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I have over 30 features: several have zero-inflated and highly positive skewed distribution. Those distributions are expected because they are semi-continuous monetary related features.

For example: Revenue earned by age.

If 70% of all the respondents are unemployed and in school, most of them will have 0.

I've read about the different methods: square/cube root, Box-Cox and logistic but I'm not sure which one would apply in my case.

  1. If I choose log and add a 1 to each value , what will be the impact? Could that make sense?

  2. How would the Box-Cox transformation be beneficial in this example and would it perform better than the logistic transformation ?

  3. Cube/square root seems to be an oversimplified technique to achieve this and doesn't seem to properly address my issue. Any thoughts?

Note: My end-goal is to apply pca and then Kmeans clustering.

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    $\begingroup$ Several posts on site discuss the problem with transforming values with one or a few large spikes of probability - whatever transformation you use leaves the spike still a spike. It might be worth trying a few searches $\endgroup$
    – Glen_b
    Nov 1, 2021 at 22:34

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Whatever you do, if there is a spike at zero, there will be a spike when you transform it, regardless of whether the transform maps zero to zero or not.

A transformation might help to pull in the tail of high values, but none of the methods you mention as a goal require a transformation absolutely.

Square roots, cube roots, log1p meaning $\log (x + 1)$, and asinh can all cope with zeros.

A transformation may help in visualization even if it is a little arbitrary. The same doesn't necessarily apply to modelling.

Details:

I've never seen any transform based on (variable $+ 1$) called logistic. (One reference to "logistic" was fixed as a typo, but another remains.)

Box-Cox(*) in my experience is defined and implemented only for entirely positive variables.

(*) Initial capitals please.

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  • $\begingroup$ typo on the loga sorry. In regards to the box-cox. My values are all positive. So in this case should i use log+1 or box-cox, which one makes more sense in my context? $\endgroup$ Nov 1, 2021 at 17:44
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    $\begingroup$ Zero-inflated does not mean "all positive". $\endgroup$
    – Nick Cox
    Nov 1, 2021 at 18:08
  • $\begingroup$ gotcha. so in order for the boxcox to work, it "must" be all positive (i.e no zeros) , should i transform 0 values by adding a one as for the log ? which technique should I choose ? $\endgroup$ Nov 1, 2021 at 18:11
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    $\begingroup$ There is no "should" here independently of your goals. Adding 1 and then applying Box-Cox is, to my taste., a bad idea when the other possibilities are one step. I can't recommend anything beyond trying your chosen goals both with and without transformations and seeing what makes sense. $\endgroup$
    – Nick Cox
    Nov 1, 2021 at 18:15

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