CFA model cannot recover simulated values

[Chen_Chen]

@edm

Chen, constraining the Z ZZ to be non-negative is not a traditional identifiability constraint. It also makes your life difficult by leading to a truncated MVN. Instead, one would typically constrain a single loading per column (of W WW ) to be positive. I suspect that the non-negative Z ZZ could cause problems with parameter recovery, because that constraint does not allow any of the posterior distributions to overlap with 0. Some related discussion is here.

Hi Ed, Thanks for your information! I am sorry I forgot to mention that my constraining for Z is also based on domain knowledge. I work on biological data, Z is interpreted as a protein activity matrix, so it has to be non-negative. I guess this is a little like bayesian NMF. Do you know if any work successfully applied stan on bayesian NMF? I wonder how they deal with so many non-negative constraints?

@edm

About bad Pareto k and the conditional likelihood, I often see the same thing and do not know of a good solution. I think the problem is that the number of latent variables increases with the sample size.

I am glad you found the same thing! But if PSIS-LOO is not great for conditional likelihood, could you let me know what other model checking you usually use?

@edm

To speed up the marginal, it is helpful to write the multivariate normal lpdf via the mean vector and covariance matrix, and define a custom function using this form of the lpdf. Then you can compute a single marginal density across all the observations, instead of separately for each observation. This is what happens in newer versions of blavaan.

This sounds very interesting. I am not sure if I understand how to do it, but I will try to look at blavaan stan code.