Parameter Estimation Strategies for Large-Scale Urban Models

Large-scale urban models often are subdivided into simpler submodels. The parameters of these models can be estimated using approaches that differ in regard to whether the full modeling system is run during an estimation procedure or whether that overall estimation is performed simultaneously with the estimation of the individual submodels. There are also ways in which extra data or extra models can be used to further inform parameter values. Five different techniques are presented (“limited view,” “piecewise” “simultaneous,” “sequential,” and “Bayesian sequential”), and the statistical theory necessary to justify each technique concurrently is described. The practical advantages and disadvantages are discussed, and each technique is illustrated using a simple nested logit model example. The concepts then are further illustrated by describing the sequential parameter estimation process for a land use/transport interaction model of the Sacramento, California, region. The ideas and examples should help modelers place more of an emphasis on overall calibration, allow them to follow a more rigorous approach in establishing the parameters of large-scale urban models, and help them understand the theory and assumptions that they are implicitly adopting. Two techniques in particular are noted as worthy of future research in large-scale urban modeling: (a) establishing the likelihood function based directly on the structural equations of the model, eliminating or reducing the need to “solve” for the model outputs during parameter estimation; and (b) using Bayesian techniques to adjust parameters in an overall estimation without discarding what is already known about those parameters.