A H C van Kampen asks:
> -----Original Message-----
> From: AHC van Kampen [mailto:a.h.vankampen@amc.uva.nl]
> Sent: Friday, August 01, 2003 1:45 AM
> To: s-news
> Subject: [S] logistic regression
>
> Hi,
>
> I'm new to logistic regression and therefore this stupid question:
>
> What I have understand from logistic regression is that the binary
> response variable is transformed to log(p/(1-p)).
[WNV] This is NOT the case and the origin of your dilemma. The
whole point of logistic regression is that it does not transform the
response, but in effect it transforms the parameter. The model is, for
binary responses,
Y ~ B(1, p) where log(p/(1-p)) = X beta.
We now estimate beta by maximising the likelihood, which is where
the iteration comes in.
It's not such a silly question because in the old days they did
transform the response and this is why probit analysis (before the Fisher
appendix to the Bliss paper in 1936) required binomial responses with n >>
1.
> 1) How is the fraction p calculated for an individual response value (0 or
> 1). Probably, if for a certain predictor value only 1 response is
> available the fraction is aslo always 1 or 0, or is the fraction p
> calculated a pre-specified range for a predictor value?
[WNV] After beta is estimated (by b, say) the probabilities p may
be estimated as exp(X b)/(1 + exp(X b)).
> 2) I'm analysing the Kyphosis dataset that comes with Splus. How are these
> binary response values transformed and how can i check in Splus how this
> was done. Is there any variable that contains the transformed response
> values?
[WNV] They are not transformed. Simple.
There is quite a good book on this kind of stuff, by the way.
Bright yellow and blue cover, Springer, chapter 7 I believe. Can't remember
the title right now, though...
> Any help is appreciated
>
> --
> ---------------------------------------
> | Dr. Antoine H. C. van Kampen |
> | Academic Medical Center Amsterdam |
> | Bioinformatics Laboratory |
> | K2-211 |
> | Postbus 22660 |
> | 1100 DD Amsterdam, the Netherlands |
> -------------------------------------------------|
> | Phone: ++31-20-5667096 |
> | Mobile 06-10213310 |
> | Email: a.h.vankampen@amc.uva.nl |
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