Hierarchical LKJ priors

Hi all,

Does it make sense to hierarchically model the \eta parameters for multiple correlation matrices modeled with LKJ priors? For instance, for i \in 1, 2, ..., N, could the following make sense, with some reasonable priors on \mu and \sigma?

\begin{aligned} \log \left( \eta_i \right) &\sim \operatorname{Normal} \left( \mu, \sigma \right) \\ \Omega_i &\sim \operatorname{LKJ} \left( \eta_i \right) \end{aligned}

Thanks!

Matt