Box-Cox Transformations for Linear Models

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Description

Computes and optionally plots profile log-likelihoods for the parameter of the Box-Cox power family, the Yeo-Johnson power family, or for either of the parameters in a skew power family. This is a slight generalization of the boxcox function in the MASS package that allows for families of transformations other than the Box-Cox power family.

Usage

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boxCox(object, ...)
  
## Default S3 method:
boxCox(object,
        lambda = seq(-2, 2, 1/10), plotit = TRUE, 
        interp = plotit, eps = 1/50,
        xlab=NULL, ylab=NULL, 
        family="bcPower", 
        param=c("lambda", "gamma"), gamma=NULL, 
        grid=TRUE, ...)
  
## S3 method for class 'formula'
boxCox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE, ...)
  
## S3 method for class 'lm'
boxCox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE, ...)

## S3 method for class 'lmerMod'
boxCox(object,
          lambda = seq(-2, 2, 1/10), plotit = TRUE, interp = plotit, eps = 1/50,
          xlab=NULL, ylab=NULL, family="bcPower", 
          param=c("lambda", "gamma"), gamma=NULL, grid=TRUE, ...)

Arguments

object

a formula or fitted model object of class lm or aov or lmerMod.

lambda

vector of values of lambda, with default (-2, 2) in steps of 0.1, where the profile log-likelihood will be evaluated.

plotit

logical which controls whether the result should be plotted; default TRUE.

interp

logical which controls whether spline interpolation is used. Default to TRUE if plotting with lambda of length less than 100.

eps

Tolerance for lambda = 0; defaults to 0.02.

xlab

defaults to "lambda" or "gamma".

ylab

defaults to "log-Likelihood" or for skewPower family to the appropriate label.

family

Defaults to "bcPower" for the Box-Cox power family of transformations. If set to "yjPower" the Yeo-Johnson family, which permits negative responses, is used. If set to skewPower the function gives the profile log-likelihood for the parameter selected via param.

param

Relevant only to family="skewPower", produces a profile log-likelihood for the parameter selected, maximizing over the remaining parameter.

gamma

For use when the family="skewPower", param="gamma". If this is a vector of positive values, then the profile log-likelihood for the location (or start) parameter in the skew power family is evaluated at these values of gamma. If gamma is NULL, then evaulation is done at 100 equally spaced points between min(.01, gmax - 3*se) and gmax + 3*se, where gmax is the maximimul likelihood estimate of gamma, and se is its estimated standard error. See skewPower for the definition of gamma.

grid

If TRUE, the default, a light-gray background grid is put on the graph.

...

passes arguments from methods to the default, or from the default to plot.

Details

This routine is an elaboration of the boxcox function in the MASS package. The first 7 arguments are the same as in boxcox, and if the argument family="bcPower" is used, the result is essentially identical to the function in MASS. Two additional families are the yjPower and skewPower families that allow a few values of the response to be non-positive. The skew power family has two parameters: a power lambda and a start or location parameter gamma, and this function can be used to obtain a profile log-likelihood for either parameter with lambda as the default.

Value

A list of the lambda (or possibly, gamma) vector and the computed profile log-likelihood vector, invisibly if the result is plotted. If plotit=TRUE plots log-likelihood vs lambda and indicates a 95 lambda. If interp=TRUE, spline interpolation is used to give a smoother plot.

Author(s)

Sanford Weisberg, <sandy@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. (2008) Applied Regression Analysis and Generalized Linear Models, Second Edition. Sage.

Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage.

Hawkins, D. and Weisberg, S. (2015) Combining the Box-Cox Power and Genralized Log Transformations to Accomodate Negative Responses, submitted for publication.

Weisberg, S. (2014) Applied Linear Regression, Fourth Edition, Wiley.

Yeo, I. and Johnson, R. (2000) A new family of power transformations to improve normality or symmetry. Biometrika, 87, 954-959.

See Also

boxcox, yjPower, bcPower, skewPower, powerTransform

Examples

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  boxCox(Volume ~ log(Height) + log(Girth), data = trees,
         lambda = seq(-0.25, 0.25, length = 10))
  
  data("quine", package = "MASS")
  boxCox(Days ~ Eth*Sex*Age*Lrn, data = quine,
         lambda = seq(-0.05, 0.45, len = 20), family="yjPower")

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