A Combined Modeling of Generalized Linear Mixed Model and LASSO Techniques for Analizing Monthly Rainfall Data

Abstract

The rainfall pattern is always interesting to be investigated. This paper discusses the performance of three methods in modeling the rainfall data namely the LASSO (Least Absolute Shrinkage and Selection Operator) and GLMM (Generalized Linear Mixed Model) methods as well as a combination of GLMM and LASSO techniques. The rainfall data is usually collected on a regular basis, hence it is longitudinal data. The GLMM methods are usually employed to analyze longitudinal data, especially when number of explanatory variables is small. If the number of explanatory variables is large and if these variables are correlated then the GLMM estimation will be suffered by ill condition problems. These problems may be overcome by adding L1 penalty and start doing variable selection and shrinkage simultaneously. In this paper a combination of GLMM and LASSO techniques is evaluated by using monthly rainfall data, a high dimensional data, collected during 1981-2014 in Indramayu sub-district. The results showed that a combination of GLMM and LASSO methods is superior when compared with GLMM and LASSO methods separately. This claim is supported by evidence that MSE of the combined method is smaller than MSEs of the other two methods for various λ (lambda).