Results of the simulation study: The table shows the bias, root mean square error (RMSE), 95% credible intervals (CI) width and coverage for the ME, H2M and H2Mjoint.

The bias and RMSE are substantially reduced for all the 6 pollutant coefficients using H2Mjoint / H2M. Coverage improves and at the same time width of the 95% credible interval increases, suggesting that the uncertainty is larger for the hierarchical two-component modelling framework, as expected, given that this comes also from the pollutant component. The comparison of H2Mjoint with H2M shows how the influence of the outcome helps reduce the bias, while at the same time the uncertainty does not increase.