On Jul 24, 2011, at 00:20 , Thomas Lumley wrote: > On Fri, Jul 22, 2011 at 8:00 PM, peter dalgaard <pda...@gmail.com> wrote: >> >> On Jul 21, 2011, at 23:11 , David Winsemius wrote: >> >>> >>> On Jul 21, 2011, at 3:38 PM, zlu wrote: >>> >>>> Hi Peter, >>> >>> I'm not sure how many people still have 9 month old postings on their mail >>> client and will know that Peter Dalgaard is the intended recipient. >>> >>>> Do you have any idea or codes of construct a score test based confidence >>>> interval for coefficients in logistic regression? >>> >>> I realize that Peter knows more than I about this, so take this as working >>> hypothesis and believe anything he says more than what I say. My idea: set >>> the glm control ..., maxit=1, so you only get one iteration and then use >>> the deviance results with the usual chi-square assuptions. I fear this >>> could be too easy or else Peter would have already thought of this dodge. >>> >> >> I did think along those lines but couldn't convince myself that it would >> work. Rather, what you need is the deviance (SSD) of the approximating >> weighted regression analysis. Anyways, anova(..., test="Rao") has been >> implemented in R-devel for a while. >> >> This doesn't do confidence intervals, though. That is a somewhat harder >> problem -- you'd basically need to redo the likelihood profiling code with a >> different criterion. >> >> For a slow and dirty technique, you could see if a parameter value beta0 is >> in the CI by including an offset of beta0*x and computing the score test for >> whether the shifted parameter (beta-beta0) is zero. Then use uniroot(). >> > > I think you basically have to do this computation. The problem is > that you may not find exactly two endpoints. For the deviance-based > intervals, a unimodal likelihood is sufficient to guarantee there are > exactly two places where the deviance differs from the maximum by the > desired amount.
Not quite, it could level off and never reach the amount. And I believe the unimodality needs to hold for the _profiled_ likelihood. Not sure it is actually guaranteed to be true for glm's with non-canonical links. > Things can be much messier when you are trying to > get the score divided by its estimated standard error to be 1.96. Yes. There is a similar issue with nonlinear regression models, although it seems that it is often not that big a problem in practice. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com "Døden skal tape!" --- Nordahl Grieg ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
