Package Comparison Details, by dataset
Cranio Dataset
Comparing the Sage code base to the UCLA-based package, we see a difference in the selection of the 'soft threshold' (beta). The former picked a value of 4.0 and the latter 4.5. Both packages save the details of the optimization process:This is the output from the UCLA algorithm:):
Sage power table / UCLA power table (The optimum chosen by each is highlighted)
| Power | p-value | Adj R^2 | Truncated Adj R^2 | slope | mean(k) | median(k) | max(k) |
|
| Power | SFT.R.sq | slope | truncated.R.sq | mean.k. | median.k. | max.k. | |||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 1 | -1 | 0.707 | 0.991 | 1.18 | 700 | 700 | 1120 |
| 1 | 1 | 0.736501290349614 737 | 1.13578366310746 14 | 0.994431751751329 | 699.572313034948 | 699.648966320864 | 1116.02918233716 .994 | 700 | 700 | 1120 |
2 | 1.5 | -1 | 0.231 | 0.969 | 0.332 | 440 | 424 | 840 |
| 2 | 1.5 | 0.251519543919548 252 | 0.297533023504088 298 | 0.97937139813633 | 439.899479746776 | 423.612496822198 | 840.47949387766 979 | 440 | 424 | 840 |
3 | 2 | -1 | 0.0114 | 0.903 | -0.136 | 296 | 269 | 668 |
| 3 | 2 | 0.119730110387487 12 | -0.163692811558184 164 | 0.91713459200463 | 295.588422458769 | 268.94730085273 | 667.945223302198 917 | 296 | 269 | 668 |
4 | 2.5 | -1 | 0.523 | 0.921 | -0.444 | 209 | 178 | 549 |
| 4 | 2.5 | 0.622896623436384 623 | -0.491086993626836 491 | 0.900740857562872 | 208.537727229792 | 177.79413914117 | 549.155319758776 901 | 209 | 178 | 549 |
5 | 3 | -1 | 0.749 | 0.914 | -0.66 | 153 | 120 | 463 |
| 5 | 3 | 0.788460807596207 788 | -0.68266797986082 683 | 0.904 | 153 | 120 | 463 | |||
6 | 3.5 | -1 | 0.903728452209731 819 | 152 0.800323593864 892 | 120.243286725551 | 463.29082261878 -0.798 | 115 | 83.7 | 399 |
| 6 | 3.5 | 0.863229344305799 863 | -0.85737992139182 857 | 0.889320106067623 889 | 115 .448359595823 | 83.7476291500883 7 | 399 .156919651325 | ||
7 | 4 | -1 | 0.864 | 0.892 | -0.918 | 89.5 | 59.4 | 351 |
| 7 | 4 | 0.894834165325891895 | -0.951860705585135952 | 0.894194460202712894 | 89.4956876275135 | 59.4342800786908 350.910943247122 .4 | 351 | |||
8 | 4.5 | -1 | 0.884 | 0.888 | -1.01 | 70.9 | 42.2 | 313 |
| 8 | 4.5 | 0.906475253699557906 | -1.0432330433276704 | 0.88699005785024887 | 70.92241915934469 | 42.2148824089728 312.992004152579 2 | 313 | |||
9 | 5 | -1 | 0.879 | 0.872 | -1.08 | 57.3 | 30.5 | 283 |
| 9 | 5 | 0.917140610429364 917 | -1.08867663568657 09 | 0.893779632076047 894 | 57.2968574266249 3 | 30.4851790719122 282.652362917002 .5 | 283 | |||
10 | 5.5 | -1 | 0.887 | 0.878 | -1.12 | 47.1 | 22.6 | 258 |
| 10 | 5.5 | 0.902963257559623 903 | -1.12874378525066 13 | 0.876283735962727 876 | 47.0867813585159 1 | 22.5831735990022 257.887940247821 .6 | 258 | |||
11 | 6 | -1 | 0.872 | 0.864 | -1.14 | 39.3 | 16.8 | 237 |
| 11 | 6 | 0.893657667984861 894 | -1.138641996747 14 | 0.872082886273499 872 | 39.2934112572874 3 | 16.7925249162364 8 | 237 .362271809525 | |||
