estimateTransform: Finding Univariate or Multivariate Power Transformations

Description

estimateTransform computes members of families of transformations indexed by one parameter, the Box-Cox power family, or the Yeo and Johnson (2000) family, or the basic power family, interpreting zero power as logarithmic. The family can be modified to have Jacobian one, or not, except for the basic power family. Most users will use the function powerTransform, which is a front-end for this function.

Usage

estimateTransform(X, Y, weights=NULL, family="bcPower", start=NULL,
         method="L-BFGS-B", ...)

Arguments

A matrix or data.frame giving the right-side variables.

A vector or matrix or data.frame giving the left-side variables.

weights

Weights as in lm.

family

The transformation family to use. This is the quoted name of a function for computing the transformed values. The default is bcPower for the Box-Cox power family and the most likely alternative is yjPower for the Yeo-

start

Starting values for the computations. It is usually adequate to leave this at its default value of NULL.

method

The computing alogrithm used by optim for the maximization. The default "L-BFGS-B" appears to work well.

...

Additional arguments that are passed to the optim function that does the maximization. Needed only if there are convergence problems.

Value

An object of class powerTransform with components
valueThe value of the loglikelihood at the mle.
countsSee optim.
convergenceSee optim.
messageSee optim.
hessianThe hessian matrix.
startStarting values for the computations.
lambdaThe ml estimate
roundlamConvenient rounded values for the estimates. These rounded values will often be the desirable transformations.
familyThe transformation family
xqrQR decomposition of the predictor matrix.
yThe responses to be transformed
xThe predictors
weightsThe weights if weighted least squares.

Details

See the documentation for the function powerTransform.

References

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations. Journal of the Royal Statisistical Society, Series B. 26 211-46. Cook, R. D. and Weisberg, S. (1999) Applied Regression Including Computing and Graphics. Wiley. Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage. Velilla, S. (1993) A note on the multivariate Box-Cox transformation to normality. Statistics and Probability Letters, 17, 259-263. Weisberg, S. (2005) Applied Linear Regression, Third Edition. Wiley. Yeo, I. and Johnson, R. (2000) A new family of power transformations to improve normality or symmetry. Biometrika, 87, 954-959.

Examples

Run this code

data(trees,package="MASS")
summary(out1 <- powerTransform(Volume~log(Height)+log(Girth),trees))
# multivariate transformation:
summary(out2 <- powerTransform(cbind(Volume,Height,Girth)~1,trees))
testTransform(out2,c(0,1,0))
# same transformations, but use lm objects
m1 <- lm(Volume~log(Height)+log(Girth),trees)
(out3 <- powerTransform(m1))
# update the lm model with the transformed response
update(m1,basicPower(out3$y,out3$roundlam)~.)

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