I am looking at the association between the application of animal control and population reduction. Population reduction is my outcome variable; it is a binomial variable where 1 = population reduction achieved, and 0 = population reduction not achieved. Animal control is my predictor variable and can be viewed in two different way; 1) control applied = 1 Vs control not applied = 0 (binomial variable); or 2) the number of times control was applied (continuous variable). I am using logistic regression to look at the association between the application of control and population reduction.
My model including animal control as a binomial variable produces a negative coefficient - i.e as the probability of animal control increases the probability of population reduction decreases. However, my model including animal control as a continuous variable produces a positive coefficient - i.e. for every unit increase in animal control the probability of population control increases. How can this be possible? Are there any other common examples of when, where or how this can happen?
I have read about sign change in logistic regression (here, here, or here) as a result of the addition of multiple predictor variables into a model where the predictors are correlated to some extent. I could not find a question/answer explaining my above described situation, I would not think possible that it could be driven by correlation given only one variable is included in the model at any one time.
