Alignment of z

[hrlai]

It is hard to examine if archetype slopes $\beta_k$ are well estimated because of misalignment in $\mathbf{z}_j$, I think...

• Is this related to the ordering of columns in the latent variable part of a GLLVM?
• Although the order of archetype is not very meaningful to real data (because archetype is nominal, not ordinal), but it matters when we are testing our model on simulated data, and it also seems to cause chain flipping in MCMC

How do / should we "align" $\mathbf{z}_j$?

[hrlai]

See https://mc-stan.org/docs/stan-users-guide/mixture-inference.html

[hrlai]

See also Nick Golding's post https://forum.greta-stats.org/t/gmm-in-greta-is-non-identifiability-a-show-stopper-in-greta/71/15?u=hrlai

[hrlai]

Francis Hui provided a more useful link https://mc-stan.org/docs/stan-users-guide/label-switching-problematic.html