Transform the elements of a vector using, the Box-Cox, Yeo-Johnson, or simple power transformations.
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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 |
jacobian.adjusted |
If |
gamma |
For bcPower or basicPower, the transformation is of U + gamma, where gamma is a positive number called a start that must be large enough so that U + gamma is strictly positive. |
The Box-Cox family of scaled power transformations
equals (U^(lambda)-1)/lambda
for lambda not equal to zero, and
log(U) if lambda = 0. If gamma is not specified, it is set equal to zero. U + gamma
must be strictly positive to use this family.
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. An alternative family to the Yeo-Johnson family is the skewPower
family that requires estimating both a power and an second parameter.
The basic power transformation returns U^{λ} if λ is not zero, and \log(λ) otherwise.
If jacobian.adjusted
is TRUE
, then the scaled transformations are divided by the
Jacobian, which is a function of the geometric mean of U for skewPower and yjpower and of U + gamma for bcPower. With this adjustment, the Jacobian of the transformation is always equal to 1.
Missing values are permitted, and return NA
where ever U
is equal to NA
.
Returns a vector or matrix of transformed values.
Sanford Weisberg, <sandy@umn.edu>
Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second Edition, Sage.
Hawkins, D. and Weisberg, S. (2015) Combining the Box-Cox Power and Genralized Log Transformations to Accomodate Negative Responses, submitted for publication.
Weisberg, S. (2014) Applied Linear Regression, Fourth Edition, Wiley 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.
powerTransform
, skewPower
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