box.cox.powers

0th

Percentile

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

boxcox, box.cox, box.cox.var, box.cox.axis

Aliases
  • box.cox.powers
  • print.box.cox.powers
  • summary.box.cox.powers
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 1.2-2, License: GPL version 2 or newer

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