# Reporting three-level multilevel model results

#1

I estimated a three-level multilevel model looking like the following: y_{ijt} = \beta_{0ij} + X'b + \varepsilon_{ijt}. Where I modelled the \beta_{0ij} parameter using non-centered parameterization. So it looks like \beta_{0ij} = \beta_0 + \xi_{i}\tau_1 + \zeta_j\tau_2, where \xi_{i} and \zeta_j are standard normal distributed. So in this case \beta_{0ij} \sim N(\beta_0, (\tau^2_1 + \tau^2_2)). Now, I want to report the results of my model in a paper. However, I am not exactly sure what is the best way to do it. Is it the best way to just report the mean \beta_0 and the variance (\tau^2_1 + \tau^2_2)? Or does someone else has an idea how I can report this?
Next to that, I have some doubts whether the variance of \beta_{0ij} really equals (\tau^2_1 + \tau^2_2) or am I missing some parts now?

Any help is really appreciated!

#2

Maybe consult this tutorial:
http://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/11-concepts-example.pdf