Section: New Results

Methods for the calibration of LUTI models

The setting up of a LUTI model requires, like most numerical models, at least one phase of parameter estimation. This is concisely referred to here as calibration, although the calibration of a LUTI model also entails other aspects such as the definition of spatial zones, of economic sectors, etc. The TRANUS LUTI model plus software, like many other existing models, come along with a relatively simple calibration methodology. Most LUTI models indeed perform parameter estimation in a piecewise fashion, by sequentially estimating subsets of parameters. While this reduces the mathematical and computational complexity of calibration, neglecting the interactions across different modules and their parameters, may result in a significant loss of a model?s quality. A second issue is that TRANUS, like several other LUTI softwares, employs rudimentary numerical routines for parameter estimation. We aim at reducing these weaknesses.

In 2014, we had obtained first results along these lines: parameter estimation of the so-called shadow prices (specific parameters of the TRANUS model) was posed as optimization problem and several solution procedures were developed which were based on “unwinding” the dynamics of the model, making the problem amenable to standard numerical optimisation techniques.

The work continued throughout 2015, along different directions. First, the calibration was extended to handle several different parameter types simultaneously (shadow prices as well as the so-called substitution parameters, which are notoriously difficult to estimate) [7] . Such a simultaneous estimation of different parameter sets seems to be rare in LUTI practice.

Second, we proposed a methodology for assessing properties (convergence, accuracy) of our (and other) LUTI calibration methods [6] . This consists in generating synthetic data, starting from a model calibrated on observed data, such that the synthetic data are completely consistent, i.e. there are a set of model parameters that exactly reproduce these data (which is not the case with the observed data). The ground truth model parameters are then easily used to assess calibration parameters. Such a methodology, akin to twin experiments in data assimilation, seems to be novel for LUTI research.

Third, LUTI models are usually calibrated on a base year or period, and used in a prospective manner (via simulated “predictions” for future periods). As with any numerical model, it is wise to make sure that a calibrated LUTI model does not overfit the observations used for calibration; otherwise, its “predictions” may be grossly erroneous. Potential overfitting does not seem to have been deeply studied in the LUTI literature. We have made an initial investigation by calibrating different versions of a TRANUS model, varying the number of shadow prices used as parameters in the model (there is, by default, one shadow price per combination of geographical zone of the study area and economic sector) [6] . For instance, after an initial calibration using all shadow prices, we then dropped the two third smallest of them and re-calibrated the model using the remaining third. The goodness-of-fit to observations was worse by only 3%. In line with well-known principles of model selection (Occam's razor), this may suggest that it is preferable to use the model with fewer parameters when doing predictions. This is still work in progress; showing its relevance is planned to be studied by a similar methodology as above, using simulated twin experiments.

This work is done in collaboration with Arthur Vidard from the AIRSEA Inria project-team and Brian Morton from the University of North Carolina at Chapel Hill.