Item is nested within Task, and Item and Subj are cross factors, personally.
(1|Task/Subj) +(1|Subj)

to test the sig. of random factor :Item
(1| Subj) + (1 | Subj:Item) + (1 | Item)
(1| Subj) + (1 | Subj:Item)

to test the sig. of random interaction factor: (Item: Subj)
(1| Subj) + (1 | Subj:Item) + (1 | Item)
(1| Subj) +  (1 | Item)

It could make sense if you anova these two models, to find a better one.
(1 | Subj) + (1 | Item)
(1 | Subj) + (1 | Subj:Item)

2010/12/9 Gang Chen <gangchen6@gmail.com>

> 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
>
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