You should direct your inquiry to R-help, not to me personally. I am
taking the liberty of cc-ing my reply back to the list.
I really haven't the time at the moment to think the issue through
thoroughly, but off the top of my head: If you are going to use
weighted log likelihoods then any comparison of models that you engage
in should involve the *same* weights, otherwise you doing the good old
apples-with-oranges thing.
So yes, the weights will change the log-likelihood and the AIC. And so
they should. And if you use AIC to compare models which are
meaningfully comparable (id est, have the same weights) this is not a
problem.
As I say, this is off the top of my head. Others older (???) and wiser
than I may correct me.
cheers,
Rolf Turner
On 05/02/14 11:56, IamRandom wrote:
I am trying to do weighted Poisson regression. I have count data.
Simple example:
set.seed(50)
x=seq(0,1,length=100)
y=numeric(100)
y[seq(1,100,by=2)]=round(exp(1.5*x[seq(1,100,by=2)]+rnorm(50,0,.1)),0)
y[seq(2,100,by=2)]=round(exp(1.5*x[seq(1,100,by=2)]+rnorm(50,0,1)),0)
weigh1=numeric(100)
weigh1[seq(1,100,by=2)]=rep(5,50)
weigh1[seq(2,100,by=2)]=rep(1,50)
The -2*loglikelihood of both of these regressions is the same with lm,
which makes sense. The scaling of the weights does not affect the
log-likelihood.
>-2*logLik( lm(y~x, weights=weigh1))[1]
>-2*logLik( lm(y~x, weights=weigh1/3))[1]
The -2*loglikelihood of these two regressions are different with glm:
> -2*logLik(glm(y~x, family="poisson", weights=weigh1))[1]
> -2*logLik(glm(y~x, family="poisson", weights=weigh1/3))[1]
This means that the AIC and other model comparison techniques with this
weighted Poisson regression are dependent on the scaling of the
weights. So I assume I misunderstand what the "weights" are doing in
the glm function.
-Tracy
On 2/4/2014 12:56 PM, Rolf Turner wrote:
On 04/02/14 20:12, IamRandom wrote:
I am running a simple example of GLM. If I include weights when
family="poisson" then the weights are calculated iteratively and
$weights and $prior.weights return different values. The $prior.weights
are what I supplied and $weights are the "posterior" weights of the
IWLS. If I include weights with family="gaussian" then the weights are
static and $weights and $prior.weights return the same values; it seems
to ignore IWLS algorithm procedure. I really want the family="poisson"
to behave like the family="gaussian" and use the static weights.
Thoughts?
As far as I understand things, your desideratum makes no sense. The
prior weights and the just-plain-weights are very different creatures.
The reason they wind up being the same for the gaussian family is that
for the gaussian family the likelihood is maximized by least squares;
there is no need for iteration or for re-weighting.
The poisson family cannot behave like the gaussian family because for
the poisson family (or any family *other* than gaussian) iteration is
necessary in order to maximize the likelihood.
You might get some insight into what's going on if you were to read
Annette Dobson's book "An Introduction to Generalized Linear Models"
(Chapman and Hall, 1990).
cheers,
Rolf Turner
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