How to interpret logarithmized variables in percentage?

[Noemi Seng]

Dear community,

I'm currently struggling with the interpretation of some regression results. My independent and dependent variable are expressed in percentage. I logarithmized them in order to account for the highly skewed data. As without the log, I would interpret the coefficient as follows: If x increases by 1 percentage point, y increases by x percentage points; this is not possible anymore when I apply the log, right? Would the interpretation change to elasticities, hence if x increases by 1%, y would increases by X%? And what would that do to my other independent variable which I don't logarithmize? How would I interpret them when the dependent variable is in log? Or would you rather recommend to not use the log for variables that are already expressed in log?

I appreciate any help.

[George Ford]

I wouldn't log a percentage; theoretically a percentage could be 0 or negative, no it's not generally applicable.

But yes, it's a %chn on a %chg (which is hard to interpret, unless you're looking for an elasticity though that could be computed using margins).

[Nick Cox]

An outcome that is a positive percentage might be better treated using a logit scale. This is just equivalent to saying that a fractional outcome is often best treated that way.

This is all assuming percentages correspond to fractions of some total and fall within (0, 100). Values of exact 0 or exact 100 don't match logit scale. As George Ford hints percentage changes that can be negative bring in extra complications.

Just showing a scatter plot of your data would allow more precise advice.

[George Ford]

fracreg might be a good option.

[Noemi Seng]

Thank you very much that was very helpful!