piecewise_ginireg - A Stata package to run piecewise Gini regressions

This presentation introduces piecewise_ginireg, an extension to Mark Schaffer’s – ginireg - command. Gini regressions are based on the Gini’s Mean Difference as a measure of dispersion and the estimator can be interpreted as a weighted average of slopes. (See for example Olkin and Yitzhaki, “Gini Regression Analysis”, International Statistical Review 60 (1992): 185-196.) In comparison to a simple OLS regression, the covariance is replaced by the Gini covariance. piecewise_ginireg splits the dataset into subsets and allows an estimation for each of these subsets, giving the possibility to gain estimated coefficients for each of the subsets and to test if the linearity assumption is held by the data. In comparison to a regular Gini regression, piecewise_ginireg runs several Gini regressions on subsets of the data. As a first step piecewise_ginireg runs a normal Gini regression on the entire dataset (Iteration 0). The estimated coefficients are saved, the residuals computed and the LMA curve calculated. The LMA allows an interpretation how the Gini covariance is composed. In the next iterations the dataset is split into separate parts defined by a rule. piecewise_ginireg allows different rules such as the min or max of the LMA or were the LMA crosses the origin. On each of the sections a Gini regression is performed, where the dependent variable is the error term of the preceding iteration. After each iteration the coefficients are saved, residuals and the LMA calculated. piecewise_ginireg allows the user to specify the maximum number of iterations is several ways. It is possible to set a fixed number or until the normality conditions of the error terms holds.