Dear stata users,

I am utilizing a a cross sectional dataset and a multinomial logit model (MNL) to compute the probability of undertaking a set of different investment types by firms localized in a certain country.

I have two questions in merit.
The first one refers to how I can measure the variability within groups. That is, after running a standard MNL and obtaining non significant estimates, I re-estimate the MNL clustering the firms by region (first) and province (after) to obtain, in both cases, a significant improvement in the level of significance of the estimates. This could hence entail that the within group variability exerts a significant effect.
However, contrary, e.g., to fixed effects model where u_ is reported (residuals within groups), in the MNL (and in probit models in general) I do not have such an information when I use the option vce(cluster).
In light of this, I was wondering how to analyze the within group variance of the two clustered specifications, to see which one is better (instead of using, e.g., the BIC criteria). Is there a way to obtain the sigma u_ in the MNL? How can I study the variance within clusters? Is there perhaps a graphical way from which I could derive some insights?

Secondly, I noticed that when I compute the marginal effects (form the MNL using the vce(cluster) option) sometimes, I obtain the coefficient estimates, whereas some other times (repeating exactly the same commands) I don't obtain anything, since I am reported that the "variance matrix is nonsymmetric or highly singular". Why does Stata report these two different outcomes in a random way?

Many thanks.

Jack