# Does logistic regression with a count predictor imply a monotonic function on the outcome?

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'..?

• Unless I misunderstand you that is the usual interpretation. Do you have some specific doubt which makes you ask? – mdewey Jan 10 '17 at 17:06
• 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. – Cliff AB Jan 10 '17 at 17:28
• 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'..? – Marina_ANOVA Jan 10 '17 at 20:43
• @Marina_ANOVA No, a constant function and a linear function are two different things. – 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 $e^a$.
• @Marina_ANOVA: also, odds $\ne$ likelihood – Cliff AB Jan 11 '17 at 20:00