What is a DMI log?

What are the downsides when using log(x + 1) as one's log-transformation?

• I see log(x + 1) used a lot to transform data that's some sort of right-skewed count (and contains zeros). This seems like a hack to make the log-transformation work. What are the downsides to this hack? This is an extension of the question

• Answer:

  All models are wrong, but some are more useful than others. All transformations fit this maxim, and there are no particular downsides unique to log(x+1); a transformation is a hack in the first place.  There are a few rare cases where there are very good reasons to expect the underlying physics/biology/mechanisms actually function has a logarithmic relationship. The only real particular problems (besides the problems with transformations in the first place): a) You can turn your analysis into a fishing expedition if you mess with the constant too much.  i.e. you may be over-fitting your distribution [not really an issue; this is more of an issue if you start really manipulating transformations like a Box-Cox] b) It makes it that little bit harder to back transform. Neither of these are particularly difficult to handle or an issue.