In the modification proposed, an influence weight is assigned to each predictor in the conditioning set with the aim of identifying nearest neighbours that represent the conditional dependence in an improved manner.
Choosing the most suitable conditioning set for the various soils requires the use of a feasible laboratory test which can permit to define the characteristics of the conditioned soils and provide measurable data.
We feel that some of the continuous variables in our conditioning set, such as pre-program earnings and spell duration on the CPPD program, would be better candidates for confounders since they are proxies for otherwise unobserved variables.
Aakvik et al. (2005) also include some pre-program variables in the conditioning set in their analysis of the Norwegian VR program as do Dean et al. (2013a, b) in their study of VR in Virginia.
If a and b are dependent for every possible conditioning set, connect a and b with an undirected edge.
We set the maximum conditioning set size parameter max-k = 3 primarily because of the sample size limitations as described in the fourth paragraph of sub-section "Causal graph-based methods for selection of SNPs" in the revised manuscript.
Theorem 2 generalizes to arbitrary q ≥ 2, dim(G2) ≥ q, where G2 instruments Y2(0),…, Y2(q−1) with any subset of Z={ X2, G1, X1, Y1 0)} together with A12 as the conditioning set.
Suppose the CLR model for 4 pathogens, the first 2 in the set for which AF is to be estimated and the last two in the conditioning set, includes terms for all main effects and 2-way interactions (but not higher-order interactions), with coefficients bijkl for combination (ijkl).
□ Corollary Theorem 2 generalizes to arbitrary q ≥ 2, dim(G 2) ≥ q, where G 2 instruments Y 2(0),…, Y 2(q−1) with any subset of Z ={ X 2, G 1, X 1, Y 1 0)} together with A 12 as the conditioning set.
