I have a functioning MMSBM for a single network….well maybe.
I had two issues – a mistake in which I constrained my model to only allow 3 groups (!) and an indentifiability issue between being in the same group and having decent within group probability vs. being in different groups and having high group-group probability. I changed the prior for the B entries so that diagonal entries are more likely to be large and off-diagonal probs are likely to be quite small.
A review of my 4 simulations. All have very high probability of belonging to one group; I am fitting more a blockmodel and MM model right now.
Test1Network N=50, 4 groups: These look great!
Test2Network N=100, 4 groups: These look awful. The only difference besides network size (which should help, right?) is the B-diag probabilities used to generate data are lower.
Test3Network N=50, 5 groups: These look better. The problem is that our results find only 4 groups. I wonder why the first turquoise group wasn’t broken up between other groups though.
Test4Network N=100, 5 groups: These look awful again. The off-diagonals for the B matrix are returning values close to the diagonals (giving us the identifiability issue again). Given a network this size, even a strong prior gets lost in the wash with the data.
Ideas: Use an even stronger prior, but the prior is depend on the network size. Use some type of truncated beta distribution to guarantee that off-diagonal probabilities are always orders of magnitude smaller.
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Regarding my HLSM, I wrote a function to adapt my tuning parameters so that I won’t have to do them manually. This should hopefully guarantee me acceptance rates between 0.35 and 0.65.
Made yet another mistake with my tuning function (this is another one of 100 or 1000 today?). Retesting now.