In classic interpretation of logistic regression, We convert the coefficients to odds changes (using exponent). For example, if the coefficient is $1.0$, $\exp(1.0)=2.7$, we say the odds is $2.7$ times higher.

My question is that: can we talk in probability changes, using odd changes is still not convinenet? Say if the coefficient is $1.0$, the probability will increase or multiply or (other relationship) by $x$ amount?

I think the relationship is just plogis (as shown in plot), but how can I talk in English?

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    $\begingroup$ Because the rate of change of probability varies (tremendously) with the probability itself, you must first name a specific point on the curve. $\endgroup$ – whuber Nov 17 '16 at 14:17
  • $\begingroup$ @whuber so I should say like. Suppose we are at 0.5 probability, increase 1 unit of x will make odds 2.7 times larger, and make the probability change by $y$ amount? $\endgroup$ – Haitao Du Nov 17 '16 at 14:31
  • $\begingroup$ @whuber is the reason we talk about odds change because it can "automatically" consider the none linear relationship "different point on the curve"? $\endgroup$ – Haitao Du Nov 17 '16 at 14:38
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    $\begingroup$ In its ordinary form, with a logistic link function, logistic regression expresses probabilities in terms of a logistic function--that is, log odds. When you use a different link the probabilities will be expressed in some different way. Thus, the right way to interpret coefficients depends on the link function you use. $\endgroup$ – whuber Nov 17 '16 at 15:25

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