Model | Objective function |
---|---|
Conditional Std | \(\sum _l\frac{1}{2n_l} \sum _i I(L_i=l) \left( y_i - \beta _0^l - \sum _j{\tilde{A}}_{ij} \beta _j^l\right) ^2 + \sum _{l,j} p_{\lambda _l}(\beta _j^l)\) |
Select L | \(\frac{1}{2n} \sum _i \left( y_i - \beta _0 - L_i\beta _\ell - \sum _j {\dot{A}}_{ij} \beta _j\right) ^2 + \sum _j p_{\lambda }(\beta _j) + p_{\lambda }(\beta _\ell )\) |
Select L EffMod | \(\frac{1}{2n} \sum _i\left( y_i - \beta _0 - L_i\beta _\ell - \sum _{l,j} I(L_i=l) {\tilde{A}}_{ij}\beta _j^l\right) ^2 + \sum _l\sum _{j} p_{\lambda }(\beta _j^l) + p_{\lambda }(\beta _\ell )\) |
Require L | \(\frac{1}{2n} \sum _i \left( y_i - \beta _0 - L_i\beta _\ell - \sum _j {\dot{A}}_{ij} \beta _j\right) ^2 + \sum _j p_{\lambda }(\beta _j)\) |
Require L EffMod | \(\frac{1}{2n} \sum _i\left( y_i - \beta _0 - L_i\beta _\ell - \sum _{l,j} I(L_i=l) {\tilde{A}}_{ij}\beta _j^l\right) ^2 + \sum _l\sum _j p_{\lambda }(\beta _j^l)\) |
Ignore L | \(\frac{1}{2n} \sum _i \left( y_i - \beta _0 - \sum _j {\dot{A}}_{ij} \beta _j\right) ^2 + \sum _j p_{\lambda }(\beta _j)\) |
Ignore L EffMod | \(\frac{1}{2n} \sum _i \left( y_i - \beta _0 - \sum _{l,j} I(L_i=l) {\tilde{A}}_{ij} \beta _j^l\right) ^2 + \sum _l\sum _j p_{\lambda }(\beta _j^l)\) |