[Frank Sulley]

Erik, thanks a lot for your time and patience, I tried what you said with centering around the overall mean but unfortunately it doesn't work

. mixed helpfulness i.l_gender##c.mean_appereance i.l_specialty || lawyer_id: mean_appereance,  cov(un)

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log likelihood = -27301.857  
Iteration 1:   log likelihood = -27195.667  
Iteration 2:   log likelihood = -27195.563  
Iteration 3:   log likelihood = -27195.537  
Iteration 4:   log likelihood = -27195.531  
Iteration 5:   log likelihood = -27195.529  
Iteration 6:   log likelihood = -27195.529  
Iteration 7:   log likelihood = -27195.529  
Hessian is not negative semidefinite
r(430);

Sorry to ask, but when you say the following, is there any specific implication for the model that I am testing ? Does this small variance hamper either the choice of using a multilevel approach or the goodness of the results ?

• You have a tiny amount of variation in helpfulness between lawyers - they aren't that different from each other. This is reflected in the small variance estimate for lawyer _id of .02.

[Erik Ruzek]

The small lawyer_id variance tells you that there is a lot more within lawyer variation in client-reported helpfulness than there is between lawyer variation. That does not mean you need to abandon a multilevel model. How would you know this information otherwise? Nor does it invalidate the results at all. It's just a really important part of the story you need to tell.

In terms of centering not helping with your estimation problems, that is not the end of the world. I recommended it because I have seen that it can be helpful in these situations.

[Frank Sulley]

lot more within lawyer variation in client-reported helpfulness than there is between lawyer variation.

yeah, this is completely in line with my intuition that the reviewer gender (not observed) might further regulate the interaction effect (a la 3-way), and thus that would be more variation within lawyer than between.
But do you think I can still go ahead without the "cov(un)" test?

[Erik Ruzek]

Yes, you have little choice. It is not supported by your data.

[Frank Sulley]

Thanks Erik and everybody for the valuable info