Bayesian Disaggregate and Aggregate Calibration of Path Logit Choice Models

In transport demand analysis, the calibration of a model means estimation of its (endogenous) parameters from observed data with an inference statistical estimator. Indeed, these considerations apply to any choice behaviour model, such as those derived from Random Utility Theory or any other choice modelling theory. Calibration of choice models can be carried out from disaggregate vs. aggregate data, while inference statistical estimators can be specified through Bayesian vs. Classic (or Frequentist) approaches. In this paper, the resulting Bayesian or Classic disaggregate or aggregate calibration methods are discussed, analysed in detail, and compared from the mathematical point of view. These methods are applied to calibrate Logit choice models for describing path choice behaviour at national scale on a small sample. The Logit choice model can be derived from Random Utility Theory (or be considered an instance of the Bradley-Terry model). Path choice set definition is also discussed, and specialised indicators are used for result comparison. The main contributions of this study concern the use of two different estimation approaches, Bayesian vs. Classic, adopting and introducing some indicators of goodness of estimation. The results of this work, relating to the sample of users adopted, show that the Bayesian approach provides a better estimate than the Classic approach because the calibrated parameters are more stable, the specific constants of the alternatives decrease, and the resulting models show better values of clearly right indicator.