Priming nonlinear searches for pathway identification

Table 4 The effect of the size of the perturbation

	Computed	5 %	10 %	50 %	200 %
a10	0	0.0000	0.0000	0.0001	0.0008
a11	-14.6780	-14.3647	-14.1817	-13.1496	-11.3439
a12	0	-0.1466	-0.1429	-0.0671	0.5735
a13	7.3390	7.3414	7.3438	7.3598	7.3735
a14	0	-0.2165	-0.3673	-1.2462	-2.7619
a15	-7.3390	-7.1723	-7.0780	-6.4846	-5.2501
a20	0	0.0000	0.0000	0.0000	-0.0003
a21	14.6780	14.6119	14.5748	14.4207	14.5029
a22	-14.6780	-14.6540	-14.6623	-14.7503	-15.1862
a23	0	-0.0009	-0.0016	-0.0054	-0.0070
a24	0	0.0494	0.0839	0.2494	0.3462
a25	0	-0.0309	-0.0464	-0.1119	-0.0951
a30	0	0.0000	0.0000	0.0004	0.0038
a31	0	-2.3527	-4.5412	-18.2307	-46.8953
a32	0	1.3989	2.6336	9.8422	24.4004
a33	-27.2517	-27.9204	-28.5955	-34.0204	-54.4047
a34	0	1.7491	3.4009	14.0961	39.3252
a35	0	-0.9955	-1.8949	-7.0627	-15.4759
a40	0	0.0000	0.0000	-0.0001	0.0001
a41	0	2.0843	3.7814	14.7316	41.5863
a42	0	-1.0925	-1.7693	-5.5766	-13.2688
a43	18.5664	19.0295	19.4964	23.2397	37.1866
a44	-18.5664	-20.2112	-21.6608	-31.4631	-58.1065
a45	-9.2832	-8.3594	-7.6404	-3.2226	6.5808
a50	0	0.0000	0.0000	-0.0001	-0.0015
a51	0	-0.4026	-0.6581	-2.5848	-10.1097
a52	0	0.1384	0.0830	-0.1317	0.1582
a53	0	-0.0059	-0.0110	-0.0435	-0.0879
a54	18.5664	18.8987	19.1602	21.0620	27.2722
a55	-18.5664	-18.7852	-18.9201	-20.0013	-24.0836

Overall, the estimated coefficients deviate more strongly from the corresponding computed values as the perturbation increases. However, there are substantial differences between variables. The coefficients associated with variable X₂, for example, are hardly influenced, while the coefficients associated with X₃ are strongly affected. Overall, the method seems to produce the best results for perturbation up to 10%. The datasets for the regression consisted of 401 data points in the interval [0,4] and the method of linearization was option II.

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