how to use the Box-Cox power transformation in R

Question

I need to transform some data into a  normal shape  and I read that Box-Cox can identify the exponent to use to transform the data   For what I understood   car  boxCoxVariable y    is used for response variables in linear models  and  MASS  boxcox object    for a formula or fitted model object  So  because my data are the variable of a dataframe  the only function I found I could use is   car  powerTransform dataframe variable  family  bcPower     Is that correct  Or am I missing something   The second question is about what to do after I obtain the  Estimated transformation parameters dataframe variable 0 6394806   Should I simply multiply the variable by this value  I did so   aaa   0 6394806 dataframe variable2    dataframe variable  aaa   and then I run the shapiro-wilks test for normality  but again my data don t seem to follow a normal distribution   shapiro test dataframe variable2  data   dataframe variable2 W   0 97508  p-value  lt  2 2e-16

User · Answer

Applying the BoxCox transformation to data  without the need of any underlying model  can be done currently using the package geoR  Specifically  you can use the function boxcoxfit   for finding the best parameter and then predict the transformed variables using the function BCtransform

User · Answer

Box and Cox  1964  suggested a family of transformations designed to reduce nonnormality of the errors in a linear model  In turns out that in doing this  it often reduces non-linearity as well    Here is a nice summary of the original work and all the work that s been done since  http   www ime usp br  abe lista pdfm9cJKUmFZp pdf  You will notice  however  that the log-likelihood function governing the selection of the lambda power transform is dependent on the residual sum of squares of an underlying model  no LaTeX on SO -- see the reference   so no transformation can be applied without a model   A typical application is as follows   library MASS     generate some data set seed 1  n  lt - 100 x  lt - runif n  1  5  y  lt - x 3   rnorm n     run a linear model m  lt - lm y   x     run the box-cox transformation bc  lt - boxcox y   x       lambda  lt - bc x which max bc y     1  0 4242424  powerTransform  lt - function y  lambda1  lambda2   NULL  method    boxcox        boxcoxTrans  lt - function x  lam1  lam2   NULL           if we set lambda2 to zero  it becomes the one parameter transformation     lam2  lt - ifelse is null lam2   0  lam2       if  lam1    0L          log y   lam2        else            y   lam2  lam1  - 1    lam1              switch method            boxcox   boxcoxTrans y  lambda1  lambda2             tukey   y lambda1           re-run with transformation mnew  lt - lm powerTransform y  lambda    x     QQ-plot op  lt - par pty    s   mfrow   c 1  2   qqnorm m residuals   qqline m residuals  qqnorm mnew residuals   qqline mnew residuals  par op      As you can see this is no magic bullet -- only some data can be effectively transformed  usually a lambda less than -2 or greater than 2 is a sign you should not be using the method   As with any statistical method  use with caution before implementing   To use the two parameter Box-Cox transformation  use the geoR package to find the lambdas   library  geoR   bc2  lt - boxcoxfit x  y  lambda2   TRUE   lambda1  lt - bc2 lambda 1  lambda2  lt - bc2 lambda 2    EDITS  Conflation of Tukey and Box-Cox implementation as pointed out by  Yui-Shiuan fixed

User · Answer

According to the Box-cox transformation formula in the paper Box George E  P   Cox D R  1964    An analysis of transformations   I think mlegge s post might need to be slightly edited The transformed y should be  y  lambda -1  lambda instead of y  lambda    Actually  y  lambda  is called Tukey transformation  which is another distinct transformation formula   So  the code should be    trans  lt - bc x which max bc y     1  0 4242424   re-run with transformation mnew  lt - lm   y trans-1  trans    x    Instead of mnew  lt - lm y trans   x     More information   Correct implementation of Box-Cox transformation formula by boxcox   in R  https   www r-bloggers com on-box-cox-transform-in-regression-models  A great comparison between Box-Cox transformation and Tukey transformation  http   onlinestatbook com 2 transformations box-cox html One could also find the Box-Cox transformation formula on Wikipedia  en wikipedia org wiki Power transform Box E2 80 93Cox transformation   Please correct me if I misunderstood it

User · Answer

If I want tranfer only the response variable y instead of a linear model with x specified  eg I wanna transfer normalize a list of data  I can take 1 for x  then the object becomes a linear model   library MASS  y   rf 500 30 30  hist y breaks   12  result   boxcox y 1  lambda   seq -5 5 0 5   mylambda   result x which max result y   mylambda y2    y mylambda-1  mylambda hist y2

[r] how to use the Box-Cox power transformation in R

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