GLIMMIX subject coding

[cgdiver]

I have a three-level logistic model: individuals, couples, countries.  I need to nest the individuals within the couple, and the couples within the countries.  I have seen several different options for programming the subject term, including:

   random int / subject = couples;

   random int / subject = countries;

   random int / couples(countries);

   random int countries / subject = couples;

Can someone explain the difference and which would be best to use for my model? Thanks! 

Thanks!

[cgdiver]

Two quick additions. Another coding option I have seen:

   Random int / subject = countries

   Random int / subject = couples(countries)

Also, regardless of which coding option I use, there is one independent variable that is so highly associated with the binary outcome that the covariance parameter estimate for all random effects is zero. The intercept and fixed effect estimates do vary depending on the code I use. If the covariance parameters estimates are zero, does that suggest that nesting is not needed or does it mean there may be a broader problem with the model?