[R] Confidence Intervals for logistic regression

[Peter Dalgaard]

Michael Bedward wrote:
> On 7 August 2010 19:56, Martin Maechler wrote:
> 
>> I'm coming late to the thread,
>> but it seems that nobody has yet given the advice which I would
>> very *strongly* suggest to anyone asking for confidence
>> intervals in GLMs:
>>
>> Use  confint()
> 
> confint was actually mentioned in the second post on the thread :)
> But it's not what the OP is after.

Yep. The problem is that we cannot (yet? easily?) do confint on a
transformation of the parameters, hence not on the predicted values (on
whatever scale).

Another thing is that confint() isn't quite a cure-all because it relies
on the distribution of the (signed square root of) the LRT, and if that
is substantially different from chi-square(1) (or N(0,1)), then you
might still not obtain improved coverage, etc.

That being said, one should probably say that it is quite common to base
CI's on the linear predictor scale, and there's nothing REALLY wrong
with that procedure. As will have transpired by now, once you leave this
rather well-trodden road, you can easily find yourself in a rather
impenetrable thicket...

As far as I recall the asymptotics, all of the "+/- 2*se" procedures
have approximation errors of the same order as that caused by the
discrete distribution of the response, so it is not like one method is
going to "win" by orders of magnitude.

> Michael


-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com