Calibrating Urban Residential Location Models 4: Effects of Log-Collinearity on Model Calibration and Formulation

Abstract

In extensive empirical testing of the disaggregated residential allocation model (DRAM), the Tanner function (a modified gamma function) was used as the work-trip-travel function. More recent application work with the model revealed difficulties in calibration due to log-multicollinearity, which led to a reexamination of the formulation of the model and the general question of the use of the Tanner function in spatial interaction models. An analytical examination of the Tanner function reveals that some of its desirable properties arise from phenomena different from the original hypotheses. The log-collinearity problem is also analyzed analytically. A set of numerical experiments and empirical tests confirm the analytical results and argue for discontinuing the use of the Tanner function as the trip function in spatial interaction models, and for using a negative power or a declining exponential function instead.