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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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    @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"...2012-02-02

2 Answers 2

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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!2012-02-02