Insoluble problems in shopping model calibration when the trip pattern is not known

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Abstract
Openshaw S. (1973) Insoluble problems in shopping model calibration when the trip pattern is not known, Reg. Studies 7, 367–371. Gravity models are often used in retail studies to describe or predict shopping turnovers, although few attempts have been made to either determine optimum parameter values or to assess the validity of the model's performance. Using model calibration based on non-linear minimization of the sum of squares of the differences between predicted and actual sales in each centre, it is possible to show that the two parameter Lakshmanan-Hansen and Wilson shopping models have a trivial solution, that the one parameter versions of the same models reached a hidden trivial solution and like the intervening opportunity version, fail to provide an acceptable fit. It is suggested on the basis of this evidence that no satisfactory shopping model calibration can be made when the trip pattern is not known and therefore model calibration based on observed trip data is urgently required.

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