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#The elbow method is pretty questionable in its current form, so we are going to try using the elbow in the curvature (degree of concavity) instead.
#We might also try using elasticities...
#Rerun the distance calculations -- avghulldisthm and avgdisthm are only computed for layers that we select with some method (like max r2). However, this table hadn't been updated for the elbow method, perhaps as well as some other methods, so some distances would have been missing (and replaced with zeros in the STATA script).
#Create and run the new max R2 layer. In this variant, we'll use "the first layer a cluster number is reached as the representative layer for that cluster number"
I built two new curvature based elbow methods and so variables: curvaturelayer and curvaturelayerrestricted. They use the method described below and are identical except that curvaturelayerrestricted can't select layer 2 (both can't select the first and last layers as they use central second differences).
====Jim's notes on the curvature====

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