bcPower
Box-Cox and Yeo-Johnson Power Transformations
Transform the elements of a vector using, the Box-Cox, Yeo-Johnson, or simple power transformations.
- Keywords
- regression
Usage
bcPower(U, lambda, jacobian.adjusted = FALSE)yjPower(U, lambda, jacobian.adjusted = FALSE)
basicPower(U,lambda)
Arguments
- U
- A vector, matrix or data.frame of values to be transformed
- lambda
- The one-dimensional transformation parameter, usually in
the range from $-2$ to $2$, or if
Uis a matrix or data frame, a vector of lengthncol(U)of transformation parameters - jacobian.adjusted
- If
TRUE, the transformation is normalized to have Jacobian equal to one. The default isFALSE.
Details
The Box-Cox family of scaled power transformations
equals $(U^{\lambda}-1)/\lambda$
for $\lambda \neq 0$, and
$\log(U)$ if $\lambda =0$.
If family="yeo.johnson" then the Yeo-Johnson transformations are used.
This is the Box-Cox transformation of $U+1$ for nonnegative values,
and of $|U|+1$ with parameter $2-\lambda$ for $U$ negative.
If jacobian.adjusted is TRUE, then the scaled transformations are divided by the
Jacobian, which is a function of the geometric mean of $U$.
The basic power transformation returns $U^{\lambda}$ if $\lambda$
is not zero, and $\log(\lambda)$ otherwise.
Missing values are permitted, and return NA where ever Uis equal to NA.
Value
- Returns a vector or matrix of transformed values.
References
Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage. Weisberg, S. (2005) Applied Linear Regression, Third Edition. Wiley, Chapter 7.
Yeo, In-Kwon and Johnson, Richard (2000) A new family of power transformations to improve normality or symmetry. Biometrika, 87, 954-959.
See Also
Examples
U <- c(NA, (-3:3))
bcPower(U, 0) # produces an error as U has negative values
bcPower(U+4,0)
bcPower(U+4, .5, jacobian.adjusted=TRUE)
yjPower(U, 0)
yjPower(U+3, .5, jacobian.adjusted=TRUE)
V <- matrix(1:10, ncol=2)
bcPower(V, c(0,1))
#basicPower(V, c(0,1))