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I want to fit a logistic function of the form $$f(t) = \frac{C}{1+ab^{-t}}$$to some data that I have, using R.

There is some uncertainty to $f(t)$, and its magnitude is assumed to be constant. There is no uncertainty in $t$.

Answers to the question Logistic regression for bounds different from 0 and 1 mention that it's possible, but don't specify how. I am interested in estimating $C$, $a$ and $b$ and also $R^2$.

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Gimelist
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  • This question appears to be off-topic because it is about how to use R. – gung - Reinstate Monica Dec 11 '14 at 13:41
  • You should review the answer to [this question](http://stackoverflow.com/questions/15931403/modify-glm-function-to-adopt-user-specified-link-function-in-r) on SO. I believe this should help you get started and update your question with some initial attempts if you get stuck. – cdeterman Dec 11 '14 at 13:49
  • There are some statistical issues that ought to be addressed before one goes blindly about implementing a solution (as seems to be suggested by previous comments). Most importantly, almost all data are uncertain. What is the nature of the uncertainties in your data? Do they come primarily from a measurement error of $f(t)$? If so, can that error be considered of (roughly) constant magnitude across the entire dataset, or might it vary? If so, how would it vary? Is there a possibility that the values of $t$ are also uncertain? – whuber Dec 11 '14 at 14:51
  • @whuber - edited. – Gimelist Dec 11 '14 at 15:20
  • Thanks. You don't need a GLM with a custom link, then; you are probably fine with a nonlinear least-squares fit. You could, for instance, implement the solution I posted at https://stats.stackexchange.com/questions/32824, which seems to be exactly the same as your problem. Is there any aspect of your question that is not answered there? – whuber Dec 11 '14 at 15:30

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