Average Marginal Effects in Logit Regressions with transformed independent variables

[daniel dilm]

Hello everyone,
i'm trying to interpret my output of average marginal effects calculated for my logistic regressions model and i am todally confused right now.

The dependent variable is equal to 1 if a project is successful and 0 if not. Due to skewness and therefore following the literature, i transformed some variables as the natural logarithm of one plus the value of the variable.

gen x_ln = ln(1+x)

I then ran my logistic regression using the logit command. As the literature recommends the use of average marginal effects, i now tried to calculate them as well using the command

margins, dydx(*)

My output for the independent variable i want to analyse is then:

dy/dx Std. Err. z P>|z| [95% Conf. Interval]
x_ln | .0253134 .0037356 6.78 0.000 .0179918 .0326349

But since i transformed my variable in the way mentioned above, i am totally confused on how this is to be interpreted.

I Hope that someone can help me out.

Kind Regards

[Clyde Schechter]

The use of a ln(1+x) transformation is pretty much never justified. It is usually done to avoid the problem of observations with x = 0. But it accomplishes this at the price of introducing massive distortion into the variable. You could equally well avoid the zeroes with ln(0.0000000000001 + x) or with ln(9876543210 + x), but the results you would get from using these variables would be very, very different.

In the unlikely situation where there might be some situation where there is really a cogent reason for specifically using ln(1+x), the drawback would be that there is no simple interpretation of a unit increase of that in terms of the metric of x itself. So the reason you are totally confused on how this is to be interpreted is that there really isn't any coherent way to interpret it in the x-metric. The best you can do is say that a unit increase in ln(1+x) is associated with an increase in the probability of your outcome variable by about 0.025 (i.e. about 2.5 percentage points).

My advice is either not to use ln(1+x) in the first place, or if there is a really persuasive reason to use it, then just interpret your results in the ln(1+x) metric.