Hierarchical Tree-Based Versus Ordinary Least Squares Linear Regression Models: Theory and Example Applied to Trip Generation

Abstract

Given the continual need for transportation professionals to forecast trends and the increasing availability of sophisticated and improved modeling methods in new and improved software packages, new methods should be explored to determine whether they can replace or supplement more classical statistical methods. One commonly used classical statistical technique for relating a continuous dependent variable with one or more independent variables (continuous or discrete) is ordinary least squares (OLS) regression. This method is routinely applied in transportation to forecast such things as energy use, trip attractions, trip productions, automobile emissions, and growth in vehicle miles traveled (VMT). Despite its widespread use and tremendous utility, however, OLS regression has limitations. It does not deal well with multicollinear independent variables, interactions between independent variables must be specified, the functional relationship between dependent and independent variables must be known (or approximated well), it cannot handle missing data well, and it does not treat satisfactorily discrete variables with more than two levels. Hierarchical tree-based regression (HTBR) may provide a better model for forecasting continuous response variables in transportation applications when the shortcomings of OLS regression are present. The theory of HTBR methods is presented. Then, an example using trip generation data is used to illustrate the types of models that result from OLS regression and HTBR methods. Finally, the limitations of HTBR are presented.