# Monotonically increasing transformation function [duplicate]

The dependent variable of my problem is highly concentrated around zero. Here is a stemplot

  The decimal point is 6 digit(s) to the right of the |

-2 | 511
-1 | 92221
-0 | 87777666666665555555555555555444444444444444444444444444444433333333+2428
0 | 00000000000000000000000000000000000000000000000000000000000000000000+2113
1 | 00000000000000000000000000000000000011111111111111111111111111111122+110
2 | 0000000000111111233333444444555666666677778889
3 | 00112457778889
4 | 11233456999
5 | 0000389
6 | 01477
7 | 259
8 | 033
9 | 002356
10 | 9
11 |
12 |
13 | 069
14 |
15 |
16 |
17 | 13


Normally when I have a dependent variable (DV) that looks like this I apply a logarithmic transformation for reasons both economical and mathematical. But obviously this will not work in this case as I have values below zero.

Is there another monotonically increasing transformation function that will reduce the peakedness of this distribution?

• Cube root. But that means sign(x) * abs(x)^(1/3) or the equivalent in your favourite language. Commented Aug 19, 2013 at 17:45
• Why would you transform your DV? It sort of sounds like your reason is "because that's what I'd do if the circumstances were different" ... which doesn't seem like an especially good reason. What's a good reason to transform this particular DV? What does it achieve? Commented Aug 19, 2013 at 17:47
• @Glen_b in my case, I care more about the elasticity with respect to my IV than the effect. Extreme values in the DV can interfere with this. Commented Aug 19, 2013 at 17:51
• Elasticity calculation depends on log scale, doesn't it? I don't think any transformation will help there, although a GLM with log link might help. Also, although I gave a specific suggestion, @Glen_b's question of why do you (think you) want to do this is much more fundamental. Commented Aug 19, 2013 at 17:59
• If zero makes substantive sense, as it usually does, then that is lost by this procedure. Worse, studies with different empirical minima are hard to compare. Commented Oct 13, 2018 at 11:32