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Urban Start-up Agglomeration and Venture Capital Investment (view source)
Revision as of 17:56, 2 December 2020
, 17:56, 2 December 2020→New Work
We could instead use the forward first difference - this isn't available for the last observation (for which we can't compute a second central anyway) but is available for the first observation - and increment the answer, much as Jim proposes decrementing it when using the backward layer. But seeing as we can't use the first observation we've gained nothing anyway! So we'll do Jim's method verbatim, and declare the result null if it comes out as either the first or last layer.
====Curvature==== {{Colored box|title=Specification|content=For layer <math>l</math>, I compute the concavity curvature as -1 times the backward first difference in the variance explained ratio from layer <math>l+1</math> divided by the central second difference in the variance explained ratio from <math>l</math>. The first and last layers are forbidden results.}} The curvature results seem somewhat better than the elbow results. Here are some things I look for and/or don't like in a layer selection method:*Interior solutions are good, collapsing to the bounds, especially the lower bound is bad*Consistent solutions are good within cities - it's nice when adjacent years in the same city have more or less the same layer selected*Consistent solutions across cities are also good - When the method picks roughly similar layer indicies (i.e., % unclustered) across cities, particularly conceptually similar cities, that's a plus*From other analysis, I know that the equilibrium of agglomeration forces occurs when agglomerations have fairly small average hull sizes, perhaps on the order of 10hm2.
===Version 3.5 build notes===
