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

2023 | OriginalPaper | Chapter

Kaiyu Markov Model and Evaluation of Retail Spatial Structures

Authors : Saburo Saito, Toru Sakamoto

Published in: Recent Advances in Modeling and Forecasting Kaiyu

Publisher: Springer Nature Singapore

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Abstract

Using an absorbing Markov chain model, we formulate consumers’ shop-around behaviors as the Kaiyu Markov model. Based on the Kaiyu Markov model, we conceptualize the shop-around effect to enable us to evaluate retail spatial structures, which we define as an increase in the frequency of visits to each commercial district due to consumers’ shop-around behaviors. We improved the traditional survey of consumers’ purchasing behaviors to collect the actual consumers’ shop-around behaviors and applied the Kaiyu Markov model to the data obtained from the improved survey conducted for the metropolitan area of Nobeoka City, Japan. We estimated the actual shop-around effects for the 17 commercial districts in the city and showed that the concept of the shop-around effects serves as a helpful tool for evaluating and planning the retail spatial structure of the city.

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previous 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
next chapter Basics of Kaiyu Markov Models: Reproducibility Theorems—A Validation of the Infinite Kaiyu Representation
Footnotes
1
It is natural to think that the probability of returning home will gradually increase as the shop-arounds proceed. Indeed, the shop-around behaviors will end after several steps. In contrast, we formulate consumers’ shop-around behaviors as an absorbing stationary Markov chain. Thus, we hypothetically assume that the shop-around does not change its transition probability as expressed in (3). Hence, the shop-around effect is formalized as the increase in the expected frequency of visits to each commercial district derived under an infinite number of shop-around behaviors. The shop-around effect of this formulation might be thought of as an approximation. However, the validation of this formulation will be given by the reproducibility theorem that states the model “exactly” reproduces the observed shop-around visit frequency. (See for details, Saito. Ishibashi, Yamashiro, Iwami [4], Chap. 4 in this volume)
 
2
The absorbing state is a state satisfying that all the transition probabilities from it to all other states are zeros.
 
3
We should note that the probabilistic model formulated here cannot be a model for policy experimentation because it does not include independent policy variables, such as time, distance, and shop floor area, which explain the transition probability. Therefore, this model looks at the structure of the current arrangement of the commercial districts (e.g., distances between commercial districts) as it is and tries to evaluate this structure from the shop-around transition probability or, more specifically, only from the shop-around effect in which the consumers’ evaluation with feet about the structure of the arrangement of the commercial districts is reflected through their shop-around behaviors.
 
4
The probability matrix is defined as a non-negative matrix satisfying every row sum equals one.
 
5
All data and the municipality divisions are as of 1983.
 
6
The original version of this chapter appeared in Sakamoto [7].
 
Literature
1.
Saito, S. (1983). Present situation and challenges for the commercial districts in Nobeoka area. In: Committee for Modernizing Commerce Nobeoka Region Section ([3]) The report of regional plan for modernizing commerce: Nobeoka area, pp. 37–96. (in Japanese).
2.
Saito, S. (1983). Design of questionnaire for consumer purchasing behavior survey and its question sheets. In: Committee for Modernizing Commerce Nobeoka Region Section ([3]) The report of regional plan for modernizing commerce: Nobeoka area, pp. 151–156. (in Japanese).
3.
Committee for Modernizing Commerce Nobeoka Region Section. (1983). The report of regional plan for modernizing commerce. Nobeoka Area. (in Japanese).
4.
Fukami, T. (1977). A study on pedestrian flows in a commercial district part 2. Papers on City Planning (12):61–66. (in Japanese).
5.
Fukami, T. (1974). A study on pedestrian flows in a commercial district part 1. Papers on City Planning (9):43–48. (in Japanese).
6.
Saito, S., Ishibashi, K., Yamashiro, K., & Iwami, M. (2023). Basics of Kaiyu Markov models: Reproducibility theorems—a validation of infinite Kaiyu representation. (Chapter 4 in this volume). Springer.
7.
Sakamoto, T. (1984). An absorbing Markov chain model for estimating consumers’ shop-around effect on shopping districts. Papers on City Planning (19):289–294. (in Japanese).
Metadata
Title
Kaiyu Markov Model and Evaluation of Retail Spatial Structures
Authors
Saburo Saito
Toru Sakamoto
Copyright Year
2023
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_3