Measure Definition Source A function specifying the expected (theoretical) or empirical (average) Ripley (1981) K-Function number of points (retail locations) within a radius around any single d (retail location) as a function of the radius from the central d point. For a random Poisson process, for example, increases with K the square of d. Kulldorff's A measure of clustering or avoidance that compares the difference in Kulldorff (1998) D the local density of a set of (retail outlets of a focal type) to “cases” the local density of a set of (all other retailers). “controls” A normalization of Kulldorff's statistic that better enables This paper Mi D comparisons across retail categories by the 90% Monte Carlo confidence intervals to scale Kulldorff's values. D Table 4. Pattern Membership Criteria Pattern Membership Criteria Hyper agglomeration > 1 for all quintiles Mi agglomeration > 1 for the first and/or second quintile, but not all five, and no quintiles Mi have < -1 Mi Auto mall > 1 for the first and/or second quintile, and < -1 for at least one of the Mi Mi third, fourth, or fifth quintiles Avoidance < -1 for at one quintile, and is never greater than one. Mi Mi No pattern Default, the criteria for membership is not met for any pattern. 5. Agglomeration Patterns Exhibited by Different Retail Types Retail with Same Nonrandom Spatial Pattern in Vancouver and Calgary Hyper Agglomeration Local Agglomeration Auto Mall Pattern Avoidance Furniture Carpets New Gas Stations Antiques Children’s Clothing Boat Dealers Supermarkets Coffee Shops Clothing Health and Diet Art Galleries Pizza Parlors Smoking Supplies Liquor, Beer, Wine
Measure Definition Source K-Function A function specifying the expected (theoretical) or empirical (average) number of points (retail locations) within a radius d around any single (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. Ripley (1981) Kulldorff's D 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). Kulldorff (1998) Mi A normalization of Kulldorff's D statistic that better enables comparisons across retail categories by the 90% Monte Carlo confidence intervals to scale Kulldorff's D values. This paper Table 4. Pattern Membership Criteria Pattern Membership Criteria Hyper agglomeration Mi > 1 for all quintiles agglomeration Mi > 1 for the first and/or second quintile, but not all five, and no quintiles have Mi < -1 Auto mall Mi > 1 for the first and/or second quintile, and Mi < -1 for at least one of the third, fourth, or fifth quintiles Avoidance Mi < -1 for at one quintile, and Mi is never greater than one. No pattern Default, the criteria for membership is not met for any pattern. 5. Agglomeration Patterns Exhibited by Different Retail Types Retail with Same Nonrandom Spatial Pattern in Vancouver and Calgary Hyper Agglomeration Local Agglomeration Auto Mall Pattern Avoidance Furniture Carpets New Gas Stations Antiques Children’s Clothing Boat Dealers Supermarkets Coffee Shops Clothing Health and Diet Art Galleries Pizza Parlors Smoking Supplies Liquor, Beer, Wine
ClusterAvoidGA.docx