box.cox.powers: Multivariate Unconditional Box-Cox Transformations

Description

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

Usage

box.cox.powers(X, start=NULL, ...)

## S3 method for class 'box.cox.powers':
print(x, ...)

## S3 method for class 'box.cox.powers':
summary(object, digits=4, ...)

Arguments

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.

...

optional arguments to be passed to the optim function.

digits

number of places to round result.

x, object

box.cox.powers object.

Value

returns an object of class box.cox.powers, which may be printed or summarized.

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.

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.

Examples

Run this code

data(Prestige)
attach(Prestige)
summary(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))

summary(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)

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