Network-based predictions of retail store commercial categories and optimal locations

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 74, Issue 3, 2006, Pages

  Jensen, Pablo ^a,b  

^a UNIVERSITÉ DE LYON   (France)

^b University of Lyon 2   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSIFICATION (OF INFORMATION); COMPUTER NETWORKS; DATA REDUCTION; INDEXING (OF INFORMATION); TRACKING (POSITION);

COMMERCIAL CATEGORIES; NETWORK-BASED PREDICTIONS; SPATIAL ORGANIZATION;

RETAIL STORES;

EID: 33748663567     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.74.035101     Document Type: Article

References (18)

1. Christophe Baume and Frederic Miribel (commerce chamber, Lyon) have kindly provided extensive location data for the 8500 stores of the city of Lyon.
2. See, for example, T. Egami and S. Billinge, Underneath the Bragg Peaks: Structural Analysis of Complex Materials (Pergamon Materials Series, Boston, 2003).
3. G. Duranton and H. G. Overman, Review of Economic Studies 72 (4), 1077 (2005).
4. E. Marcon and F. Puech, http://team.univ-paris1.fr/teamperso/puech/ textes/Marcon-Puech_ImprovingDistance-BasedMethods.pdf (accessed Sept. 7th 2005).
5. One could argue that the average is dominated by the denser regions, thus eliminating the influence of peripheral areas. This effect exists, even if it is partially corrected through the ponderation by the total number of stores. I have tried several other statistical representations of the relative concentration, such as the mode or the median, but none performed as well as the average. The median, for example, fails because most A stores have no B stores around them, leading to mostly null interaction coefficients.
6. To ascertain the statistical significance of the repulsion or attraction, I have simulated 800 random distributions of nB stores on all possible sites, calculating for each distribution the nB ntot ratio around the same A locations. This gives the statistical fluctuations and allows us to calculate how many times the random ratio deviates from 1 as much as the real one. I assume that if there are less than 3% random runs that deviate more than the real one, the result is significant (97% confidence interval).
7. Alternatively, one can fully count stores closer than 50 m and linearly decrease the counting coefficient until 150 m. This leads to similar results.
8. Important differences introduced by including weighted links are stressed, for example, in M. Barthelemy, A. Barrat, R. Pastor-Satorras, and A. Vespignani, Physica A PHYADX 0378-4371 10.1016/j.physa.2004.08.047 346, 34 (2005).
9. For a pair interaction to be significant, I demand that both aAB and aBA be different from zero, to avoid artificial correlations. For Lyon, I end up with 300 significant interactions (roughly 10% of all possible interactions), of which half are repulsive.
10. While store-store attraction is easy to justify (the "market share" strategy, where stores gather in commercial poles, to attract costumers), direct repulsion is generally limited to stores of the same trade which locate far from each other to capture neighbor costumers (the "market power" strategy). The repulsion quantified here is induced (indirectly) by the price of space (the square meter is too expensive downtown for car stores) or different location strategies. For introductory texts on retail organization ans its spatial analysis, see B. J. L. Berry, Market Centers and Retail Location: Theory and Application (Prentice-Hall, Englewood Cliffs, NJ, 1988) and the Web book on regional science by E. M. Hoover and F. Giarratani, available at http://www.rri.wvu.edu/WebBook/Giarratani/contents.htm
11. J. Reichardt and S. Bornholdt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.218701 93, 218701 (2004). Note that the presence of antilinks automatically ensures that the ground state is not the homogeneous one, when all spins point into the same direction (i.e., all nodes belong to the same cluster). Then, there is no need of a γ coefficient here.
12. F. Radicchi, C. Castellano, F. Cecconi, V. Loreto, and D. Parisi, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.0400054101 101, 2658 (2004).
13. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science SCIEAS 0036-8075 220, 671 (1983).
14. A frustrated (A,B,C) triplet is one for which A attracts B, B attracts C, but A repels C, which is the case for the triplet shown in Fig. 1.
15. M. E. J. Newman and M Girvan, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.026113 69, 026113 (2004).
16. See, for example, the U.S. Department of Labor Internet page http://www.osha.gov/pls/imis/sic_manual.html (accessed Sep. 28th, 2005).
17. To calculate the correlation of store and population density for a given activity, I count both densities for each of the 50 Lyon sectors. I then test with standard econometric tools the hypothesis that store and population densities are uncorrelated (zero slope of the least squares fit), with a confidence interval of 80%.
18. Several retail categories defined by the Commerce Chamber are unfortunately heterogeneous: for example, "bookstores and newspapers" refers to big stores selling books and CDs as well as to the proximity newspaper stand. Instead, bakeries are precisely classified in four different categories: it is a French commercial structure!