Maximum likelihood estimation for combined travel choice model parameters

Equilibrium models of combined location and travel choices solve for the modal link flow pattern, which simultaneously solves a constrained minimization problem and satisfies a set of equilibrium conditions characterizing a rational behavior for traveler choices in an urban transportation system. The minimization problem typically is made to be representative df the particular urban area being studied by including coefficients of travel costs and travel choices that have been estimated from locally available observed data. For large urban areas, in practice, it is possible to derive interzonal travel times and costs only from the travel model, because suitable observed data are nonexistent. In this case, the estimation problem is a function of the travel model variables and, at the same time, the travel model is a function of the parameters determined by the estimation problem. Procedures to computationally search for a stable solution to this bilevel optimization problem have been addressed with limited success. The parameter estimation is solved in an iterative procedure in which first parameters are held fixed and the travel model is solved, then travel patterns are held fixed and the maximum likelihood parameters are solved by the Newton-Raphson method. Each successive parameter estimation resulting from these two steps results in a new set of parameter values for the next iteration until stable values for the parameters are achieved. The quality of the convergence of the parameter estimates is reported.