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Electronic Letters to:
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eLetters: Electronic letters published:
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Appropriate use of the k-function in urban environments with geocoded data
- Seth E Spielman (14 September 2005)
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THE FAST-FOOD ENVIRONMENT AND SPATIAL STATISTICS
- Mark F. Guagliardo, (no others) (14 September 2005)
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Seth E Spielman, Adj. Assoc. Research Scientist Columbia University, SUNY Buffalo
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ses89{at}columbia.edu Seth E Spielman
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There is clearly a need to understand neighborhood food environments and how they contribute to behavior. "Clustering of Fast-Food Restaurants Around Schools: A Novel Application of Spatial Statistics to the Study of Food Environments" in the current issue (9/05) of the AJPH is an interesting approach to this important question. However, the paper raises a number of methodological issues around the use of spatial statistics in urban environments. First and foremost is that planar k-functions, the statistical technique used in the paper, may not be appropriate for data based on street addresses. The k-function used in the paper employs an "as the crow flies" measure of distance. Children are not crows and tend to navigate urban environments using streets and sidewalks. In cities a straight line measure of distance can dramatically underestimate the actual travel distance thus network based k-functions are more appropriate for urban analysis. Yamada and Thill found that the use of the planar k-function with network constrained point data leads to an over detection of clusters and suggest the use of network k-functions as an alternative (Yamada I., 2004). Second, urban land use is generally regulated through zoning ordinances that dictate what can locate where. Modern zoning practice generally clusters like uses. The location of fast food restaurants in Chicago is not a random process therefore comparisons to complete spatial randomness are not meaningful. While K-functions can be used effectively to detect clusters interpreting the significance of the observed k- function is tricky. The article is unclear about the confidence intervals and how they were derived; it states they are based on simulation but simulation of what? Restaurants can only locate in areas that are zoned appropriately. Confidence intervals to be meaningful should be based upon simulation of random restaurant locations within this defined space of zones suitable for commercial fast food. A corollary concern is that the areas suitable for fast food restaurants may be clustered. A univariate k-function examining only the location of restaurant might help in answering this question. Understanding how neighborhood characteristics relate to diet is critical work for public health and urban planning practitioners. I think this article is an important examination of that question. However it seems to me that the methods used in the study do not bear out the conclusions about clustering. A more careful application of the k- function is required to address to question of the location of fast food joints relative to schools. Yamada I., T., J.C. (2004). Comparison of planar and network k- functions in traffic accident analysis. Journal of Transport Geography, 12, 149-158. |
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Mark F. Guagliardo, Assistant Professor George Washington University & Children's National Medical Center, (no others)
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markg{at}gwu.edu Mark F. Guagliardo, et al.
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The paper by Austin and colleagues(1) on the clustering of fast-food restaurants around Chicago schools (September 2005) is a welcome addition to the food environment literature. Their traditional statistics demonstrating that unhealthy food outlets are near schools are unassailable. Furthermore, they are correct to claim that their spatial clustering method is a novel application of spatial statistics to the food environment problem. Unfortunately, their results for the level of clustering around schools can be misleading without proper consideration for an important assumption of their chosen test. Like other point pattern tests, the bivariate K function is evaluated against the assumption of complete spatial randomness.(2) In the present example restaurant locations are initially assumed to be free to vary over the entire Chicago area. However, they actually lack such freedom. A casual comparison of Austin et al.’s Figure 1 to a city map shows that virtually all of the larger gaps between locations are due to large parks, bodies of water, and other urban features and zones off-limits to restaurants. The effect of this unaccounted constraint on location is to force restaurants and schools to be closer together. The effect is exacerbated to the extent that school locations are under the same constraints. While this does not invalidate the K values of Austin et al., it puts the question of cause of clustering in a different light. It is less likely that the reported strength of clustering is any different than would be found for other types of retail establishments, or for random points in “allowed” areas for that matter. Nor do the findings support the notion that fast-food restaurants are targeting kids. The authors are careful to avoid such a suggestion, but a casual reader could easily come away with this impression. More applications of spatial statistics are needed if we are to succeed in stemming the ubiquity of unhealthy foods available to America’s children. However, it is important that we apply them in a useful and convincing manner. Fast food corporations are well-financed, with well- trained spatial analysts at their disposal to advise them on retail site selection. There is little doubt that these experts could detect weaknesses such as that cited above, and will be called upon to criticize such work if the industry feels threatened by public health research. The argument that fast-food restaurants are too close to schools is supported by simple distance measurements. The argument for spatial clustering should await stronger analyses. 1. Austin SB, Melly SJ, Sanchez BN, Patel A, Buka S, Gortmaker SL. Clustering of fast-food restaurants around schools: A novel application of spatial statistics to the study of food environments. Am J Public Health. 2005;95:1575-1581. 2. Bailey TC, Gatrell AC. Interactive Spatial Data Analysis. New York, NY: Prentice Hall; 1995. |
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