[R] score test for logistic regression

[peter dalgaard]

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().

-- 
Peter Dalgaard
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com