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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 7, 2011 5:29 PM
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On Dec 7, 4:48 pm, Rich Ulrich <rich.ulr...@comcast.net> wrote:
> On Wed, 7 Dec 2011 08:07:23 -0800 (PST), R <br74...@yahoo.com> 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?


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