Table 1.

The detailed subdivided result of decision coefficient

Subcategory/the secondary pathways	x i1	⋯	x ij	⋯	x it	⋯	x ip
Direct and indirect determination factor (b *j)2 and (2b *j r jt b *t) (j, t = 1, 2, ⋯, p; j ≠ t)	(b *1)2	⋯	2b *j r j1 b *1	⋯	2b *t r t1 b *1	⋯	2b *p r p1 b *1
	⋮	⋱	⋮	⋮	⋮	⋮	⋮
	2b *1 r 1j b *j	⋯	(b *j)2	⋯	2b *t r tj b *j	⋯	2b *p r pj b *j
	⋮	⋮	⋮	⋱	⋮	⋮	⋮
	2b *1 r 1t b *t	⋯	2b *j r jt b *t	⋯	(b *t)2	⋯	2b *p r pt b *t
	⋮	⋮	⋮	⋮	⋮	⋱	⋮
	2b *1 r 1p b *p	⋯	2b *j r jp b *p	⋯	2b *t r tp b *p	⋯	(b *p)2
DC (R (j))	R (1)	⋯	R (j)	⋯	R (t)	⋯	R (p)

r _jt (j, t = 1, 2, ⋯, p; j ≠ t) indicates the correlation coefficient x _ij and x _it. Obviously, the data satisfy r _jt = r _tj and $R_{\left(j\right)}={\left(b_j^{*}\right)}^2+2{\displaystyle \sum _{\begin{array}{l}t=1\\ j\ne t\end{array}}^p{b}_j^{*}{r}_{jt}{b}_t^{*}}$ according to the decision analysis method. In order to distinguish between the direct and indirect determination factor clearly, the direct determination factor has been indicated in bold italics