Fighting Collinearity in QSPR Equations for Solution Kinetics with the Monte Carlo Method and Total Weighting

Elvas-Leitão, Ruben A.

doi:10.5935/0103-5053.20160097

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Journal of the Brazilian Chemical Society

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Articles • J. Braz. Chem. Soc. 27 (11) • Nov 2016 • https://doi.org/10.5935/0103-5053.20160097 copy

Fighting Collinearity in QSPR Equations for Solution Kinetics with the Monte Carlo Method and Total Weighting

Authorship SCIMAGO INSTITUTIONS RANKINGS

A Monte Carlo method is used in addition to functional and individual weighting to overcome multicollinearity problems in multiple linear regression equations applied as quantitative-structure-property-relationships, allowing the estimation of correct coefficient confidence intervals. The method was applied to rate constants for the Menschutkin reaction between Et₃N and EtI in mono- and di-alcohols, at 25.00 ºC. Results show that the use of our methodology produces a significant improvement upon confidence interval estimates regardless of the level of collinearity present. Addition of weighting shows additional advantages, increasing the overall consistency of the regression process.

Keywords:
Monte Carlo; multicollinearity; correlation; MLR

Solvent	k × 10⁵ / (mole fraction-1 s^-1)	σ(k) × 10⁵ / (mole fraction^-1 s^-1)	ε	n_D	π*	α	β	C × 10^-3 / MPa
Water	191.40	0.001	78.30	1.3330	1.13	1.16	0.50	2.307
Methanol	10.02	0.07	32.66	1.3284	0.6	1.09	0.73	0.887
Ethanol	5.151	0.009	24.55	1.3614	0.55	0.88	0.80	0.703
1-Propanol	2.686	0.012	20.45	1.3856	0.53	0.79	0.85	0.59
2-Propanol	4.079	0.008	19.92	1.3772	0.48	0.68	0.93	0.552
1-Butanol	1.968	0.017	17.51	1.3993	0.54	0.74	0.84	0.485
2-Butanol	3.231	0.012	16.56	1.3971	0.54	0.54	0.91	0.488
1-Pentanol	1.269	0.010	13.9	1.4100	0.5	0.73	0.88	0.497
2-Methyl-1-butanol	1.047	0.002	15.63	1.4088	0.51	0.64	0.93	0.482
3-Methyl-1-butanol	1.429	0.006	15.19	1.4072	0.48	0.74	0.91	0.497
1-Hexanol	0.819	0.03	13.30	1.4178	0.52	0.68	0.86	0.471
1,2-Ethanediol	18.842	0.140	37.7	1.4318	0.89	0.88	0.72	0.887
1,2-Propanediol	21.393	0.046	28.59	1.4324	0.76	0.83	0.78	0.881
1,3-Propanediol	49.69	0.02	34.98	1.4398	0.84	0.80	0.77	0.847
1,2-Butanediol	11.16	0.05	22.35	1.4378	0.71	0.80	0.71	0.600
1,3-Butanediol	16.70	0.02	28.57	1.4410	0.75	0.76	0.74	0.562
2,3-Butanediol	10.56	0.04	21.65	1.4310	0.75	0.68	0.88	0.602
1,5-Pentanediol	12.26	0.04	27.17	1.4494	0.76	0.70	0.82	0.603
Diethylene glycol	55.33	0.043	31.69	1.4475	0.92	0.72	0.67	0.615
Triethylene glycol	45.52	0.028	23.69	1.4558	0.88	0.66	0.69	0.48

r^²	π*	α	β	C
π*	1	0.1930	0.7513	0.4487
α	-	1	0.4861	0.6398
β	-	-	1	0.5425
C	-	-	-	1

r2	f(e)	g(n_D)	E_T^N	C
f(e)	1	0.0108	0.7952	0.6843
g(n_D)	-	1	0.0423	0.0430
E_T^N	-	-	1	0.7576
C	-	-	-	1

R²	β + α	α + C	C + β
π*	0.8043	0.4745	0.7535
	π* + β	π* + C	C + β
α	0.5956	0.6566	0.6653
	π* + α	α + C	π* + C
β	0.8754	0.5749	0.7954
	α + β	π* + β	π* + α
^eC	0.7020	0.5464	0.7654

R²	g(n_D) + E_T^N	g(n_D) + C	E_T^N + C
f(ε)	0.8954	0.7364	0.9063
	f(ε) + E_T^N	f(ε) + C	E_T^N + C
g(n_D)	0.0731	0.3583	0.4450
	f(ε) + C	g(n_D) + f(ε)	g(n_D) + C
E_T^N	0.9122	0.8080	0.8054
	g(n_D) + f(ε)	f(ε) + E_T^N	g(n_D) + E_T^N
C	0.6538	0.7712	0.7376

Method	Weights	a₀ ± σ(a₀)	a₁ ± σ(a₁)	σ_fit
Classical	No	-6.37 ± 0.21	3.33 ± 0.30	0.232
Monte Carlo	No	-6.37 ± 0.23	3.33 ± 0.28	0.232

Method	Weights	a₀ ± σ(a₀)	a₁ ± σ(a₁)	a₂ ± σ(a₂)	a₃ ± σ(a₃)	σ_fit
Classical	No	-26.4 ± 2.7	41.4 ± 6.4	10.9 ± 3.2	0.48 ± 0.22	0.22
Monte Carlo	No	-26.8 ± 2.0	41.2 ± 3.1	11.2 ± 2.0	0.47 ± 0.08	0.28
Δσ / %		-26	-53	-38	-64	-

Weights	n	a₀ ± σ(a₀)	a₁ ± σ(a₁)	a₂ ± σ(a₂)	a₃ ± σ(a₃)	σ_fit
Yes	20	-28.6 ± 1.2	46.2 ± 2.0	10.6 ± 1.8	0.44 ± 0.07	0.16
Yes	19	-26.9 ± 1.0	42.4 ± 1.0	9.7 ± 1.6	0.74 ± 0.02	0.09
No	20	-26.8 ± 2.0	41.2 ± 3.1	11.2 ± 2.0	0.47 ± 0.08	0.28
No	19	-29.6 ± 1.5	49.8 ± 2.2	9.8 ± 1.8	-0.44 ± 0.14	0.20

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