st: xtmelogit: comparing models

[Luca Campanelli <l.campanelli@yahoo.it>]

Dear Stata users, 
I’d like to fit and compare mixed effects logistic regression models with crossed random effects using the function xtmelogit (Stata 12IC for Windows). 

For example (“group” has 2 levels[0,1] and “condition” has 3 levels[1,2,3]): 
(1) xtmelogit resp i.group i.condition , || _all: R.item, covariance(id)  || sbj: , covariance(id)
(2) xtmelogit resp i.group i.condition i.group#i.condition , || _all: R.item, covariance(id)  || sbj: , covariance(id)

In comparing two models, I found a big discrepancy between lrtest on one side, and AIC-BIC on the other side. lrtest was highly significant, indicating that (2) was better than (1), while AIC and BIC values were clearly smaller for model (1). 
Which should I trust? 

Does this apply to my case http://www.stata.com/support/faqs/statistics/likelihood-ratio-test/ ; ? 
If yes, how can I do the Wald test? 
Would it be: 
test 1.group#2.condition 1.group#3.condition

Is it correct? I saw others using testparm or lincom. 
I would appreciate any help to understand what the appropriate thing to do is. 

thank you, 
Luca

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/