On 2010-05-16 6:22, Holger Steinmetz wrote:
Dear experts, I tried to learn about Box-Cox-transformation but found the following thing: When I had to add a constant to make all values of the original variable positive, I found that the lambda estimates (box.cox.powers-function) differed dramatically depending on the specific constant chosen.
Let's say that x is such that 1/x has a Normal distribution, i.e. lambda = -1. Then y = (1/x) + b also has a Normal distribution. But you're expecting 1/(x+b) to also have a Normal distribution.
In addition, the correlation between the transformed variable and the original were not 1 (as I think it should be to use the transformed variable meaningfully) but much lower.
Again, your expectation is faulty. The relationship between the original and transformed variables is not linear (otherwise, why do the transformation?), but cor() computes the Pearson correlation coefficient by default. Try method='spearman'. Better yet, plot the transformed variables vs the original variable for further enlightenment. -Peter Ehlers
With higher added values (and a right skewed variable) the lambda estimate was even negative and the correlation between the transformed variable and the original varible was -.91!!? I guess that is something fundmental missing in my current thinking about box-cox... Best, Holger P.S. Here is what i did: # Creating of a skewed variable X (mixture of two normals) x1 = rnorm(120,0,.5) x2 = rnorm(40,2.5,2) X = c(x1,x2) # Adding a small constant Xnew1 = X +abs(min(X))+ .1 box.cox.powers(Xnew1) Xtrans1 = Xnew1^.2682 #(the value of the lambda estimate) # Adding a larger constant Xnew2 = X +abs(min(X)) + 1 box.cox.powers(Xnew2) Xtrans2 = Xnew2^-.2543 #(the value of the lambda estimate) #Plotting it all par(mfrow=c(3,2)) hist(X) qqnorm(X) qqline(X,lty=2) hist(Xtrans1) qqnorm(Xtrans1) qqline(Xtrans1,lty=2) hist(Xtrans2) qqnorm(Xtrans2) qqline(Xtrans2,lty=2) #correlation among original and transformed variables round(cor(cbind(X,Xtrans1,Xtrans2)),2)
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