# [R] glm specification where response is a 2col matrix

Prof Brian Ripley ripley at stats.ox.ac.uk
Tue Jan 11 19:01:02 CET 2011

```Your first model is a binomial glm witb 4 observations of 6,6,4,4
trials.

Your second model is a Bernoulli glm with 20 observations of one trial
each.

The saturated models are different, as are the likelihoods
(unsurprising given the data is different): the binomial model has
comnbinarial factors (e.g. choose(10,5)*choose(6,3)*choose(4,2)) that
the Bernoulli model does not have, so the AICs differ.

I am not sure where these issues of aggregating Bernoulli trials is
explained (nor am I near my books), but this is a common question.

On Tue, 11 Jan 2011, Uwe Ligges wrote:

> Hi,
>
> when I apply a glm() model in two ways,
> first with the response in a two column matrix specification with successes
> and failures
>
> y <- matrix(c(
>    5, 1,
>    3, 3,
>    2, 2,
>    0, 4), ncol=2, byrow=TRUE)
>
> X <- data.frame(x1 = factor(c(1,1,0,0)),
>                x2 = factor(c(0,1,0,1)))
>
> glm(y ~ x1 + x2, data = X, family="binomial")
>
>
> second with a model matrix that full rows (i.e. has as many rows as real
> observations) and represents identical data:
>
>
> Xf <- data.frame(x1 = factor(rep(c(1,1,0,0), rowSums(y))),
>                 x2 = factor(rep(c(0,1,0,1), rowSums(y))))
> yf <- factor(rep(rep(0:1, 4), t(y)))
>
> glm(yf ~ x1 + x2, data = Xf, family="binomial")
>
>
> we will find that the number of degrees of freedom and the AIC etc. differ --
> I'd expect them to be identical (as the coefficient estimates and such things
> are).
>
> maybe I am confused tonight, hence I do not file it as a bug report right
> away and wait to be enlightened ...
>
>
> Thanks and best wishes,
> Uwe

--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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