Suppose we have an explanatory variable – GDP per capita – of which we take the natural log. Suppose further that our dependent variable is the occurrence of civil war.
Running a logistic regression, we get a beta of 0.337.
If I understand correctly, we can use the odds ratio to interpret this as follows: A 1-unit increase in ln(GDP) increases the odds of war by a factor of exp(0.337)=1.40 or about 40%.
But a 1-unit increase in ln(GDP) is not very intuitive. Unless I am mistaken, this means: Increasing GDP by a factor of e (=2.718) increases the odds of war by a factor of 1.40.
How would I get a more intuitive interpretation? For example, could I get the odds ratio for a $100 increase in GDP?
I know there have been several feeds about interpreting log-transformed independent variables in logistic regression models. However, I am still having difficulties getting an answer to this specific question.
