I am currently working on modeling ANOVA using a Gaussian mixture model. In my model, I have included both fixed and random effects. I used a normal distribution for both the fixed and random effects. However, I encountered a problem where my model diverged when I set the sigma for the random effects to 5. Surprisingly, it converged when I set it to 0.005. I’m unsure whether this value is advisable or not.

We would need much more detail about your data and model to be able to say anything useful about your priors. Can you put together a small, self-contained example that demonstrates what you are seeing?

If your model diverged but still ran to completion, you can look at trace plots to see whether if what you are experiencing is a mixing problem. Some advised tricks of the trade are using Multivariate Normals if in higher dimensions, using ordering transformation on one of the coordinates, supplying initial conditions to your priors, using ‘advi+adapt_diag’ initialization. If these don’t remedy the mixing, you may need to restrict your priors or choose a coordinate system where ordering priors becomes more natural (for instance if you are in 2D and you can not really order your clusters based on x or y but each cluster seems to have different radius from some centre point then you may want to formulate the question in polar coordinates etc).