Quantitative Marketing and Economics

, Volume 10, Issue 4, pp 419–452 | Cite as

Bayesian multi-resolution spatial analysis with applications to marketing

  • Sam K. Hui
  • Eric T. Bradlow


Marketing researchers have become increasingly interested in spatial datasets. A main challenge of analyzing spatial data is that researchers must a priori choose the size and make-up of the areal units, hence the resolution of the analysis. Analyzing the data at a resolution that is too high may mask “macro” patterns, while analyzing the data at a resolution that is too low may result in aggregation bias. Thus, ideally marketing researchers would want a “data-driven” method to determine the “optimal” resolution of analysis, and at the same time automatically explore the same dataset under different resolutions, to obtain a full set of empirical insights to help with managerial decision making. In this paper, we propose a new approach for multi-resolution spatial analysis that is based on Bayesian model selection. We demonstrate our method using two recent marketing datasets from published studies: (i) the Netgrocer spatial sales data in Bell and Song (Quantitative Marketing and Economics 5:361–400, 2007), and (ii) the Pathtracker® data in Hui et al. (Marketing Science 28:566–572, 2009b; Journal of Consumer Research 36:478–493, 2009c) that track shoppers’ in-store movements. In both cases, our method allows researchers to not only automatically select the resolution of the analysis, but also analyze the data under different resolutions to understand the variation in insights and robustness to the level of aggregation.


