Fitting Flexible Parametric Regression Models with GLDreg in R

This article outlines the functionality of the GLDreg package in R which fits parametric regression models using generalized lambda distributions via maximum likelihood estimation and L moment matching. The main advantage of GLDreg is the provision of robust regression lines and smooth regression quantiles beyond the capabilities of existing known methods. The GLDreg package in R is designed to implement the Generalized Lambda Distribution (GλD) regression model outlined in Su (2015) with some extensions. Currently, it is possible to fit GλD regression to data using maximum likelihood estimation (MLE) (Su, 2007a; b) and L moment matching (Asquith, 2007; Karvanen & Nuutinen, 2008). Users may also chose initial values to start the model building process, or use the default searching algorithm using the ordinary least square regression model (Su, 2015). The GLDreg package also allows user to fit quantile regressions parametrically and non-parametrically by: 1) fixing the intercept, 2) fixing coefficients other than the intercept, and 3) allowing all coefficients to vary. The GLDreg package requires GLDEX (Su, 2007a; 2010). The GLDEX 2.0.0.1 package has a faster implementation of the GλD fitting algorithm compared to its predecessors. This is because a number of frequently used codes have been written in C. In addition, the GLDEX 2.0.0.1 package has faster maximum likelihood fitting functions fun.RMFMKL.