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2023 | OriginalPaper | Chapter

Disaggregate Hierarchical Decision Huff Model Incorporating Consumer Kaiyu Choices Among Shopping Sites

Author : Saburo Saito

Published in: Recent Advances in Modeling and Forecasting Kaiyu

Publisher: Springer Nature Singapore

Abstract

A classical Huff model is extended to a disaggregated hierarchical Huff model, which incorporates the consumers’ multi-stage decisions concerning shopping destinations and shop-arounds. We represent the consumers’ multi-stage decisions as four stages; the first stage is a choice among destination cities, the second is between two alternatives of the set of large stores and small shops, the third is a choice of an individual destination shop, and the last is a choice to shop-around from those large stores chosen to the next destination shop. We formulated the extended model as a fully recursive joint probability model expressed as a multivariate log-linear model and estimated as disaggregate conditional logit models.

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next chapter A Dynamical Huff Model: Computing the Competitive Equilibrium Distribution of Shop Floor Areas over a City Center Commercial District Using a Fixed-Point Algorithm

Saga City Comprehensive Plan with the target year of 1989 was formulated in 1982. This Plan reconfirmed again the importance of the tertiary industry, especially commerce, to achieve the planned population of 200,000, and set out the redevelopment of the city center commercial district and establishing a symbolic zone as its crucial urban development policies. However, these urban development policies have a close relation to commercial policies. What size is appropriate for the city center commercial district for a prefectural capital city of 200,000 population, whether we should allocate it in a multi-core manner, and how we should make the links between cultural and tourism functions in the symbolic zone and the retail functions at the city center commercial district. Thus, these commercial policies play critical roles in the urban development policy in Saga City.

Initials of Saga COmmercial Policy Evaluation System.

The report was presented to Saga City Government. Refer to Saito [1].

When the destination shopping sites are far from each other, the importance of the shop-around between shopping sites is not so high. Thus, in such a case, there is little necessity to treat the shopping trip as a loop-like shopping trip, which is the case that Huff initially assumed to develop his model [5].

Saito [6] pointed out this point. Refer to pp. 64–65 in [7].

Saito [8] gives an example of the guideline of questionnaire design for the survey of consumer purchasing behaviors based on this concept as well as a concrete example of survey questionnaire.

As will be described in Sect. 3.1, as for the estimation of Kaiyu choice model, we used responses to the question items with multiple-choice formats. This assumption was made to avoid double counting. If there is a question item directly asking about the shop-around history as in [8], such an assumption is unnecessary, and the estimation method employed in this paper can be applied without any change in this case.

For details, refer to [1].

Refer to [6].

Huff [5] formulated his original model for the case that μ = 1. The model with two unknown parameters, μ and λ is usually called the modified Huff model.

For details about the log-linear models, refer to [13].

For the examples which applied the modified path analysis, refer to Saito [16, 17].

The structure of the survey sheet does not ask the respondents who chose cities other than Saga City as the city choice about which commercial district they further chose. Thus, note that our model differs from the nested model.

All of the administrative divisions of municipalities, including the Saga City area, as of 1983.

The alternative cities are ten cities, i.e., nine listed cities by their names as the choice options for the question item and the respondents’ own cities, which are listed not by their names but by the choice option of ‘city you reside.’ The names of nine cities are shown in Table 1.

The questionnaire indicates to the respondents that the shop-around shopping goods are items such as clothing (street clothes, etc.), personal belongings (bags, shoes, accessories, etc.), and cultural items (home electronics, cameras, furniture, records, books, etc.).

The question item for the frequency of visits is the single answer question composed of seven choice options: (1) More than once per week, (2) Two or three times per month, (3) Once per month, (4) Once per 2 or 3 months, (5) Two or three times per year, (6) Once per year, (7) Almost never visit. The alternatives of large retail stores used are six large retail shops in Saga City. Table 3 shows their names, and Fig. 4 depicts their locations.

The question item to ask about using 13 commercial districts at Saga City is as follows: Did you go shopping at each of the following 13 commercial districts the last month? It requires to answer yes or no for each of the 13 commercial districts. Thus, this question item has a multiple-answer format. Table 5 shows the 13 commercial districts.

The other helpful use of the large-scale home-based survey of consumers’ purchasing behaviors referred in Sect. 1.1 other than constructing the Huff model is the estimation of interregional in and out flow matrix of regional retail-related purchasing power. Saito [21] employed the generalized RAS method or Iterative Proportional Fitting Procedure to estimate the interregional in and out flow matrix of regions’ purchasing powers among cities in the KitaKyushu Metropolitan Area.

