Measure
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Definition
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Source
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K-Function
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A function specifying the expected (theoretical) or empirical (average) number of points (retail locations) within a radius d around any single point (retail location) as a function of the radius d from the central point. For a random Poisson process, for example, K increases with the square of d.
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Ripley (1981)
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Kulldorff's D
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A measure of clustering or avoidance that compares the difference in the local density of a set of “cases” (retail outlets of a focal type) to the local density of a set of “controls” (all other retailers).
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Kulldorff (1998)
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Mi
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A normalization of Kulldorff's D statistic that better enables comparisons across retail categories by using the 90% Monte Carlo confidence intervals to scale Kulldorff's D values.
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This paper
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Table 4. Pattern Membership Criteria
Pattern
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Membership Criteria
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Hyper agglomeration
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Mi > 1 for all quintiles
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Local agglomeration
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Mi > 1 for the first and/or second quintile, but not all five, and no quintiles have Mi < -1
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Auto mall
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Mi > 1 for the first and/or second quintile, and Mi < -1 for at least one of the third, fourth, or fifth quintiles
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Avoidance
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Mi < -1 for at least one quintile, and Mi is never greater than one.
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No pattern
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Default, the criteria for membership is not met for any other pattern.
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Table 5. Agglomeration Patterns Exhibited by Different Retail Types
Retail Types with Same Nonrandom Spatial Pattern in Vancouver and Calgary
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Hyper Agglomeration
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Local Agglomeration
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Auto Mall Pattern
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Avoidance
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Furniture
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Carpets
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New Autos
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Gas Stations
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Antiques
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Children’s Clothing
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Boat Dealers
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Supermarkets
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Coffee Shops
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Clothing
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Health and Diet
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Art Galleries
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Pizza Parlors
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Smoking Supplies
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Liquor, Beer, Wine
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Used Autos
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Pets and Supplies
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Gift shops
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Paint
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Bookstores
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Nonrandom Spatial Patterns Unique to Vancouver
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Hyper Agglomeration
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Local Agglomeration
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Auto Mall Pattern
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Avoidance
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Cosmetics*
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Bridal*
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Pubs
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Women’s Clothing*
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Delicatessen*
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Ice Cream Parlors
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Men’s Clothing*
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Kitchen Cabinets*
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Lumber
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Shoes*
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Hearing Supplies*
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Jewelry*
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Auto Parts*
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Music CDs & Tapes
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Sporting Goods
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Fabric
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Bakery
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Tailors
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Meat
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Opticians
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Nonrandom Spatial Patterns Unique to Calgary
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Hyper Agglomeration
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Local Agglomeration
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Auto Mall Pattern
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Avoidance
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Bridal*
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Cosmetics*
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Housewares
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Meat
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Delicatessen*
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Women’s Clothing*
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Wedding Supplies
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Fabric
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Kitchen Cabinets*
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Men’s Clothing*
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Doors
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Pharmacies
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Hearing Supplies*
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Shoes*
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Lumber
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Convenience Stores
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Auto Parts*
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Jewelry*
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Pubs
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Opticians
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Lumber
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Tires
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Glass
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*Differ between cities by hyper versus local agglomeration only.
Figure 1. Illustrations of Ripley’s K-Function
 
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