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In R, I am using the bc function to do a box-cox transformation. What factors do I need to consider when setting p (the power argument)?

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    $\begingroup$ The answer varies according to your reason for considering the transformation: whether it is for exploratory or confirmatory purposes, whether it is a dependent or independent variable in a regression, and so on. Could you perhaps share some of that relevant information with us so we can give you appropriate, focused answers? $\endgroup$
    – whuber
    May 30, 2012 at 1:15
  • $\begingroup$ It's for exploratory purposes. I'd like to transform certain measures of an event into a comparable space for clustering (euclidean distance perhaps?). In order to get a roughly normal distribution in order to use scale to get standard scores, I'm transforming these measures $\endgroup$ May 30, 2012 at 8:32

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I've found that I can use the following to get a transformation that best approximates a normal distribution:

library(geoR)
bc(x=vecToTransform, p=boxcoxfit(y)$lambda)
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If this is on a single variable, a likelihood profile wrt p is typically used, as in Wikipedia example. Note that you need to use the right scale with geometric means of your variable and such for it to make sense.

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    $\begingroup$ Thanks. What do you mean by "Note that you need to use the right scale with geometric means of your variable and such for it to make sense." How can I implement this? $\endgroup$ May 29, 2012 at 23:16
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    $\begingroup$ Box-Cox transformation is not just $x^\lambda$, it is $\lambda\frac{x^\lambda - 1}{\dot x^{\lambda-1}}$ where $\dot x$ is the geometric mean. The reason for introducing this geometric mean is to provide correct likelihood ratio tests. $\endgroup$
    – StasK
    May 30, 2012 at 1:27
  • $\begingroup$ @StasK: Can you provide a reference for your claim? $\endgroup$ Feb 25, 2017 at 14:11

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