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Topic: Correct Offset in Logistic Regression
Replies: 4   Last Post: Dec 8, 2011 1:06 AM

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Posts: 31
Registered: 10/8/10
Re: Correct Offset in Logistic Regression
Posted: Dec 8, 2011 1:06 AM
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On Dec 7, 5:29 pm, R <> wrote:
> On Dec 7, 4:48 pm, Rich Ulrich <> wrote:

> > On Wed, 7 Dec 2011 08:07:23 -0800 (PST), R <> wrote:
> > [snip, a bunch]
> > >Here's the catch. I want to obtain the hand calculated rates from the
> > >parameter estimates derived from a standard binary logistic regression
> > >on the rolled out data.

> > >So,  I thought the correct approach would be to apply the logit
> > >transformation to x/100,000 before entering it into the linear
> > >predictor as an offset:

> > You don't ever "apply the logit transformation"  to anything
> > other than P/Q  where Q is 1-P.  That is the definition of a logit.
> > So if I understand what you are saying here, it is not sensible.

> > >offset= ln[x_per100,000 / (1 - x_per100,000)]
> > >(Note that if I use x_per1000, I am not able to calculate the x logits
> > >because I end up trying to take the natural log of a negative value.)

> >  ... and that is not correct arithmetic.
> > x as a rate per 100,000  is a 10 times larger number than the
> > same x per 10,000;  where the *latter*, in the example given, was a
> > fraction, and lets you compute that (meaningless) natural log.

> >  ... and, as a general principal, if your model leads you to taking
> > the log of a negative value (either for data-in-hand, or for
> > conceivable data), then you need a new model.

> > --
> > Rich Ulrich

> Hi Rich,
> Thank you for your reply.
> I misspoke by calling the term "x_per100000". It really is event per
> 100,000 x units. Regardless, the general question stands. Is it
> possible to obtain the desired "rate" via logistic regression? Suppose
> you were presented with the data above and were asked to obtain the
> probability of event per 1000 "x" units using parameter estimates from
> logistic regression. Clearly a log-binomial or poisson model would
> *work* by transforming x, ln(x/1000), and enetering it into the linear
> predictor as an offset. Can a transformation be applied to "x" such
> that one could obtain the same "rate" via logistic question?
> Ryan

Please disregard this thread. It wasn't fully thought through, and
there are far more direct, pragmatic ways to construct a model which
serve my purposes. It was really more of an intellectual exercise
which requires further thought.



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