Sample item group-specific variances through Gibbs sampler
sample_sigmasq(shape0, rate0, dist_mat, item_membership_list, locations)a numeric vector of G elements, each being the newly sampled variance of the latent location of this group
a vector of G elements, each being the shape of the Inverse-Gamma prior of group g
a vector of G elements, each being the rate of the Inverse-Gamma prior of group g
a list, containing the KxK tree-structured matrix of leaf nodes, where K is the number of leaves / latent classes, and SVD components
a vector of G elements, each indicating the number of items in this group
a KxJ matrix of leaf parameters