Notably in the first section of the base results, specifically with plotted lines comparing randomly generated and existing.

fits

A follow up question one might have after looking at this plot is: Is there any potential problem with randomly generated parcellations extending out beyond sizes 1000 whereas the existing based parcellations do not? The best way to answer this question is to compare the fits from the original results to fits on a set of truncated results considering parcellations of size only up to 1000.

First the base results:

OLS Regression Results
Dep. Variable: Mean_Rank R-squared: 0.901
Model: OLS Adj. R-squared: 0.899
Method: Least Squares F-statistic: 459.6
Date: Tue, 11 Jan 2022 Prob (F-statistic): 6.68e-100

coef std err t P>|t| [0.025 0.975]
Intercept 2.6119 0.015 171.406 0.000 2.582 2.642
C(Parcellation_Type)[T.Freesurfer Extracted] 0.0154 0.042 0.367 0.714 -0.067 0.098
C(Parcellation_Type)[T.Icosahedron] -0.0040 0.025 -0.159 0.874 -0.054 0.046
C(Parcellation_Type)[T.Random] 0.0485 0.009 5.597 0.000 0.031 0.066
Size -0.2774 0.007 -41.980 0.000 -0.290 -0.264

Truncated to 1000 results:

OLS Regression Results
Dep. Variable: Mean_Rank R-squared: 0.875
Model: OLS Adj. R-squared: 0.873
Method: Least Squares F-statistic: 316.0
Date: Mon, 03 Jan 2022 Prob (F-statistic): 3.29e-80

coef std err t P>|t| [0.025 0.975]
Intercept 2.6288 0.018 144.702 0.000 2.593 2.665
C(Parcellation_Type)[T.Freesurfer Extracted] 0.0148 0.043 0.343 0.732 -0.070 0.100
C(Parcellation_Type)[T.Icosahedron] -0.0347 0.035 -0.980 0.328 -0.105 0.035
C(Parcellation_Type)[T.Random] 0.0469 0.009 5.185 0.000 0.029 0.065
Size -0.2855 0.008 -35.225 0.000 -0.302 -0.270

The conclusion after a bit of squinting is pretty clear, there is no real difference, the fits stay quite simmilar.