Not taking the log of a variable with lots of 0 observations I have some variables in an OLS that are very skewed to the right, so it could make sense to the log transformation of it, however there are lots of 0s in the variable, so that would mean I have to remove those, thus resulting in a loss of observations. Can I argue that I didn't want to take the log for this reason? (These are salaries, many have 0)
 A: It is common to use $\log(1+x)$ in such a situation, so common that a collaborator or reviewer is likely to suggest doing so, yet this is problematic for a number of reasons.

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*There are no distribution assumptions on regression features, so there is not necessarily a requirement to transform at all.


*A typical reason for taking the $\log$ of a variable is to make the interpretation in terms of percentages change. This is a legitimate reason to take a logarithm. However, when you take $\log(1+x)$, two issues get introduced. First, you are shoehorning a percent change from zero into such a framework. Second, you are changing the starting values of the nonzero elements. A claimed $5\%$ change does not have nearly the same meaning when the starting value is $1$ vs when it is $2$. Consequently, much of the desired “percent change” interpretation is lost. For an extreme example, consider how damaging adding one would be if all of y he $x$ values are less than one, and you go and double (triple, increase $100$-fold…) them.


*If you just want to introduce nonlinear behavior, there are many other ways to do it, and taking the $\log(1+x)$ isn’t necessarily a good nonlinear feature. If you do it because it’s easy, your model performance might not be so great compared to other ways to introduce nonlinearity.


*Why add $1?$ Why not add $0.1$ or $2$ or $\pi?$
I had to criticize such a $\log(1+x)$ feature yesterday, and if you don’t do it, someone is likely to say that you should, so you need to be prepared to offer a rebuttal.
My suggestion is to think hard about why you wanted to use a $\log$ transformation in the first place. Once you figure out why, you may want to ask an additional question (or several) on here asking how to proceed.
Finally, one of the comments remarks that zero salary isn’t a real salary at a job and probably indicates missing data. For the particular problem at hand, I find that quite reasonable.
