# box.cox.powers

##### Multivariate Unconditional Box-Cox Transformations

Estimates multivariate unconditional power transformations to multinormality by the method of maximum likelihood. The univariate case is obtained when only one variable is specified.

- Keywords
- multivariate, models

##### Usage

```
box.cox.powers(X, start=NULL, hypotheses=NULL, ...)
## S3 method for class 'box.cox.powers':
print(x, digits=4, ...)
## S3 method for class 'box.cox.powers':
summary(object, digits=4, ...)
```

##### Arguments

- X
- a numeric matrix of variables (or a vector for one variable) to be transformed.
- start
- start values for the power transformation parameters;
if
`NULL`

(the default), univariate Box-Cox transformations will be computed and used as the start values. - hypotheses
- if non-
`NULL`

, a list of hypotheses to be tested; each hypothesis should be a vector of values giving the power for each column of`X`

. Note that the hypotheses that all powers are 1 and that all powers are 0 (log) ar - ...
- optional arguments to be passed to the
`optim`

function. - digits
- number of places to round result.
- x, object
`box.cox.powers`

object.

##### Details

Note that this is *unconditional* Box-Cox. That is, there is
no regression model, and there are no predictors. The object is to
make the distribution of the variable(s) as (multi)normal as possible.
For Box-Cox regression, see the `boxcox`

function in the
`MASS`

package.
The function estimates the Box-Cox powers,
$x_{j}^{\prime }=(x_{j}^{\lambda _{j}}-1)/\lambda _{j}$
for $\lambda _{j} \neq 0$ and $x_{j}^{\prime }=\log x_{j}$
for $\lambda _{j}=0$. Subsequently using ordinary power
transformations (i.e., $x^p$ for $p \neq 0$)
achieves the same result.

##### Value

- returns an object of class
`box.cox.powers`

, which may be printed or summarized. the`print`

and`summary`

methods are now identical; I've retained the latter for backwards compatibility.

##### References

Box, G. E. P. and Cox, D. R. (1964)
An analysis of transformations.
*JRSS B* **26** 211--246.
Cook, R. D. and Weisberg, S. (1999)
*Applied Regression, Including Computing and Graphics.* Wiley.

##### See Also

##### Examples

```
attach(Prestige)
box.cox.powers(cbind(income, education))
## Box-Cox Transformations to Multinormality
##
## Est.Power Std.Err. Wald(Power=0) Wald(Power=1)
## income 0.2617 0.1014 2.580 -7.280
## education 0.4242 0.4033 1.052 -1.428
##
## L.R. test, all powers = 0: 7.694 df = 2 p = 0.0213
## L.R. test, all powers = 1: 48.8727 df = 2 p = 0
plot(income, education)
plot(box.cox(income, .26), box.cox(education, .42))
box.cox.powers(income)
## Box-Cox Transformation to Normality
##
## Est.Power Std.Err. Wald(Power=0) Wald(Power=1)
## 0.1793 0.1108 1.618 -7.406
##
## L.R. test, power = 0: 2.7103 df = 1 p = 0.0997
## L.R. test, power = 1: 47.261 df = 1 p = 0
qq.plot(income)
qq.plot(income^.18)
```

*Documentation reproduced from package car, version 1.2-16, License: GPL (>= 2)*