THE STRUCTURE OF PROBABILISTIC TRADE AREA DELIMITATION MODELS

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Since D. L. Huff proposed a probabilistic trade area delimitation model for the delimitation of a trade area (the Huff model), a number of attempts applying the extentions of the Huff model have been devised to analyze competitive market behavior. These models are generally called the Huff type model or the multiplicative competitive interaction (M. C. I.) model. The theoretical basis of these models relies to a large extent on the Luce choice axiom. It assumes the one-to-one correspondence between choice ratio which is the probability of a consumer in an area shopping at a certain store and relative utility which is the utility ratio. of a certain store to an aggregate utility of all stores which the consumer can patronage. However, there is no proof of the existence of one-to-one correspondence. Therefore, the Huff' and Hufftype models which rely on the Luce choice axiom do not have the evident store choice mechanism. The purpose of this study is to build an alternative probabilistic model which is strictly defined in terms of consumer behavior, and to compare this model with the Huff and Huff-type models. Main charateristics of this new model are as follows: Let Xi be consumers' utility on the ith store in a given district. As the utility Xi is not the same to all consumers in the district, we assume that randam variable Xi is normally distributed with mean μi and variance σi2. Furthermore, we assume that the probability choosing a certain store is equal to the probability that a certain sore's utility is greater than the . other stores' utility. In case of three stores (denoted 1, 2, 3), the probability that store 1 would be chosen (P1) may be stated as follows _??_here fi(xi) is the probability density function of Xi, the function Zi=(Xi-μi)/σi is normally distributed with mean zero and variance one, and Kj=(X1-μj)/σj. The following results were obtained applying this model to the data about Matsuyama city. 1) Assuming that the consumers evaluations of store attraction is normally distributed and that the choice ratio in which consumers choose a certain store is equal to the probability that the evaluationn of the store is greater than those of the other stores, the author was able to build an alternative probabilistic model which has more clear choice mechanism than the usual ones. 2) The proposed model, as the probabilistic model satisfies the necessary conditions, _??_ 3) The R. M. S. error obtained from the Huff-type model is 9.5% and that obtained from the Huff model is 15.86%. In terms of fitness the former is about 6% better than the latter. This difference is considered to be caused by applying both models to close-by stores which have different selling space. Accordingly, if the Huff model is applied to this situation, it is expected that stores having greater selling space have larger expect ed values than observed ones. 4) As the R. M. S. error obtained from the proposed model is 10.5%, there is no significant difference in terms of the goodness of fit between the proposed model and the Huff-type model. Furthermore, both models have similar distributions of predicted values. 5) Therefore, the proposed model has the same performance as the Huff-type model, and at the same time it has more clear store choice mechanism than the usual probabilistic models.
The Association of Japanese Geographersの論文

THE STRUCTURE OF PROBABILISTIC TRADE AREA DELIMITATION MODELS

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The Association of Japanese Geographers | 論文

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