powerTrans: Power Transformation

In RRPP: Linear Model Evaluation with Randomized Residuals in a Permutation Procedure

Power Transformation

Description

A function that transforms a vector of statistics or data to be approximately normally distributed.

Usage

powerTrans(
  y,
  eps = 0.001,
  target = NULL,
  interp = FALSE,
  forceYJ = FALSE,
  useStDev = FALSE
)

Arguments

y	A vector of values to use.
eps	Tolerance for lambda = 0.
target	The value to target in the distribution. (If null, the first value in the vector is used.) This will be moved to the first value in results.
interp	Logical value for whether to spline interpolate lambda (ideal for vectors of small length). This will default if the number of values is less than 100, as in boxcox.
forceYJ	A logical value whether to force a Yeo-Johnson transformation for non-negative values. Negative values trigger the transformation, but positive values can be transformed similarly.
useStDev	A logical value whether to initially use standard deviates of y. This might be useful if the range of y is restricted, say between 0 and 1.

Details

This function uses a Box-Cox power transformation for a vector of values, (presumably statistics from RRPP) with the following conditions:

(1) If any values are 0 or negative, a Yeo-Johnson transformation is performed to optimize lambda with only positive values.

(2) The lambda parameter is optimized over a range of -2 to +2, as is typical for most applications.

(3) The first (or targeted) value (assumed to be the observed value in a distribution of random values) is removed from the vector to perform optimization of lambda, but is returned to the vector for transformation. This assures that large, aberrant values, such as might be found via RRPP for large effects, do not have leverage for the optimization.

A Yeo-Johnson transformation can be forced, which for positive values merely shifts the distribution by adding 1. For most RRPP statistics (SS. MS, Rsq, F, d), this is not needed for effect sizes, as values are positive. However, for log-likelihoods, this might be a good idea for comparisons, because values might be strongly positive or strongly negative.

Using standard deviates (useStDev) is a good idea for statistics with aberrant ranges (like 0 to 1, or 1,000 to 2,000). If used, a Yeo-Johnson transformation is implicit, since standardizing introduces negative values.

Value

A list containing the following:

opt.lambda	The optimized lambda parameter.
transformed	The power-transformed values.
lambda	If spline interpolation is used, the values of lambda used.
loglik	If spline interpolation is used, the log-liklihoods calculated for lambda.

Author(s)

Michael Collyer

References

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations (with discussion). Journal of the Royal Statistical Society B, 26, 211–252.

Yeo, I. and Johnson, R. (2000) A new family of power transformations to improve normality or symmetry. Biometrika, 87, 954-959.

RRPP documentation built on July 7, 2026, 1:07 a.m.