[R-sig-eco] Logistic Regression
Philip Dixon
pdixon at iastate.edu
Wed Jun 8 14:24:02 CEST 2011
Luiz,
Gavin gave a nice explanation. Another way to think about the issue is
to remember that Xb models the logit of the probability of predation.
When P[pred] = 0, the logit is -inf. Hence, the b coefficient for that
group is estimated at -inf (or usually something between -12 and -18,
because the software gives up and P[pred | Xb = -18] is numerically
indistinguishable from 0. This is still useful, because the b's for
other covariates still have meaning, even for that group with P[pred =
0]. If you look at predicted Xb's for obs in the group with P[pred =
0], you will see they are not exactly the same (on the Xb scale).
That's the effect of the other covariates. Those effects are estimated
from the observed covariate effect in other groups. When you
backtransform from Xb to P[pred], the predicted P[pred] are all
essentially 0, which is fine. So, use all the groups!
If you really want estimates of the coefficients, you should consider
regularizing, as suggested by Eric. There are Bayesian approaches and
penalized likelihoods, e.g., Firth's penalized likelihood. The Bayesian
approach is probably the easier to compute.
However, your e-mail suggested you fit this model to use in a model
comparison. All you need for model comparison is the lnL or something
derived from that (AIC, BIC, ...). The lnL is computed correctly even
if the estimate is -12 or -18 or -inf. If all you need is a model
comparison, no need to regularize.
Best wishes,
Philip Dixon
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