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Table 1 Summary of the Monte-Carlo simulation study.

From: An evaluation of R2 as an inadequate measure for nonlinear models in pharmacological and biochemical research: a Monte Carlo approach

s.d = 0.01 Model R 2 adj AICc Akaike weights BIC resVar red. Chi 2
  L5 0.99999471 -156.22 0.0818 -156.35 0.00009933 0.9924
  L4 0.99999471 -158.36 0.2389 -158.33 0.00009935 0.9930
  L3 0.99999470 -160.20 0.5969 -160.33 0.00009959 0.9927
  B5 0.99999258 -147.31 0.0010 -147.44 0.00013945 1.4739
  B4 0.99975702 -57.72 0.0000 -57.69 0.00456696 42.5939
  B3 0.99959911 -47.29 0.0000 -47.42 0.00734455 63.5805
  W4 0.99853046 -10.89 0.0000 -10.85 0.02762048 282.3939
  W3 0.99829856 -7.91 0.0000 -8.04 0.03336157 334.1353
  baro5 0.99999471 -156.21 0.0814 -156.34 0.00009936 0.9927
s.d = 0.02 L5 0.99997869 -119.98 0.0774 -120.11 0.00040059 0.9946
  L4 0.99997868 -122.13 0.2273 -122.10 0.00040068 0.9959
  L3 0.99997871 -124.06 0.5954 -124.19 0.00040007 0.9957
  B5 0.99997653 -117.49 0.0224 -117.62 0.00044108 1.1135
  B4 0.99974038 -56.14 0.0000 -56.11 0.00487955 11.4098
  B3 0.99958227 -46.30 0.0000 -46.43 0.0076527 16.6958
  W4 0.99851513 -10.64 0.0000 -10.61 0.02790803 71.2971
  W3 0.99828395 -7.71 0.0000 -7.84 0.03364791 84.1649
  baro5 0.99997869 -119.98 0.0775 -120.11 0.00040044 0.9956
s.d. = 0.05 L5 0.99986676 -72.33 0.0765 -72.46 0.00250459 0.9897
  L4 0.99986656 -74.44 0.2194 -74.41 0.00250829 0.9904
  L3 0.99986662 -76.34 0.5674 -76.47 0.00250720 0.9882
  B5 0.99986439 -71.87 0.0608 -72.00 0.00254924 1.0096
  B4 0.99962966 -47.44 0.0000 -47.40 0.00696139 2.6343
  B3 0.99946832 -40.44 0.0000 -40.57 0.00973888 3.4859
  W4 0.99839915 -8.85 0.0000 -8.81 0.03009194 12.3020
  W3 0.99817327 -6.21 0.0000 -6.34 0.03582530 14.3447
  baro5 0.99986669 -72.32 0.0759 -72.45 0.00250592 0.9902
s.d. = 0.1 L5 0.99947371 -36.57 0.0742 -36.70 0.00989448 0.9984
  L4 0.99947362 -38.73 0.2180 -38.70 0.00989607 0.9972
  L3 0.99947374 -40.62 0.5618 -40.75 0.00989674 0.9972
  B5 0.99947135 -36.46 0.0701 -36.59 0.00993888 1.0037
  B4 0.99923746 -29.03 0.0017 -28.99 0.01433573 1.4052
  B3 0.99907025 -26.35 0.0004 -26.48 0.01703305 1.6200
  W4 0.99800791 -3.50 0.0000 -3.47 0.03745226 3.8282
  W3 0.99779177 -1.55 0.0000 -1.68 0.04333951 4.3370
  baro5 0.99947355 -36.56 0.0737 -36.69 0.00989740 0.9982
s.d. = 0.2 L5 0.99786138 -0.07 0.0675 -0.20 0.04025347 0.9948
  L4 0.99785879 -2.18 0.1942 -2.15 0.04030142 0.9940
  L3 0.99785563 -4.04 0.4930 -4.17 0.04035658 0.9928
  B5 0.99785959 -0.05 0.0668 -0.18 0.04028754 0.9960
  B4 0.99762513 0.49 0.0512 0.52 0.04470201 1.1027
  B3 0.99740761 0.20 0.0592 0.06 0.04751535 1.1543
  W4 0.99640798 11.41 0.0002 11.44 0.06760434 1.6764
  W3 0.99625943 11.71 0.0002 11.58 0.07350697 1.8059
  baro5 0.99786149 -0.07 0.0676 -0.20 0.04025146 0.9941
s.d. = 0.4 L5 0.99160836 35.58 0.0490 35.45 0.15887711 0.9987
  L4 0.99157911 33.50 0.1387 33.53 0.15941969 0.9981
  L3 0.99158878 31.58 0.3613 31.45 0.15928956 0.9980
  B5 0.99154493 35.68 0.0466 35.55 0.15991031 1.0001
  B4 0.99135309 34.16 0.0996 34.19 0.16370200 1.0242
  B3 0.99098926 32.68 0.2084 32.55 0.16621846 1.0372
  W4 0.99017401 37.58 0.0180 37.61 0.18602148 1.1663
  W3 0.99028174 36.53 0.0305 36.40 0.19208006 1.1995
  baro5 0.99159379 35.62 0.0480 35.49 0.15915529 0.9989
  1. Six different magnitudes of gaussian noise (low: s.d. = 0.01, 0.02; medium: s.d. = 0.05, 0.1; high: s.d. = 0.2, 0.4) were added to the fitted data of a three-parameter log-logistic model (L3). Nine different sigmoidal models were fit by nonlinear least-squares to the perturbed data and different measures for the goodness of fit (see Materials & Methods) averaged after all 2000 iterations. From the AICc values, Akaike weights were calculated in order to obtain the weight of evidence of the models.