a simple question I suspect. I have a logistic model with a count predictor (#times some event happened) as a predictor of a binary outcome. Am I correctly interpreting the odds ratio as 'the constant and linear increase in the likelihood of being in the category coded as a '1' on the outcome for each additional event'..?

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    $\begingroup$ Unless I misunderstand you that is the usual interpretation. Do you have some specific doubt which makes you ask? $\endgroup$ – mdewey Jan 10 '17 at 17:06
  • $\begingroup$ You have the basic concept of the interpretation correct, but many of the details are incorrect (i.e. "...linear increase in the likelihood..."). See @Kodiologist's answer for more specifics. $\endgroup$ – Cliff AB Jan 10 '17 at 17:28
  • $\begingroup$ Thanks all - yes, my question was specifically about the constant nature of the effect over each integer increase in the predictor - is it technically correct to say 'constant and linear'..? $\endgroup$ – Marina_ANOVA Jan 10 '17 at 20:43
  • $\begingroup$ @Marina_ANOVA No, a constant function and a linear function are two different things. $\endgroup$ – Kodiologist Jan 11 '17 at 13:17

Pretty much. More precisely, if the coefficient is $a$, then the model says that each occurrence of the event increases the log odds of the outcome by $a$.

Transforming from the logs-odds scale to the odds scale (which is probably easier to imagine), the model dictates that each occurrence multiplies the odds by $e^a$.

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  • $\begingroup$ Ok thanks again for the responses but they have left me more confused... I am talking specifically about the odds ratio interpretation, not the logistic coefficient. Isn't the odds ratio already on an odds scale (e.g. already transformed from log-odds?). So the interpretation is a linearly increasing constant function of OR? (the odds of being in the outcome category = 1 increases by OR for each 1 unit increase in the predictor?). $\endgroup$ – Marina_ANOVA Jan 11 '17 at 16:45
  • $\begingroup$ "Isn't the odds ratio already on an odds scale" — Yes. "a linearly increasing constant function" — No, see my comment on the question. "1 increases by OR for each 1 unit increase in the predictor" — No, the relationship is multiplicative, not additive. $\endgroup$ – Kodiologist Jan 11 '17 at 18:15
  • $\begingroup$ @Marina_ANOVA: also, odds $\ne$ likelihood $\endgroup$ – Cliff AB Jan 11 '17 at 20:00

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