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

[a y]

I answered my own question, so feel free to disregard this topic.

On Fri, Jul 1, 2016 at 6:37 PM, a y <beermewi at gmail.com> wrote:

> 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
>

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