On Dec 7, 5:29 pm, R <br74...@yahoo.com> wrote: > 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? > > 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.