12 | 6.5 | -1 | 0.853 | 0.849 | -1.16 | 33.2 | 12.5 | 220 |
| 12 | 6.5 | 0.877096891199445 877 | -1.16563222664169 17 | 0.860765166816465 861 | 33.2467401837027 2 | 12.5431252833217 5 | 220 .116544465302 | |||
13 | 7 | -1 | 0.849 | 0.857 | -1.16 | 28.5 | 9.75 | 205 |
| 13 | 7 | 0.867836927064159 868 | -1.17261710771242 17 | 0.86332246600206 863 | 28.4861111749774 5 | 9.75194877632007 75 | 205 .448215921732 | |||
14 | 7.5 | -1 | 0.836 | 0.861 | -1.16 | 24.7 | 7.44 | 193 |
| 14 | 7.5 | 0.868548947706417 869 | -1.15942033025233 16 | 0.888456324814093 888 | 24.6879610646154 7 | 7.43724266918352 192.83304720061 .44 | 193 | |||
15 | 8 | -1 | 0.831 | 0.873 | -1.15 | 21.6 | 5.73 | 182 |
| 15 | 8 | 0.85993341256465 86 | -1.14979252940141 15 | 0.889730024616774 89 | 21.6207148555113 | 5.72770680062926 | 181.87355758458 .6 | 5.73 | 182 | |
16 | 8.5 | -1 | 0.807 | 0.87 | -1.15 | 19.1 | 4.43 | 172 |
| 16 | 8.5 | 0.839526774373017 84 | -1.1454863855111 15 | 0.889555649590024 89 | 19.1158525842939 1 | 4.42968785517107 43 | 172 .264089318976 | |||
17 | 9 | -1 | 0.78 | 0.858 | -1.14 | 17 | 3.49 | 164 |
| 17 | 9 | 0.828450334938823 828 | -1.12976930526696 13 | 0.896114026911798 896 | 17 .0489014282755 | 3.48574207332117 | 163.766610421789 | 3.49 | 164 | |
18 | 9.5 | -1 | 0.792 | 0.889 | -1.11 | 15.3 | 2.75 | 156 |
| 18 | 9.5 | 0.824533609394867 825 | -1.10327784158547 1 | 0.912422650093755 912 | 15.3266812705319 3 | 2.74605181254734 75 | 156 .193631947154 | |||
19 | 10 | -1 | 0.782 | 0.906 | -1.09 | 13.9 | 2.18 | 149 |
| 19 | 10 | 0.805943284944799 806 | -1.08884406876998 09 | 0.914807175372563 915 | 13.8785832450612 9 | 2.18328519701562 18 | 149 .395941841956 | |||
20 | 10.5 | -1 | 0.759 | 0.897 | -1.07 | 12.7 | 1.74 | 143 |
| 20 | 10.5 | 0.800039898486579 8 | -1.0763656575682 08 | 0.920931944553393 921 | 12.6505039786172 7 | 1.74424089765862 74 | 143 .266795277355 | |||
21 | 11 | -1 | 0.747 | 0.902 | -1.06 | 11.6 | 1.4 | 138 |
| 21 | 11 | 0.788808310243576 789 | -1.05656008289991 06 | 0.933254569845571 | 11.6005616530767 | 1.40321696471758 | 137.745622540377 933 | 11.6 | 1.4 | 138 |
22 | 11.5 | -1 | 0.752 | 0.914 | -1.04 | 10.7 | 1.14 | 133 |
| 22 | 11.5 | 0.779205608927366 779 | -1.03924741920651 04 | 0.935482608107987 935 | 10.696027985041 | 1.14073738236037 | 132.707798864861 .7 | 1.14 | 133 | |
23 | 12 | -1 | 0.743 | 0.924 | -1.01 | 9.91 | 0.926 | 128 |
| 23 | 12 | 0.779321654012786 779 | -1.02460870779617 02 | 0.947336705575843 947 | 9.91110282257499 91 | 0.925552317403238 128.118730788473 926 | 128 |
Both algorithms try to find the lowest power whose R^2 is above the given threshold (0.90). If no power achieves the threshold then the threshold is decremented repeatedly by 0.05 until a solution is found. Since the Sage version finds a maximum of 0.887, it carries out the decrementing procedure. The UCLA version finds three values just above 0.90, and picks the lowest.