[R-sig-ME] Comparing models with different random effects

[Gang Chen]

Suppose that there are multiple task types (Task) and each task type
is represented with a few questions (Item). And all subjects (Subj)
answer the same questions (Item).

How do I compare a model with (1 | Subj) + (1 | Item) versus one with
(1 | Subj) + (1 | Subj:Item) in lmer()? Through AIC/BIC (assuming the
fixed effect remain the same)? Would it make more sense to consider (1
| Subj) + (1 | Subj:Item) + (1 | Item)?

Is (1 | Subj) considered as nested within (Task | Subj)?

Thanks,
Gang