A Typology of Spatial Patterns The Kulldorff's plots are very informative with respect to clustering/avoidance patterns for a particular D retail type in a particular city. To compare and contrast the patterns of 108 plots across 54 retail types in two cities without information overload, we next classify the results into a limited number of categories. Two complications arise when doing this. First, the absolute value of the Kulldorff's statistic that is D likely to be outside a Monte Carlo confidence interval for a given distance varies systematically with the proportion of cases to controls. The more cases—the number of outlets of a store type—the smaller the value of that is likely to be viewed as just barely significant clustering or avoidance. We develop a D measure (Mi) that addresses this problem by normalizing the value of the Kulldorff's statistic by the D upper or lower 90% confidence limits. Specifically, for taken at distance the measure is D i, Mi calculated as (4) is the 95th percentile confidence level for the Kulldorff's statistic, and is the fifth DiU D DiL percentile confidence level at distance Thus, measures the proportion of the confidence interval i. Mi attained by Di. A second problem is that the Kulldorff's statistic is a continuous measure over distance. D Creating a typology is facilitated by converting it to a more discrete measure. We address this issue by calculating at 200 meter intervals for each retail category in each city. This results in 50 values for Mi each category, which, while retaining interesting detail, is too many to easily summarize with a parsimonious categorization scheme. Inspection of how rapidly the plots change with distance and how much they differ from each other suggest that the main discriminating features of the spatial distributions could be captured with a data point every two kilometers. This resolution reduces the number of values characterizing each store type to five, which is both manageable and retains the overall location structure of the store types. Thus, the values were averaged over each 2 kilometer quintile of the 10 kilometer Mi range. These five values are then used to classify retail store types.
A Typology of Spatial Patterns The Kulldorff's D plots are very informative with respect to clustering/avoidance patterns for a particular retail type in a particular city. To compare and contrast the patterns of 108 plots across 54 retail types in two cities without information overload, we next classify the results into a limited number of categories. Two complications arise when doing this. First, the absolute value of the Kulldorff's D statistic that is likely to be outside a Monte Carlo confidence interval for a given distance varies systematically with the proportion of cases to controls. The more cases—the number of outlets of a store type—the smaller the value of D that is likely to be viewed as just barely significant clustering or avoidance. We develop a measure (Mi) that addresses this problem by normalizing the value of the Kulldorff's D statistic by the upper or lower 90% confidence limits. Specifically, for D taken at distance i, the measure Mi is calculated as (4) DiU is the 95th percentile confidence level for the Kulldorff's D statistic, and DiL is the fifth percentile confidence level at distance i. Thus, Mi measures the proportion of the confidence interval attained by Di. A second problem is that the Kulldorff's D statistic is a continuous measure over distance. Creating a typology is facilitated by converting it to a more discrete measure. We address this issue by calculating Mi at 200 meter intervals for each retail category in each city. This results in 50 values for each category, which, while retaining interesting detail, is too many to easily summarize with a parsimonious categorization scheme. Inspection of how rapidly the plots change with distance and how much they differ from each other suggest that the main discriminating features of the spatial distributions could be captured with a data point every two kilometers. This resolution reduces the number of values characterizing each store type to five, which is both manageable and retains the overall location structure of the store types. Thus, the Mi values were averaged over each 2 kilometer quintile of the 10 kilometer range. These five values are then used to classify retail store types.
ClusterAvoidGA.docx