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This question is more about the math terminology than about the math itself. Say we have x = logit(p). If one says "logit scale" does he mean:

  1. the scale of p, or
  2. the scale of x, i.e. the scale of logit(p)?

The same principle would probably apply if I asked about "log scale", right?

Thank you very much!

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I think I see how "bgins" missed the point in his or her answer, but I also would hesitate to reply to the question that you appear to intend without knowing the context in which the term is used. My guess, so far, is that (2) is right. But it may be just a guess until I see the context. – Michael Hardy Feb 2 '12 at 13:55
@MichaelHardy, the context is a GLM, where you logit transform the probability to do regression: logit(p) = a*x + b and then you speak about parameters "on a logit scale"... – Tomas Feb 2 '12 at 14:04
@MichaelHardy, thanks, please post this as an answer, I'll accept. – Tomas Feb 2 '12 at 17:24
up vote 1 down vote accepted

It is the possibility 2, i.e. the term "log scale" or "logit scale" refers to the scale of the function's output, not to the scale of its input parameter.

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Logit and Log scale are different. Both involve transforming by an increasing function, hence preserving the notion of scale. See the graphs at these links. $\text{logit}(p)=\log(\frac{p}{1-p})$.

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OMG... people still misunderstand this question. It is so simple, much simpler than you think! I know the scales are different!!! Please, don't focus on the math behind the functions and just answer the terminology question I've asked. Is it the option 1) or 2)? Many thanks! – Tomas Feb 2 '12 at 13:08

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