Table 1 Imputation based approach of mediation analysis.
W | \(W^{*}\) | \(M^{w^{*}}\) | \(Y^{w^{*}, M^w}\) | ||
|---|---|---|---|---|---|
1st dataset | \(w_1\) | \(w_1\) | \(M^{w_1}\) | \(Y^{w_1, M^{w_1}} = Y_1\) | Fit \(\mathbb {E}(Y\, \vert \, w, m, \pmb {c})\) using first dataset |
\(w_2\) | \(w_2\) | \(M^{w_2}\) | \(Y^{w_2, M^{w_2}} = Y_2\) | ||
\(\vdots\) | \(\vdots\) | \(\vdots\) | \(\vdots\) | ||
\(w_n\) | \(w_n\) | \(M^{w_n}\) | \(Y^{w_n, M^{w_n}} = Y_n\) | ||
2nd dataset | \(w_1\) | \(w^{*}_1\) | \(M^{w^{*}_1}\) | \(Y^{w^{*}_1, M^{w_1}} = \mathbb {E}(Y_1 \, \vert \, w^{*}_1, M_1, \pmb {c})\) | Predict counterfactual outcome using the fitted model |
\(w_2\) | \(w^{*}_2\) | \(M^{w^{*}_2}\) | \(Y^{w^{*}_2, M^{w_2}} = \mathbb {E}(Y_2\, \vert \, w^{*}_2, M_2, \pmb {c})\) | ||
\(\vdots\) | \(\vdots\) | \(\vdots\) | \(\vdots\) | ||
\(w_n\) | \(w^{*}_n\) | \(M^{w^{*}_n}\) | \(Y^{w^{*}_n, M^{w_n}} = \mathbb {E}(Y_n\, \vert \, w^{*}_n, M_n, \pmb {c})\) |