Spatial analysis Bayesian modeling Bayesian model selection 


  1. Banerjee, S., Gelfand, A. E., & Carlin, B. P. (2003). Hierarchical modeling and analysis of spatial data. Chapman and Hall.Google Scholar
  2. Barbujani, G., Jacquez, G. M., & Ligi, L. (1990). Diversity of some gene frequencies in European and Asian populations V. Steep multilocus clines. American Journal of Human Genetics, 47, 867–875.Google Scholar
  3. Bell, D., & Song, S. (2007). Neighborhood effects and trial on the internet: evidence from online grocery retailing. Quantitative Marketing and Economics, 5(4), 361–400.CrossRefGoogle Scholar
  4. Bertsimas, D., & Tsitsiklis, J. (1993). Simulated annealing. Statistical Science, 8(1), 10–15.CrossRefGoogle Scholar
  5. Bithell, J. F. (2000). A classification of disease mapping methods. Statistics in Medicine, 19, 2203–2215.CrossRefGoogle Scholar
  6. Bloom, P. N., Gundlach, G. T., & Cannon, J. P. (2000). Slotting allowances and fees: schools of thought and the views of practicing managers. Journal of Marketing, 64, 92–108.CrossRefGoogle Scholar
  7. Bocquet-Appel, J. P., & Bacro, J. N. (1994). Generalized wombling. Systematic Biology, 43(3), 442–448.Google Scholar
  8. Booth, J. G., Caselle, G., & Hobert, J. P. (2008). Clustering using objective functions and stochastic search. Journal of Royal Statistical Society (Series B), 70, 119–139.CrossRefGoogle Scholar
  9. Bradlow, E. T., Bronnenberg, B., Russell, G. J., Arora, N., Bell, D. R., Duvvuri, S. D., et al. (2005). Spatial models in marketing. Marketing Letters, 16, 267–678.CrossRefGoogle Scholar
  10. Bronnenberg, B. J., Dhar, S. K., & Dube, J.-P. (2007). Consumer packaged goods in the United States: national brands, local branding. Journal of Marketing Research, 44, 4–13.CrossRefGoogle Scholar
  11. Choi, J., Hui, S. K., & Bell, D. (2010). Spatio-temporal analysis of imitation behavior across new buyers at an online grocery retailer. Journal of Marketing Research, 47(1), 65–79.CrossRefGoogle Scholar
  12. Farley, J. U., & Winston Ring, L. (1966). A stochastic model of supermarket traffic flow. Operations Research, 14(4), 555–567.CrossRefGoogle Scholar
  13. Ferligoj, A., & Batagelj, V. (1982). Clustering with relational constraints. Psychometrika, 47, 413–426.CrossRefGoogle Scholar
  14. Fong, D., Wayne, K. H., & DeSarbo, S. (2007). A Bayesian methodology for simultaneously detecting and estimating regime change points and variable selection in multiple regression models for marketing research. Quantitative Marketing and Economics, 5(4), 427–453.CrossRefGoogle Scholar
  15. Fortin, M.-J., & Drapeau, P. (1995). Delineation of ecological boundaries: comparison of approaches and significance test. OIKOS, 72, 323–332.CrossRefGoogle Scholar
  16. Francois, O., Ancelet, S., & Guillot, G. (2006). Bayesian clustering using hidden Markov random fields in spatial population genetics. Genetics, 174, 805–816.CrossRefGoogle Scholar
  17. Gangnon, R. E., & Clayton, M. K. (2000). Bayesian detection and modeling of spatial disease clustering. Biometrics, 56, 922–935.CrossRefGoogle Scholar
  18. Garber, T., Goldenberg, J., Libai, B., & Muller, E. (2004). From density to destiny: using spatial dimension of sales data for early prediction of new product success. Marketing Science, 23(3), 419–428.CrossRefGoogle Scholar
  19. Goffe, W. L., Ferrier, G. D., & Rogers, J. (1994). Global optimization of statistical functions with simulated annealing. Journal of Econometrics, 60, 65–99.CrossRefGoogle Scholar
  20. Hajek, B. (1988). Cooling schedules for optimal annealing. Mathematics of Operations Research, 13(2), 311–329.CrossRefGoogle Scholar
  21. Hoeting, J., Madigan, D., Raftery, A. E., & Volinsky, C. T. (1999). Bayesian model averaging: a tutorial. Statistical Science, 14(4), 382–417.CrossRefGoogle Scholar
  22. Huang, Y., Hui, S., Inman, J., & Suher, J. (2012). Capturing the ‘First Moment of Truth’: Understanding point-of-purchase drivers of unplanned consideration and purchase. Working Paper.Google Scholar
  23. Hui, S. K., Fader, P. S., & Bradlow, E. T. (2009a). Path data in marketing: an integrated framework and prospectus for model building. Marketing Science, 28(2), 320–335.CrossRefGoogle Scholar
  24. Hui, S. K., Fader, P. S., & Bradlow, E. T. (2009b). The traveling salesman goes shopping: the systematic deviations of grocery paths from TSP optimality. Marketing Science, 28(3), 566–572.CrossRefGoogle Scholar
  25. Hui, S. K., Bradlow, E. T., & Fader, P. S. (2009). Testing behavioral hypotheses using an integrated model of grocery store shopping path and purchase behavior. Journal of Consumer Research, 36, 478–493.CrossRefGoogle Scholar
  26. Jacquez, G. M., Maruca, S., & Fortin, M. J. (2000). From fields to objects: a review of geographic boundary analysis. Journal of Geographical Systems, 2(3), 221–241.CrossRefGoogle Scholar
  27. Jacquez, G. M., & Greiling, D. A. (2003). Geographic boundaries in breast, lung, and colorectal cancers in relation to exposure to air toxics in Long Island, New York. International Journal of Health Geographics, 2(4), available at