Two large retail stores are Seiyu Supermarket and Topos discount store. Seiyu is located in front of Saga Station and Topos in Muzugae Shopping Street in Fig. 3. The other four large stores, Tamaya Department Store, Daiei, Kotobukiya, Nichiyu supermarkets, are in Fig. 4.

From the survey of consumer purchasing behaviors we used, only the time distances from the respondents’ residences to Saga City are available from their responses to the questionnaire. We employ the following procedure to obtain the time distance from their residence to each of the large retail stores in Saga City. First, we determine the nearest large retail store for each of the six blocks. Then the time distances to Saga City the respondents answered are regarded as the time distances from their residences to the determined nearest large retail store. Next, we measure the time distance from the nearest large store to the other five large stores. The distance from the nearest large store to itself is zero. Finally, we obtain the time distance from the respondents’ residences to each of the six large retail stores as the sum of that from their residence to the nearest large store and that from the nearest large store to each of the six large retail stores.

The six commercial districts we regard as identical to the large stores are (1) Prefectural Government (Kenchodori) shopping street (including Tamaya department store), (2) Shirayama (Daiei supermarket), (3) GofukuMachi (Kotobukiya supermarket), (4) Mizugae (Topos discount shop), (5) Saga Station Area (Seiyu supermarket), and (6) ChuoHonmachi (Nichiyu supermarket).

The total number of visitors to each of commercial districts is decomposed into the number of entrance visitors and that of Kaiyu (shop-around) visitors. For these concepts, refer to Saito, Ishibashi, Yamashiro, and Iwami [22], which discusses in details the Kaiyu Markov model in Chap. 4 in this volume.

We must distinguish between the on-site and the home-based distributions of the number of visitors to commercial districts. The on-site distribution of the number of visitors to commercial districts is the true distribution of the number of visitors to commercial districts when we observe and count the number of visitors at the commercial districts or the sites. Suppose that the respondents were drawn by random sampling from the survey area in the sense that they are drawn at random according to the true distribution of municipal populations, age, gender, etc., over the survey area. Then, we can recover the home-based distribution of the number of visitors to commercial districts by cross-tabulating the respondents’ responses. The on-site distribution of the number of visitors to commercial districts can be obtained by the weighted cross-tabulation while giving the weight to each respondent by their frequency of visits to the place they visited, i.e., Saga City. (Also refer to the next footnote and Saito et al. [23])

The topic of how accurately we can estimate and forecast the number of visitors to the whole city center commercial district and each commercial district within the city center is the core theme for the studies on Kaiyu modeling and forecasting. This topic is closely related to the concepts of on-site sampling and the distinction between the on-site and home-based distribution of the frequency of visits to commercial districts. For further details, refer to the consistent estimation of consumers’ Kaiyu patterns due to Saito et al. [23].

In retrospect, this spatial structure is interpreted as a small-sized two-core (Daiei and Kotobukiya) and one-mall (Motomachi) type shopping mall. Later in 1986, Saito carried out a home-based survey of consumer shop-around behaviors by utilizing Saga Citizen Opinion Survey conducted by Saga City Government. According to the analysis result of this survey, 84% of the visitors to Motomachi were shop-around visitors. (Cf. Saito [24, 25]).

Note that the time distance, T_Li,_j, is the sum of the time distance from the residence to the origin large retail store, L_i, plus the time distance from the origin large retail store, L_i, to the destination commercial district, C_j.

Here, the expansion of the shop floor area is assumed to be an expansion that does not include large retail stores, and Tojinmachi is assumed to remain a commercial district without the large retail stores after the policy is implemented. However, in the SCOPES model, it is possible to simulate a case when a large retail store is located in Tojinmachi, and Tojinmachi itself becomes a large store or a commercial district with a large retail store after the policy implementation.

In the policy experimentation phase, the arcade connected dummy variable or the arcade connection policy should not be interpreted as being the construction of the physical facility of the arcade but as being the effective means to activate the shop-around among the commercial districts connected by the arcade to the same extent as the arcade connected dummy has.

The original version of this chapter appeared in Saito [26].

Saito, S. (1984). A survey report on the modified huff model: The development of SCOPES (Saga commercial policy evaluation system). Saga City Government. (in Japanese).

Fukami, T. (1974). A study on pedestrian flows in a commercial district part 1. Papers on City Planning, 9. (in Japanese).

Fukami, T. (1977). A study on pedestrian flows in a commercial district part 2. Papers on City Planning 61–66. (in Japanese).

