I am working with a cross-classified MLM where there are three non-hierarchically nested effects: Geo1 Geo2 and Time (repeated cross-section). My interest is with a predictor at the Geo1 level and I seek to control for all Geo2 and Time variance. Hence, I am using fixed effects (i.e. dummies) at these levels.

My questions are:

- If I use MCMC and cross-classified models (additive) I need to specify these three levels and will have random effects at Geo2 and Time, but at the same time also fixed effects for Geo2 and Time are included. What is the consequence of this for the standard errors and estimates? Intuitively, I would -perhaps naively- think that because of the inclusion of the dummies, the random effects wont do anything?

I have also experimented with a multiplicate cross-classified model where I have spelt out all random terms that could arise as a product of Geo1 Geo2 and Time. By mistake, I estimated a model where I included both fixed and random effects at the Geo2*Time level. The random-effects parameters for this turned out 20times as large as all others, something I have also observed in the previous point when only using Geo2 and Time fixed and (cross-classified) random effects. What's driving this surprising explosion?

Thank you in advance for your guidance.

Best

J