[R] Confidence Intervals for logistic regression

[Peter Dalgaard]

Michael Bedward wrote:
>> I was aware of this option.  I was assuming it was not ok to do fit +/- 1.96
>> se when you requested probabilities.  If this is legitimate then all the
>> better.
> 
> I don't think it is.  I understood that you should do the calculation
> in the scale of the linear predictor and then transform to
> probabilities.
> 
> Happy to be corrected if that's wrong.

Probably, neither is optimal, although any transformed scale is
asymptotically equivalent. E.g., neither the probability scale nor the
logit scale stabilizes the variance of a simple proportion (the arcsine
transform does), so test-based CIs should really be asymmetric in both
cases rather than just +/- 1.96se.

However, working on the linear predictor scale has the advantage that
CIs by definition will not cross the boundaries of the parameter space.
(For the "usual" link functions: logit, probit, cloglog, that is; it's
not true for the identity link, obviously.)

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