Committee for Modernizing Commerce. (1982). Manual for modernizing commerce regional planning, The Japan Chamber of Commerce and Industry. (in Japanese).

Huff, D. L. (1964). Defining and estimating a trading area. Journal of Marketing, 28, 34–38. CrossRef

Saito, S. (1983). Present situation and challenges for the commercial districts in Nobeoka area. Chapter 6 in The report of regional plan for modernizing commerce: Nobeoka Area, ed: Committee for Modernizing Commerce Nobeoka Region Section, pp. 37–96. (in Japanese).

Committee for Modernizing Commerce Nobeoka Region Section. (1983). The report of regional plan for modernizing Commerce : Nobeoka Area. (in Japanese).

Saito, S. (1983). Document 6-1-1 Design of questionnaire for consumer purchasing behavior survey and its question sheets. In The report of regional plan for modernizing commerce: Nobeoka Area, ed: Committee for Modernizing Commerce Nobeoka Region Section, pp. 151–156. (in Japanese).

Takeuchi, S. (1981). A model for location planning of commercial functions. Planning and Public Management, 5, 25–33. (in Japanese).

10.

Domencich, T. A. & McFadden, D. L. (1975). Urban travel demand. North-Holland.

11.

Matsumoto, S., Kumakura, S., & Matsuoka, K. (1983). Joint-choice model for destination and travel mode for non-grocery shopping trips. Papers on City Planning, 18, 469–474. (in Japanese).

12.

Honda, H. (1983). Basic research for the analysis of preference for shopping areas. Papers on City Planning, 18, 463–467. (in Japanese).

13.

Bishop, Y. M. M., Holland, P. W., & Fienberg, S. E. (1975). Discrete multivariate analysis: Theory and practice. MIT Press.

14.

Amemiya, T. (1981). Qualitative response models. A survey. Journal of Economic Literature, 19, 1493–1536.

15.

Maddala, G. S. (1983). Limited-dependent and qualitative variables in econometrics. Cambridge University Press. CrossRef

16.

Saito, S. (1982). Role development paths of governmental planners. Papers on City Planning, 169–174. (in Japanese).

17.

Saito, S. (1984). The role development paths of government planners and the evaluation of their assignment department history. Saga University Economic Review, 16, 31–51. (in Japanese).

18.

Goodman, L. A. (1973). The analysis of multidimensional contingency tables when some variables are posterior to others: A modified path analysis approach. Biometrika, 60, 179–192. CrossRef

19.

Lee, L.-F. (1981). Fully recursive probability models and multivariate log-linear probability models for the analysis of qualitative data. Journal of Econometrics, 16, 51–69. CrossRef

20.

Amemiya, T. (1978). On a two-step estimation of a multivariate logit model. Journal of Econometrics, 8, 13–21. CrossRef

21.

Saito, S. (1982). Estimating the interregional flows of purchasing power based on the generalized RAS method. In: Addendum, Saito S (1882) NorthKyushu metropolitan area regional econometric model (pp. 386–425). Kitakyushu City Government Commerce Modernizing Committee. (in Japanese).

22.

Saito, S., Ishibashi, K., Yamashiro, K., & Iwami, M. (2023). Basics of Kaiyu Markov models: Reproducibility theorems—A validation of infinite Kaiyu representation. (Chap. 4 in this volume). Springer.

23.

Saito, S., Nakashima, T., & Kakoi, M. (2001). The consistent OD estimation for on-site person trip survey. Studies in Regional Science, 31, 191–208. (in Japanese). CrossRef

24.

Saito, S. (1986). Analysis report of Saga citizen opinion survey: City attractiveness and policy demand of Saga City. Saga City Government. (in Japanese).

25.

Saito, S. (1988). Evaluating space of city center viewed from Kaiyu: A case study in Saga City. Fukuoka University Economic Review, 33, 47–108. (in Japanese).

26.

Saito, S. (1984). A disaggregate hierarchical huff model with considering consumer’s shop-around choice among commercial districts: Developing SCOPES (Saga commercial policy evaluation system). Planning and Public Management, 13, 73–82. (in Japanese).

Title: Disaggregate Hierarchical Decision Huff Model Incorporating Consumer Kaiyu Choices Among Shopping Sites
Author: Saburo Saito
Publisher: Springer Nature Singapore
Book: Recent Advances in Modeling and Forecasting Kaiyu
Print ISBN: 978-981-9912-40-7

Electronic ISBN: 978-981-9912-41-4

Copyright Year: 2023
DOI: https://doi.org/10.1007/978-981-99-1241-4_1

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