hi all,
I am fitting a logistic regression model on binary data. I care about
the fitted probabilities, so I am not worried about infinite
(or non-existent) MLEs. I use:
> glm(Y~., data=X, weights=wgt, family=binomial(link=logit), maxit=250)
I understand the three ways to fit model, and in my case Y is a factor,
one column
> Y <- c(rep("A",679), rep("B",38))
> Y <- as.factor(Y)
My question is about the weights. I can use integer weights, which
makes more mathematical sense, and
> wgt <- c(rep(1,679), rep(17,38))
or i can use
> wgt <- c(rep(38/679,679, rep(1,38))
which makes more sense for my problem, but the mathematic is weak as I am
using non integer successes in a bernoulli... I estimate the accuracy
'out of the bag' over 10000 experiments to get
| integer wgt | non-int wgt
-------- + -------------------- + --------------------
accuracy | A = 94.9% B = 82.3% | A = 94.7% B = 83.3%
std.dev. | 2.3% 15.4% | 2.6% 13.2%
avg. AIC | 707 | 124
As I understand, non-integer weights are more respectful of what I
observe since instead of augmenting the successes on the rare class, which
I did not observe, they simply down-weight the successes on the populus
class. The populations can be thought as equal, and only the sample sizes
are unbalanced.
Predictions also look better, so I was hoping that the continuity of the
Binomial for N in [0,1] ans X in [0,1] could guarantee me that my results
still make sense, but I am not sure. Any thoughts?
Thanks
Edo
