I have a bunch of independent variables which are skewed and have negative and zero values. I am seeing a lot of suggestions of using cube root as a transformation.

What would be the harm in using $\text{sign}(x)\log(1+|x|)$ instead?

  • 4
    $\begingroup$ Why are you transforming these independent variables? $\endgroup$ – Glen_b Jun 8 '16 at 17:28
  • $\begingroup$ Because the distributions are very skewed and outliers prone. I'm Afraid that it'll affect the estimates. $\endgroup$ – IamNotLegend Jun 8 '16 at 17:46
  • $\begingroup$ What do you intend to do with these variables (after a possible transformation)? $\endgroup$ – Joris Bierkens Jun 8 '16 at 20:17
  • $\begingroup$ Use it as a predictor in a logistic regression $\endgroup$ – IamNotLegend Jun 8 '16 at 20:30
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    $\begingroup$ Why do you think skewness or outliers are a problem for these variables? $\endgroup$ – Glen_b Jun 9 '16 at 1:34

One reason to avoid such a transformation is that it will make the interpretation of the regression coefficient very difficult.

Moreover, there is no requirement for independent variables to be normally distributed, and as a rule you should avoid doing so unless there are substantive reasons for it, such as a known nonlinear relationship, to deal with heteroscedasticity, or to help interpretation


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