1
$\begingroup$

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'..?

$\endgroup$
  • 2
    $\begingroup$ 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
3
$\begingroup$

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 $e^a$.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.