If the domain of your variable includes negative values, it makes no sense to use the logarithms at all. If the variable can have negative values because of some "background (baseline) substraction", then you should reconsider the correction. Maybe subtraction is wrong anyway, but even f not: there are normal/exponential deconvolution techniques that allow a correction without giving negative values.

Andrey Davydenko : Box Cox transformation requires positive values as well. Adding an arbitrary constant (they call it lambda2) comes with a lot of problems. This "solution" could be used in the case of the simple log-trafo (no need to reference the more complicated Box-Cox procedure) to make all values positive, but as I said: this does notsolve theproblem; it just covers it and produces even more problems.

You need to use the formula presented on slide 3:

https://www.ime.usp.br/~abe/lista/pdfm9cJKUmFZp.pdf

If the domain of your variable includes negative values, it makes no sense to use the logarithms at all. If the variable can have negative values because of some "background (baseline) substraction", then you should reconsider the correction. Maybe subtraction is wrong anyway, but even f not: there are normal/exponential deconvolution techniques that allow a correction without giving negative values.

Andrey Davydenko : Box Cox transformation requires positive values as well. Adding an arbitrary constant (they call it lambda2) comes with a lot of problems. This "solution" could be used in the case of the simple log-trafo (no need to reference the more complicated Box-Cox procedure) to make all values positive, but as I said: this does notsolve theproblem; it just covers it and produces even more problems.

Jochen Wilhelm : Sure, first of all it is important to understand why we have those negative values.

This is what people usually totally ignore or are unaware of... that's why I wrote it.