Insufficient convergence in mixture Generalized Partial Credit Model

[abeeisnotabug]

Thanks a lot for your replies!

@bbbales2

Here’s a recent thing by @yuling on trying to get around this by focusing on predictive performance that might be relevant: https://arxiv.org/abs/2006.12335 .

That is an interesting read. However, do you think this solution applies in my case? It seems like a method to get inferences from chains that behave well when taken separately but explore different modes of the posterior. However, in my case, the chains all sample from roughly the same area of the posterior but do so too fuzzily. For example, split Rhats for the \lambda_1 parameter in model 7 for every chain are:

1.05 1.00 1.03 1.00 1.01 1.01 1.03 1.04

@bbbales2

For instance, what happens if you drop the ‘c’ index from \alpha, \theta, and \beta? Then the only mixture component parameter is \lambda_c. Are you able to simulate and recover parameters from that model?

This is something I should explore again. Interestingly, when I started, I restricted the \theta parameters to be equal across groups (i.e. dropping the c). When I loosened that restriction, it vastly improved the fit, however. This is how I got Rhats even close to 1.

@bbbales2

Also do a non-centered parameterization for these (it’s just usually the right decision):

target += normal_lpdf(alpha_times_beta_raw[c, k] | 0, alpha[c, k]);
target += normal_lpdf(alpha_times_mu_beta[c, k] | 0, alpha[c, k]);

Would you mind expanding on that a little? I suppose you mean reparameterizing in a way that there are no model parameters in the priors? This would inadvertently mean splitting up the \alpha from alpha_times_.... such that we have

target += normal_lpdf(beta_raw[c, k] | 0, 1);
target += normal_lpdf(mu_beta[c, k] | 0, 1);

and then alpha * (mu_beta + beta_raw) in the model. But the combination was done to improve the fit in the first place, as I asked about in this thread (Convergence depending on parameterization of discrimination parameter in the GPCM). Is there a way to both non-centralize and remove the multiplicative identifiability issue?

Thanks again for your help!