# How to model the size of a trade area?

I would like to model the dimensions of the trade areas for a group of stores. I have geocoded sales data for each store, which I used to construct a convex hull using a GIS program. Essentially, I took the nearest 80 percent of sales for each store, and then snapped a rubber band around those points to get a trade area boundary for each store. Then I calculated the area of these regions, and modeled the radii as if the trade areas were circles, using the characteristics of the area right around the store as predictors. This gives terrible predictions since many of the areas are elliptical or have spike-like bulges. Does any one have any suggestions for how to model the shape and size of these regions in a better way?

• It all depends on what you mean by "trade area," which usually comes down to how you intend to use the result of the analysis. Could you elaborate on this? (Note that even a concept like "nearest 80% of sales" is ambiguous without specifying, in a quantitative way, how one set of locations contributing 80% of sales is considered "nearer" than another set.) – whuber Oct 26 '11 at 15:14
• I define z to be the sales divided by the straight line distance from the store. I rank the customers using z from largest to smallest. Then I grab customers based on this ranking until I have ~80% of total stores sales. I put a convex hull around all the customers that I've grabbed, but that hull will also include other customers that were not selected. I then trim the farthest customers in the hull until I get back down to 80% of sales. – Dimitriy V. Masterov Oct 26 '11 at 18:36
• OK, you have described a procedure that appears to estimate a region (although the "trim farthest customers" is a little vague, but I get the idea). But--because your question refers to predictions--we need a way to compare the results of your procedure to something real that it is attempting to estimate. Alternatively, we need to know what decisions will be made based on your predictions. Will you be siting stores? Closing stores? Targeting marketing campaigns? Estimating future revenues? Creating sales territories? Optimizing distribution and supply systems? Etc. – whuber Oct 26 '11 at 18:41
• 80% is just threshold, because I may have a few customers who live very far away, and I don't want them to be part of the trade area. I've also tried using higher % thresholds, which produced very large and jagged trade areas. I am trying to capture geographic area around the store that represents the closest 80%, while allowing important customers who are distant to enlarge that area somewhat. – Dimitriy V. Masterov Oct 26 '11 at 18:43
• I see. I would like to predict what a potential trade area might look like for a new store. I have a holdout set of stores that I can compare my predictions to the actual. I don't yet have a metric to compare my predictions with the actuals. – Dimitriy V. Masterov Oct 26 '11 at 18:46