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About calculation of the gravity model in R and STATA software

I am not the person to answer your question, but have some suggestions:

Make your examples reproducible so others can confirm your results and explore other issues you may not have seen. [1] [2] 

Post your question on the R-sig-mixed mailing list, where mixed models experts hang out, instead of here where the R language is on topic rather than contributed packages like glmm.

I don't know SAS or the glmm package, but the fact that the top description line for the glmm package says it uses Monte  Carlo suggests to me that it might not be "standard" in SAS or R and that your results may vary depending on how you configure it and how the random number seed is initialized. 

[1] http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example
[2] See also the Posting Guide mentioned at the bottom of this and every email on this list.