[R-sig-ME] Specifying outcome variable in binomial glmm: single responses vs cbind?

[a y]

What is the difference between fitting a binomial glmm (without random item
effects) in the following two ways?

1.
Data formatted in the following way:

(data_long)
ID    correct    condition    itemID
1      1             A               i1
1      0             A               i2
1      1             A               i3
1      1             A               i4
2      0             B               i1
2      1             B               i2
2      1             B               i3
2      0             B               i4

Fitting a model without item random effects:

glmer(correct ~ condition + (1|ID), family = binomial, data = data_long)


2.
Data formatted this way (summing over the correct responses):

(data_short)
ID     sum_correct    condition     itemID
1       3                      A                NA
2       2                      B                NA

Fitting the following model, assuming there were only 4 items  (I've seen
dozens of examples like this):
glmer(cbind(sum_correct, 4 - sum_correct) ~ condition + (1|ID), family =
binomial, data = data_short)

---
I figured these models should be identical, but in my experience they are
very much not. What am I missing? When is the second (more) appropriate?

Thanks for any help,
Andrew

	[[alternative HTML version deleted]]