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Urban Start-up Agglomeration and Venture Capital Investment (view source)
Revision as of 20:37, 8 November 2020
, 20:37, 8 November 2020→Another list of items
1 and 2 are now done. 3 has some comparisons in the do file/log file, in terms of hull counts, hull areas, number of startups in hulls, hull densities, etc. We should absolutely use these (the medians and the means?) but I will also build some layer index scatter plots. I think I'll also try to render some city-year (perhaps Portland-2018) using each of the lenses too. I haven't done the heatmap(s) yet.
====Comparing the Methods====
Summaries of the meta-data on geometries created by each lens is probably the best method of comparison. These are in the do file:
. //Compare how their lenses look:
. tabstat nohull tothullcount tothullarea tothulldensity growthinv18 numdeals numstartups if regmaxr2==1, stats(p50
> mean sd N min max p10 p90) columns(statistics)
variable | p50 mean sd N min max p10 p90
-------------+--------------------------------------------------------------------------------
nohull | 2 3.531407 7.07922 2977 1 68 1 6
tothullcount | 8 17.4565 35.65118 2977 3 380 3 30
tothullarea | 14.76523 448.029 2063.824 2977 .0049029 34780.04 .5275311 732.4005
tothullden~y | .7640136 11.32988 63.62256 2977 .0002282 1425.338 .0115537 16.15439
growthinv18 | 33.53101 142.5 561.6696 2977 0 22282.6 1.53118 309.0208
numdeals | 3 6.71347 17.06682 2977 0 275 0 15
numstartups | 16 41.28955 89.98027 2977 6 1317 7 90
----------------------------------------------------------------------------------------------
. tabstat nohull tothullcount tothullarea tothulldensity growthinv18 numdeals numstartups if regheur1==1, stats(p50
> mean sd N min max p10 p90) columns(statistics)
variable | p50 mean sd N min max p10 p90
-------------+--------------------------------------------------------------------------------
nohull | 2 4.305768 8.498714 3797 0 119 1 9
tothullcount | 8 20.27153 43.51017 3797 0 675 3 43
tothullarea | 11.43336 49.81455 159.0983 3797 0 2569.169 1.661926 94.14735
tothullden~y | .9422739 3.452804 10.89704 3797 0 212.8198 .06182 7.47113
growthinv18 | 31.8453 133.0608 508.1196 3797 0 22282.6 1.235763 292.4397
numdeals | 2 6.629181 16.46614 3797 0 275 0 15
numstartups | 15 38.74743 83.6814 3797 6 1317 7 83
----------------------------------------------------------------------------------------------
. tabstat nohull tothullcount tothullarea tothulldensity growthinv18 numdeals numstartups if regelbow==1, stats(p50
> mean sd N min max p10 p90) columns(statistics)
variable | p50 mean sd N min max p10 p90
-------------+--------------------------------------------------------------------------------
nohull | 2 3.152638 3.973168 3374 0 48 0 7
tothullcount | 12 37.32721 87.6828 3374 0 1303 0 91
tothullarea | 55.78572 898.919 3849.938 3374 0 74067.25 0 1589.324
tothullden~y | .169715 31.79024 1726.042 3374 0 100257.3 0 1.841935
growthinv18 | 36.56511 146.5069 537.3532 3374 0 22282.6 1.816288 326.6357
numdeals | 3 7.232662 17.32508 3374 0 275 0 16
numstartups | 17 42.33225 88.08184 3374 6 1317 7 98
----------------------------------------------------------------------------------------------
Another way to compare the methods is to look at the layers they select. This is visible in a box plot as well as summary statistics. The following is from ResultsV3.xlsx
'''Separate Samples (All Available City-Years)'''
{| class="wikitable" style="vertical-align:bottom;"
|- style="font-weight:bold;"
! Method
! N
! Avg Layer Index
! Std. Dev Layer Index
|-
| Maximum R2
| 3080
| 39%
| 18%
|-
| Startups in Clusters Inflection
| 6,743
| 35%
| 16%
|-
| Variance Explained Elbow
| 4,799
| 43%
| 30%
|}
'''Using Common City-Years'''
{| class="wikitable" style="vertical-align:bottom;"
|- style="font-weight:bold;"
! Method
! N
! Avg Layer Index
! Std. Dev Layer Index
! L Index < Peak
! L Index < Max R2
! X < Max R2
|-
| Maximum R2
| 2662
| 40%
| 24%
| 0
| 2662
|
|-
| Startups in Clusters Inflection
| 2662
| 44%
| 5%
| 1102
| 167
| 6%
|-
| Variance Explained Elbow
| 2662
| 31%
| 22%
| 53
| 297
| 11%
|}
[[File:BoxPlot.PNG|left|300px]]
Finally, we can look at a city where different methods select different layers and look at those layers:
[[File:Cincinnati2018_Level8of25(VarianceExplainedElbow).png|300px]][[File:Cincinnati2018_Level12of25(FractionInHullsInflection).png|300px]][[File:Cincinnati2018_Level16of25(MaximumR2).png|300px]]
====Implementing the '''Real Elbow Method'''====
