The use of mathematical models in urban planning : the case of shopping models
This thesis presents the results of an empirical study of variants
of five shopping models (central place theory, and the gravity, entropy
intervening opportunities, and Building Research Establishment models),
calibrated to data for four towns, using a range of estimation procedures
(least-squares, chi-squares, maximum-likelihood). Various forecast
scenarios, the effects of variations in the data, and disaggregating
shopping trips by mode were also considered.
The breadth of the study enabled it to systematically identify the
scale of relative uncertainties: the largest source of overall
uncertainty arose through model choice, then choice of calibration
statistic, and finally through variations in the data. The general
uncertainty was of a substantial degree - similar in magnitude to
the forecasts themselves - and would therefore have ramifications
for any policies based on the forecasts (some welfare implications
The methodological principle adopted demanded that genarisations
should be made from relatively aggregate results, further investigated
at disaggregated levels only when anomalies appear. Hence, rather than
deal with turnovers of individual centres the study dealt with the
turnovers of 'local' centres taken together, 'district' centres taken
together, and the 'town centre' treated seperately. This approach
enabled a consideration of how the models 'trade-off' centre attractiveness
against trip deterrence. The conclusion was' drawn that the
largest modelling uncertainty occurs for local centres.
The thesis also questioned whether present models constructively
add to our understanding of the processes underlying urban change,
Qr'whether.they actually deflect attention away from such considerations.
The conclusion drawn was that the state of the art is impoverished in
two respects: current modelling techniques provide forecasts with a wide
degree of uncertainty when used practically; and they have theoretical
deficiencies which do not enable them to handle the practical problems
encountered • In planning this contradiction may be concealed by
posing results as if they were relatively certain.