  28. Ju, J., Gopal, S., & Kolaczyk, E. D. (2005). On the choice of spatial and categorical scale in remote sensing land cover characterization. Remote Sensing of Environment, 96(1), 62–77.CrossRefGoogle Scholar
  29. Kaufman, L., & Rousseeuw, P. J. (1990). Finding groups in data: An introduction to cluster analysis. New York: Wiley.CrossRefGoogle Scholar
  30. Keane, M. J. (1978). A functional distance approach to regionalisation. Regional Studies, 12, 379–386.CrossRefGoogle Scholar
  31. Kolaczyk, E. D., & Huang, H. (2001). Multiscale statistical models for hierarchical spatial aggregation. Geographical Analysis, 33(2), 95–118.CrossRefGoogle Scholar
  32. Larson, J. S., Bradlow, E. T., & Fader, P. S. (2007). An exploratory look at supermarket shopping paths. International Journal of Research in Marketing, 22, 395–414.CrossRefGoogle Scholar
  33. Lawson, A. B. (2006). Disease cluster detection: a critique and a Bayesian proposal. Statistics in Medicine, 25, 897–916.CrossRefGoogle Scholar
  34. Lawson, A. B., Biggeri, A., Bohning, D., Lesaffre, E., Viel, J.-F., & Bertollini, R. (1999). Disease mapping and risk assessment for public health decision making. Chichester: Wiley.Google Scholar
  35. Liechty, J., Pieters, R., & Wedel, M. (2003). Global and local covert visual attention: evidence from a Bayesian hidden Markov model. Psychometrika, 68(4), 519–541.CrossRefGoogle Scholar
  36. Louie, M. M., & Kolaczyk, E. D. (2006a). Multiscale detection of localized anomalous structure in aggregate disease incidence data. Statistics in Medicine, 25(5), 787–810.CrossRefGoogle Scholar
  37. Louie, M. M., & Kolaczyk, E. D. (2006b). A multiscale method for disease mapping in spatial epidemoiology. Statistics in Medicine, 25(8), 1287–1308.CrossRefGoogle Scholar
  38. Lu, H., & Carlin, B. P. (2005). Bayesian areal wombling for geographical boudnary analysis. Geographical Analysis, 37, 265–285.CrossRefGoogle Scholar
  39. Ma, H., & Carlin, B. P. (2007). Bayesian multivariate areal wombling for multiple disease boundary analysis. Bayesian Analysis, 2(2), 281–302.CrossRefGoogle Scholar
  40. Manning, C. D., Raghavan, P., & Schutze, H. (2008). Introduction to information retrieval. New York: Cambridge Unviersity Press.CrossRefGoogle Scholar
  41. Mollie. (1996). Bayesian mapping of disease. In W. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice. London: Chapman and Hall.Google Scholar
  42. Montgomery, A. L., Li, S., Srinivasan, K., & Liechty, J. C. (2004). Modeling online browsing and path analysis using clickstream data. Marketing Science, 23(4), 579–595.CrossRefGoogle Scholar
  43. Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika, 37, 17–33.Google Scholar
  44. Murtagh, F. (1985). A survey of algorithms for contiguity-constrained clustering and related problems. The Computer Journal, 28(1), 82–88.CrossRefGoogle Scholar
  45. Pieters, R., Rosbergen, E., & Wedel, M. (1999). Visual attention to repeated print advertising: a test for scanpath theory. Journal of Marketing Research, 36(4), 424–438.CrossRefGoogle Scholar
  46. Pukkala, E. (1989). Cancer maps of Finland: An example of small-area based mapping. In P. Boyle, C. S. Muir, & E. Grundmann (Eds.), Cancer mapping (pp. 208–215). Berlin: Springer.CrossRefGoogle Scholar
  47. Raftery, A. E. (1995). Bayesian model selection in social research. Sociological Methodology, 25, 111–163.CrossRefGoogle Scholar
  48. Richardson, S., Montfort, C., Green, M., Draper, G., & Muirhead, C. (1995). Spatial variation of natural radiation and childhood leukaemia incidience in Great Britain. Statistics in Medicine, 14(21/22), 2487–2501.CrossRefGoogle Scholar
  49. Robert, C., & Casella, G. (2004). Monte Carlo statistical methods, 2nd Edn, Springer.Google Scholar
  50. Rossi, P. E., Allenby, G. M., & McCulloch, R. (2005). Bayesian statistics and marketing., Wiley.Google Scholar
  51. Rousseeuw, P. (1987). Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Computational and Applied Mathematics, 20, 53–65.CrossRefGoogle Scholar
  52. Sorensen, H. (2003). The science of shopping. Marketing Research, 15(3), 30–35.Google Scholar
  53. Ter Hofstede, F., Wedel, M., & Steenkamp, J.-B. E. M. (2002). Identifying spatial segments in international markets. Marketing Science, 21, 160–177.CrossRefGoogle Scholar
  54. Theil, H. (1954). Linear aggregate of economic relations. Amsterdam: North-Holland.Google Scholar
  55. der Lans, V., Ralf, R. P., & Wedel, M. (2008). Eye-movement analysis of search effectiveness. Journal of the American Statistical Association, 103(482), 452–461.CrossRefGoogle Scholar
  56. Womble, W. H. (1951). Differential systematics. Science, 114(2961), 315–322.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Stern School of Business of New York UniversityNew YorkUSA
  2. 2.Wharton School of the University of PennsylvaniaPhiladelphiaUSA

Personalised recommendations