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Urban Start-up Agglomeration and Venture Capital Investment (view source)
Revision as of 20:04, 18 November 2020
, 20:04, 18 November 2020→Heuristic Layer
However, the inflectionlayer is really meaningless. The sign of the second central switches back and forward due to integer effects and I can't find a straight forward algorithm to pick the "correct" candidate from the set of results. Picking the '''first one''', which I currently pick, is completely arbitrary. There are a bunch of examples of the curves and the issue(s) in Results3-4.xlsx sheet 'Inflection'. I expect that if I put a bunch of time into this I could come up with some change thresholds to rule candidate answers in or out, but even then this isn't a good method.
Ultimately, the individual city-year inflection curves (i.e., across layers within a city-year) are just way too noisy. A variant of this noise problem is what makes the elbow method so problematic, but the noise is even worse with the inflection method. Using the heuristic result above (i.e., the one using all city-years) solves this noise problem by aggregating city-years together.
One complaint made about the heuristic results is that it is near the middle (i.e., it's 48.7717%, which happens to be near 50%). Although the nature of any HCA on geographic coords implies that the result is unlikely to the close to the bounds (0 or 100%) and more likely to be near the middle (50%), it could be in an entirely different place. '''This result (i.e., the heuristic layer at 48.7717%) characterizes the agglomeration of venture-backed startup firms'''. You'd get a very different number if you studied gas stations, supermarkets, airports, or banana plantations!
