R: Finding Univariate or Multivariate Power Transformations

estimateTransform {car}

R Documentation

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

`X`	A matrix or data.frame giving the “right-side variables”.
`Y`	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-Johnson family of transformations.
`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.

Details

See the documentation for the function powerTransform.

Value

An object of class powerTransform with components

`value`	The value of the loglikelihood at the mle.
`counts`	See `optim`.
`convergence`	See `optim`.
`message`	See `optim`.
`hessian`	The hessian matrix.
`start`	Starting values for the computations.
`lambda`	The ml estimate
`roundlam`	Convenient rounded values for the estimates. These rounded values will often be the desirable transformations.
`family`	The transformation family
`xqr`	QR decomposition of the predictor matrix.
`y`	The responses to be transformed
`x`	The predictors
`weights`	The weights if weighted least squares.

Author(s)

Sanford Weisberg, <sandy@stat.umn.edu>

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

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)~.)

[Package car version 2.0-12 Index]