to develop a prediction model to anticipate the impact of extreme rainfall phenomenon. The statistical downscaling is one of the existing methods to analyze the rainfall data based on Global Circulation Model (GCM) output. The rainfall data can be Gamma distribution because the data can be zero or more than zero. The extreme rainfall data could be in the tail of Gamma distribution and so General Linier Model (GLM) with Gamma response variable.The GCM output is usually high dimensional data and multicollinearity. Least absolute shrinkage and selection operator (lasso) and ridge penalty included in a model can overcome such problems. The value of optimum penalty can be estimated using cross validation. However, the method is very sensitive tothe k-fold size and the results are unstable. This weakness is overcome by repeating cross validation and finding some percentiles. This paper discusses a regression model with the response of Gamma distribution to predict extreme rainfall based on the25th,50th,75th,90th,and95thpercentiles. The result shows that,based on the value of root mean square error of prediction (RMSEP), the model with lasso (RMSEP=48.42 mm/month) on percentile 75th is better than that with ridge (RMSEP=50.44 mm/month) on percentile 25th.