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Table 1 An example of using posterior samples from model development data analysis for prediction in a new cluster

From: Prediction models for clustered data with informative priors for the random effects: a simulation study

Posterior from model development data      Prediction for new cluster c
Iteration      Subject 1 Subject nc
k \( {\overset{\sim }{\beta}}_0^{(k)} \) \( {\overset{\sim }{\beta}}_1^{(k)} \) \( {{\overset{\sim }{\sigma}}_u^2}^{(k)} \) \( {\widehat{u}}_c^{(k)} \) a x 1 c \( {\widehat{p}}_{1c}^{(k)} \) b \( {x}_{n_cc} \) \( {\widehat{p}}_{n_cc}^{(k)} \) b
. . . . . . . . . .
. . . . . . . . . .
5001 −1.35 1.07 1.17 .50 1.11 .58 −.46 .21
5011 −1.24 1.08 .88 −1.89 1.11 .13 −.46 .03
5021 −1.36 1.18 1.28 −.06 1.11 .47 −.46 .12
5031 −1.31 1.05 .98 −.64 1.11 .31 −.46 .08
5041 −.94 .98 1.37 .26 1.11 .60 −.46 .24
. . . . . . . . . .
. . . . . . . . . .
Median       .52    .15
  1. arandom effect sampled from the normal distribution \( N\left(0,{{\overset{\sim }{\sigma}}_u^2}^{(k)}\right) \)
  2. bpredicted risk calculated by \( {\widehat{p}}_{\mathrm{sc}}^{(k)}=\frac{1}{1+\exp \left(-{\overset{\sim }{\beta}}_0^{(k)}+{\overset{\sim }{\beta}}_1^{(k)}{x}_{sc}+{\widehat{u}}_c^{(k)}\right)} \)