Log transformation of different explanatory- and control variables

[Alessio Scarpa]

Hi everybody,

I am working on a fixed-effects model for my master thesis and facing a problem regarding the transformation of different introduced variables. Hopefully somebody can give me a hand.

One of my control variables (Cash Flow) also takes on negative values. Other control variables such as Expenditures can only be positive or zero. I would like to transform at least the Expenditure-variables into logs. In my opinion it makes no sense to also transform Cash Flow (due to the negative values). Is it appropriate to transform just a part of my regressors and to leave other arithmetically?

Thank you for your help.

Best regards
Alessio

[Nick Cox]

It's entirely in order to have predictors on different scales. Otherwise it would not be legitimate to combine indicator variables with variables in any other form, for example.

Clearly you can't take logarithms of Cash Flow without omitting the negative values. What's not so clear is why you think it should be logged in the first place. Ideally it is to improve linearity. Note that non-normal marginal distributions of predictors are not in themselves a problem. (Otherwise it would not be legitimate to use indicator variables as predictors, for example.)

What some people do is use cube root, neglog or inverse hyperbolic sine as transforms if there are grounds for using logarithms but they are thwarted by negative or zero values. But there is a sacrifice of simplicity and interpretability in doing that.

neglog(x) = sign(x) * log(1 + abs(x))

In your case, I would think first about neglog if other loosely similar predictors are being logged.

[Alessio Scarpa]

Thank you for your quick response Nick.
In case Cash Flow data fulfills the linearity assumption I could just introduce the arithmetical Cash Flow beside several other predictors which are logged right?

[Nick Cox]

You're writing a Master's thesis. I know I won't be an examiner, but I don't know what your examiners would expect.

I'd expect in assessing any project

1. explanation of why predictors were treated as they are

2. explanation of why "similar" predictors are treated differently, if they are

3. discussion of the advantages and disadvantages of any choice.