Nesting terminology in mixed models

Suppose I have the following nested lmer structure:

lmer(Y ~ X1 + X2 + X1:X2 + (1 | A) + (1 | A:B), data=d)


which is the same as:

lmer(Y ~ X1 * X2 + (1 | A/B), data=d)


Now if I would write it out in a report, I'd say something like:

Y modelled by X1 and X2 including the interaction of X1 and X2 (as the fixed effects) and B nested in A (as the random effects).

Both + (1 | A/B) and + (1 | A) + (1 | A:B) symbolize nesting and are equivalent. But how about when I don't want the effect of A to be estimated:

lmer(Y ~ X1 + X2 + X1:X2 + (1 | A:B), data=d)


Can I still simply say:

1. B nested in A (even though the random effect for A is now omitted?)

Or should it be:

2. B nested in A without the effect of A

Or since the : in the fixed effects part denotes for an interaction, could I potentially say:

3. The random effects part of the model was given as the interaction of A and B.

• "with a random intercept for every observed combination of A and B"? – conjugateprior Feb 22 '16 at 21:44
• @conjugateprior that's sounds perfect and is exactly what it is! Thanks! What do you think about naming it an "interaction"? – Stefan Feb 23 '16 at 1:22
• I think that'd be slightly confusing actually. You're just using R's interaction syntax to redefine a grouping variable, in a slightly more agnostic / less structured way than in previous specifications. fwiw the last time I did this was with countries and government ministries (also nested), so I referred to the country:ministry group as a 'work context'. – conjugateprior Feb 23 '16 at 14:32
• Thanks, that makes sense @conjugateprior . If you want to summarize your comments to an answer, I'd accept it. – Stefan Feb 23 '16 at 14:40