Iteratively Specified Tree-Based Regression: Theory and Trip Generation Example

Ordinary least-squares (OLS) regression is routinely applied by transportation analysts to forecast energy use, trip attractions, trip productions, automobile emissions, VMT growth, pavement condition, and accident occurrence to name a few examples. An important challenge when estimating OLS models is to derive an appropriate specification. Common misspecification errors include omission of important variables, inclusion of irrelevant variables, and inclusion of variables in an incorrect functional form. These errors often produce biased parameter estimates, inefficient parameter estimates, and an inability to conduct accurate hypothesis tests. Analysts typically rely on previous empirical research, a priori knowledge, and underlying theory to identify acceptable model functional forms, to determine important interactions, and to derive defensible models. In exploratory research, however, the analyst rarely knows a priori the correct form of the relationships being modeled, and previous research illuminating the “correct” relationships is scant. This paper presents an iterative modeling method that combines desirable properties of OLS with a heuristic procedure known as hierarchical tree-based regression (HTBR). This combined approach, named iteratively specified tree-based regression (ISTBR), is shown to provide insight into data structure provided by hierarchical tree-based regression, while retaining the desirable parametric properties of OLS. ISTBR equips the modeler with improved tools for exploring and identifying alternative model specifications and affords the analyst insight into systematic patterns or “structure” in data that might otherwise go undetected. An example of the ISTBR approach is provided using trip generation data from Michigan.