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I am having some problems interpreting the odds. I run a logistic regression for an out come 'Yes' or 'no'. My reference category is 'No'.

I have 2 variables and this are the log(odds) and the odds: Variable A -> It is a integer with values 2 to 80. logodds: -0.014078787; odds: 0.9860199 Variable B -> It is a integer with values 1 to 30. logodds: 0.214099984; odds: 1.2387465

What is a correct statement to interpret these odds?

And how do I transform this in real probabilities? I would like to say something like: Every extra point of variable A causes an decrease of x in the probabilities of going from 'No' to 'Yes' If I do exp(coef(model)) /(1+exp(coef(model))) for Variable A I obtain 0.49. This is the probability right? Is it correct to say that each point of variable A makes the probability go down 0.01%

I am really confussed about this so would thank any help!

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Remember that only the coefficient for the constant from logitsitc regression are log odds; the remaining coefficients are log odds ratios.

Lets say your baseline odds ($\exp(constant)$) is .8. This would mean that there are 0.8 people who say yes for every person who says no when all explanatory variables are 0. Your odds ratio for A says that a unit increase in A is associated with a 1% decrease in the odds of saying yes, while the odds ratio for B says that a unit increas in B is associated with a 24% increase in the odds of saying yes.

If you want your effects in terms of probabilities you can look up "marginal effects".

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  • $\begingroup$ But if my variable B is associated with a 24% increase in the odds and it is an integer ranging from 1 to 30, I would get more than a 100% increase with more than 4 units increase in B? $\endgroup$ – DroppingOff Jul 28 '14 at 13:57
  • $\begingroup$ It is not a straight line I gues. How can I plot it in R. $\endgroup$ – DroppingOff Jul 28 '14 at 13:58
  • $\begingroup$ Remember, when talking about odds ratios we are talking about odds not probabilities. The odds is the expected number of people who say yes per person who says no. So, the odds, unlike a probability, can be larger than 1; that just means that there are more people who say yes than there are people who say no. $\endgroup$ – Maarten Buis Jul 28 '14 at 14:13
  • $\begingroup$ How do I extract the marginal effects in R? I have done this: exp(coef(model)) /(1+exp(coef(model))) $\endgroup$ – DroppingOff Jul 28 '14 at 14:57
  • $\begingroup$ And I would like to plot the curve of the marginal effects. How can I do it in R? What I have tried does not work: plot(outcome ~ variableA, data=ml) $\endgroup$ – DroppingOff Jul 28 '14 at 14:58

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