Table 1. Data reduction and structural equations model.

	Principal components analysis: data reduction step
Eq. A.1	$Ferriti{n}_{(i)}={\mu }_{a1}+{\lambda }_{(i)a1}Iro{n}_{st}+e_{(i)a1}$
Eq. A.2	$T{S}_{(i)}={\mu }_{a2}+{\lambda }_{(i)a2}Iro{n}_{st}+e_{(i)a2}$
Eq. B.1.	$FO{L}_{serum}{}_{(i)}={\mu }_{b1}+{\lambda }_{(i)b1}OneCarb+e_{(i)b1}$
Eq. B.2.	$B-{12}_{(i)}={\mu }_{b2}+{\lambda }_{(i)b2}OneCarb+e_{(i)b2}$
Eq. B.3.	$tHc{y}_{inv}{}_{(i)}={\mu }_{b3}+{\lambda }_{(i)b3}OneCarb+e_{(i)b3}$
Eq. B.4.	$MM{A}_{inv}{}_{(i)}={\mu }_{b4}+{\lambda }_{(i)b4}OneCarb+e_{(i)b4}$
Eq. C.1.	$Vit{A}_{(i)}={\mu }_{c1}+{\lambda }_{(i)c1}Antiox+e_{(i)c1}$
Eq. C.2.	$Vit{E}_{(i)}={\mu }_{c2}+{\lambda }_{(i)c2}Antiox+e_{(i)c2}$
	Structural Equations Model
Eq. 1.	$H{p}_s={\beta }_{01}+{\displaystyle \sum _{i=1}^k{\beta }_{1i}{W}_i}+{\varepsilon }_1$
Eq. 2.	$Iro{n}_{st}={\beta }_{02}+{\beta }_{12}H{p}_s+{\displaystyle \sum _{i=1}^k{\beta }_{2i}{W}_i}+{\varepsilon }_2$
Eq. 3	$OneCarb={\beta }_{03}+{\beta }_{13}H{p}_s+{\beta }_{23}Iro{n}_{st}+{\displaystyle \sum _{i=1}^k{\beta }_{3i}{W}_i}+{\varepsilon }_3$
Eq. 4	$Antiox={\beta }_{04}+{\beta }_{14}H{p}_s+{\beta }_{24}Iro{n}_{st}+{\beta }_{34}OneCarbon+{\displaystyle \sum _{i=1}^k{\beta }_{4i}{W}_i}+{\varepsilon }_4$