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

Spiess, Andrej-Nikolai; Neumeyer, Natalie

doi:10.1186/1471-2210-10-6

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

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.

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