Table 1 List of sample quality weights
Standardized ratio weights (wS, ij) | Zero-to-one weights (wP, ij) | |
|---|---|---|
\( {w}_{S1}={\left({\sigma}_g^2+{s}_{ij}{\widehat{\tau}}_g^2\right)}^{-1} \) \( {w}_{S2}={\left({s}_{ij}{\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right)}^{-1} \) \( {w}_{S3}={\left({s}_{ij}\left({\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right)\right)}^{-1} \) \( {w}_{S4}={2}^{-\left({\sigma}_{ig}^2+{s}_{ij}{\widehat{\tau}}_g^2\right)} \) \( {w}_{S5}={2}^{-\left({s}_{ij}{\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right)} \) \( {w}_{S6}={2}^{-\left({s}_{ij}\left({\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right)\right)} \) | \( {w}_{P1}\in \left\{{2}^{-{s}_{ij}},0.01{\overset{\sim }{p}}_{ij}\right\} \) \( {w}_{P2}={\left({\sigma}_{ig}^2+\left(1-{w}_{P1}\right){\widehat{\tau}}_g^2\right)}^{-1} \) \( {w}_{P3}={\left(\left(1-{w}_{P1}\right){\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right)}^{-1} \) \( {w}_{P4}={\left(\left(1-{w}_{P1}\right)\left({\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right)\right)}^{-1} \) \( {w}_{P5}={\left({\sigma}_{ig}^2+{\widehat{\tau}}_g^{2\left({w}_{P1}\right)}\right)}^{-1} \) \( {w}_{P6}={\left({\sigma}_{ig}^{2\left({w}_{P1}\right)}+{\hat{\tau}}_g^2\right)}^{-1} \) \( {w}_{P7}={\left({\left({\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right)}^{\left({w}_{P1}\right)}\right)}^{-1} \) | \( {w}_{P8}={2}^{-\left({\sigma}_{ig}^2+\left(1-{w}_{P1}\right){\widehat{\tau}}_g^2\right)} \) \( {w}_{P9}={2}^{-\left(\left(1-{w}_{P1}\right){\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right)} \) \( {w}_{P10}={2}^{-\left(\left(1-{w}_{P1}\right)\left({\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right)\right)} \) \( {w}_{P11}={2}^{-\left({\sigma}_{ig}^2+{\widehat{\tau}}_g^{2\left({w}_{P1}\right)}\right)} \) \( {W}_{P12}={2}^{-\left({\sigma}_{ig}^{2\left({w}_{P1}\right)}+{\widehat{\tau}}_g^2\right)} \) \( {w}_{P13}={2}^{-\left(\left({\sigma}_{ig}^2+{\widehat{\tau}}_g^2\right){w}_{P1}\right)} \) |