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, rip...@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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