# boxCox

##### Box-Cox Transformations for Linear Models

Computes and optionally plots profile log-likelihoods for the parameter of the
Box-Cox power transformation. This is a slight generalization of the
`boxcox`

function in the

- Keywords
- regression

##### Usage

```
boxCox(object, ...)
## S3 method for class 'default':
boxCox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
interp = (plotit && (m < 100)), eps = 1/50,
xlab = expression(lambda),
ylab = "log-Likelihood", family="bcPower", grid=TRUE, ...)
## S3 method for class 'formula':
boxCox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
interp = (plotit && (m < 100)), eps = 1/50,
xlab = expression(lambda),
ylab = "log-Likelihood", family="bcPower", ...)
## S3 method for class 'lm':
boxCox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
interp = (plotit && (m < 100)), eps = 1/50,
xlab = expression(lambda),
ylab = "log-Likelihood", family="bcPower", ...)
```

##### Arguments

- object
- a formula or fitted model object. Currently only
`lm`

and`aov`

objects are handled. - 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"`

. - ylab
- defaults to
`"log-Likelihood"`

. - 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. - grid
- If TRUE, the default, a light-gray background grid is put on the graph.
- ...
- additional parameters to be used in the model fitting.

##### Details

This routine is an elaboration of the `boxcox`

function in the
`family`

and `grid`

are
identical, and if the arguments
`family = "bcPower", grid=FALSE`

is set it gives an identical graph. If
`family = "yjPower"`

then the Yeo-Johnson power transformations, which
allow nonpositive responses, will be used.

##### Value

- A list of the lambda 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 95lambda. If`interp=TRUE`

, spline interpolation is used to give a smoother plot.

##### 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.
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

##### Examples

```
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")
```

*Documentation reproduced from package car, version 2.0-20, License: GPL (>= 2)*