bcPower {car} | R Documentation |

Transform the elements of a vector or columns of a matrix using, the Box-Cox, Box-Cox with negatives allowed, Yeo-Johnson, or simple power transformations.

bcPower(U, lambda, jacobian.adjusted=FALSE, gamma=NULL) bcnPower(U, lambda, jacobian.adjusted = FALSE, gamma) bcnPowerInverse(z, lambda, gamma) yjPower(U, lambda, jacobian.adjusted = FALSE) basicPower(U,lambda, gamma=NULL)

`U` |
A vector, matrix or data.frame of values to be transformed |

`lambda` |
Power transformation parameter with one element for each
column of U, usuallly in the range from |

`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. For the bcnPower, Box-cox power with negatives allowed, see the details below. |

`z` |
a numeric vector the result of a call to |

.

The Box-Cox
family of *scaled power transformations*
equals *(x^(lambda)-1)/lambda*
for *lambda not equal to 0*, and
*log(x)* if *lambda = 0*. The `bcPower`

function computes the scaled power transformation of
*x = U + gamma*, where *gamma*
is set by the user so *U + gamma* is strictly positive for these
transformations to make sense.

The Box-Cox family with negatives allowed was proposed by Hawkins and Weisberg (2017). It is the Box-Cox power transformation of

*z = .5 (U + √[U^2 + gamma^2])*

where for this family *gamma* is either user selected or is estimated. `gamma`

must be positive if *U* includes negative values and non-negative otherwise, ensuring that *z* is always positive. The bcnPower transformations behave similarly to the bcPower transformations, and introduce less bias than is introduced by setting the parameter *gamma* to be non-zero in the Box-Cox family.

The function `bcnPowerInverse`

computes the inverse of the `bcnPower`

function, so `U = bcnPowerInverse(bcnPower(U, lambda=lam, jacobian.adjusted=FALSE, gamma=gam), lambda=lam, gamma=gam)`

is true for any permitted value of `gam`

and `lam`

.

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.

The basic power transformation returns *U^{lambda}* if
*lambda* is not 0, and *log(lambda)*
otherwise for *U* strictly positive.

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. Jacobian adjustment facilitates computing the Box-Cox estimates of the transformation parameters.

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. (2019)
*An R Companion to Applied Regression*, Third Edition, Sage.

Hawkins, D. and Weisberg, S. (2017)
Combining the Box-Cox Power and Generalized Log Transformations to Accomodate Nonpositive Responses In Linear and Mixed-Effects Linear Models *South African Statistics Journal*, 51, 317-328.

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.

U <- c(NA, (-3:3)) ## Not run: bcPower(U, 0) # produces an error as U has negative values bcPower(U, 0, gamma=4) bcPower(U, .5, jacobian.adjusted=TRUE, gamma=4) bcnPower(U, 0, gamma=2) basicPower(U, lambda = 0, gamma=4) yjPower(U, 0) V <- matrix(1:10, ncol=2) bcPower(V, c(0, 2)) basicPower(V, c(0,1))

[Package *car* version 3.0-11 Index]