Table 2

Results from the multilevel (s)PLS analyses regressing the four exposures (predictors) against the 13 assayed proteins (response). Results are presented for the PLS analyses, for sparse PLS models performing variable selection on exposures (sPLS on X), on proteins (sPLS on Y) and on both exposures and proteins sPLS on X and Y. We report in the table the loadings coefficients for the (s)PLS components of exposures (top table) and proteins (bottom table). For the (sPLS) components of exposures, we report the per-component proportion of variance (in both X and Y) explained, and for components of the proteins we only report the proportion of the variance in Y. For all sparse PLS models, results are only presented for the first PLS component, which is the only one to be retained according to the Q² criterion (see methods)

	PLS				sPLS on X	sPLS on Y	sPLS on X and Y
Exposures (X matrix)	C _1X	C _2X	C _3X	C _4X	C _1X′	C _1X″	C _1X‴
CHCl₃	− 0.50	− 0.60	− 0.60	− 0.17	− 0.48	− 0.50	-0.48
BDCM	−0.52	−0.21	0.45	0.70	−0.67	−0.52	−0.66
DBCM	−0.51	0.11	0.51	−0.68	−0.57	−0.51	−0.58
CHBr₃	−0.46	0.76	−0.42	0.15	0.00	−0.46	0.00
Explained Variance in X	94.8%	4.5%	0.6%	0.04%	94.0%	94.8%	94.0%
Explained Variance in Y	10.1%	1.3%	1.9%	1.3%	10.4%	14.2%	16.1%
Protein levels (Y matrix)	C_1Y	C_2Y	C_3Y	C_4Y	C_1Y'	C_1Y'’	C_1Y'’’
CCL2	0.12	0.195	−0.09	−0.02	0.13	0.00	0.00
IL-8	0.31	0.062	0.19	0.12	0.32	0.30	0.29
EGF	−0.10	0.216	−0.38	−0.11	−0.09	0.00	0.00
MPO	−0.14	0.310	0.18	0.05	−0.13	−0.02	0.00
VEGF	0.21	−0.266	−0.11	−0.36	0.20	0.13	0.11
IL-17	0.03	0.169	0.20	0.22	0.03	0.00	0.00
CCL22	0.42	−0.131	−0.32	−0.09	0.41	0.44	0.43
G-CSF	0.05	−0.079	−0.41	−0.43	0.05	0.00	0.00
CCL11	0.29	0.221	−0.27	−0.16	0.30	0.26	0.26
CRP	0.19	0.367	−0.11	−0.53	0.20	0.09	0.11
CXCL10	0.57	0.121	−0.05	0.46	0.57	0.68	0.67
Periostin	−0.18	−0.318	−0.31	−0.08	−0.18	−0.08	−0.08
IL-1ra	−0.38	−0.627	0.52	−0.28	−0.40	−0.39	−0.41
Explained Variance in Y	19.7%	6.9%	19.5%	23.3%	19.8%	17.7%	17.4%

Results are presented for the PLS analyses, for sparse PLS models performing variable selection on exposures (sPLS on X), on proteins (sPLS on Y) and on both exposures and proteins sPLS on X and Y. We report in the table the loadings coefficients for the (s)PLS components of exposures (top table) and proteins (bottom table). For the (sPLS) components of exposures, we report the per-component proportion of variance (in both X and Y) explained, and for components of the proteins we only report the proportion of the variance in Y. For all sparse PLS models, results are only presented for the first PLS component, which is the only one to be retained according to the Q ² criterion (see methods).
BDCM, bromodichloromethane; CCL11, C-C motif chemokine 11, CCL2 motif, chemokine (C-C motif) ligand 2; CCL22, C-C motif chemokine 22; CHBr₃, bromoform; CRP, C reactive protein; CHCl₃, chloroform; CXCL10, C-X-C motif chemokine 10; DBCM, dibromochloromethane; EGF, epidermal growth factor, G-CSF, granulocyte colony-stimulating factor; IL, interleukin; MPO, myeloperoxidase; PLS, partial least squares; sPLS, sparse partial least squares; VEGF, vascular endothelial growth factor.