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Table 1 Specifications of the four models (simple linear regression and RE)

From: Use of Bayesian methods to model the SF-6D health state preference based data

Model Conditional Distribution Specification of the mean
M1- Linear regression Yi~N(μi, σ2)
εi~N(0, σ2)
μi = β0 + Parai
M2- Random effect Yij~N(μij, σ2)
\( {u}_i\sim N\left(0,{\upsigma}_u^2\right) \)
\( {e}_{ij}\sim N\left(0,{\upsigma}_e^2\right) \)
μij = β0 + Paraij + ui
M3- Random effect: intercept forced to unity Yij~N(μij, σ2)
\( {u}_i\sim N\left(0,{\upsigma}_u^2\right) \)
\( {e}_{ij}\sim N\left(0,{\upsigma}_e^2\right) \)
μij = Paraij + ui
M4- Random effect: intercept forced to unity and inclusion of most Yij~N(μij, σ2)
\( {u}_i\sim N\left(0,{\upsigma}_u^2\right) \)
\( {e}_{ij}\sim N\left(0,{\upsigma}_e^2\right) \)
μij = Paraij + βmostmostij + ui
  1. Paraij = βPF2PF2ij + βPF3PF3ij + βPF4PF4ij + βPF5PF5ij + βPF6PF6ij + βRL2RL2ij + βRL3RL3ij + βRL4RL4ij + βSF2SF2ij + βSF3SF3ij + βSF4SF4ij + βSF5SF5ij + βPAIN2PAIN2ij + βPAIN3PAIN3ij + βPAIN4PAIN4ij + βPAIN5PAIN5ij + βPAIN6PAIN6ij + βMH2MH2ij + βMH3MH3ij + βMH4MH4ij + βMH5MH5ij + βVIT2VIT2ij + βVIT3VIT3ij + βVIT4VIT4ij + βVIT5VIT5ij