Here we propose a fast but approximate approach for estimating the distribution parameters, , in equation 16. First, we assume high degrees of freedom at the first-level, i.e. for all . We then obtain a point estimate of , and use this point estimate to compute a point estimate of . For the details of how we obtain these point estimates and , see appendix 10.7.
We then make the assumption that the effect of uncertainty in
is the same as the effect of uncertainty in
in a first-level model. This means that
is a multivariate non-central t-distribution: