In these less-stable cases, there seemed to be an interaction between the variance and the choice between head conventions.
instead of parameterizing the objective in Section 2.4 in terms of multiple sets of weights, one at each node in the phylogeny (the hierarchical parameterization, described in Section 2.4), it is equivalent to parameterize this same objective in terms of a single set of weights on a larger of group features (the flat parameterization).