Yeo-Johnson Transformation

Computes the Yeo-Johnson transformation, which is a normalizing transformation.

Usage

yeo.johnson(y, lambda, derivative = 0,
            epsilon = sqrt(.Machine$double.eps), inverse = FALSE)

Arguments

y: Numeric, a vector or matrix.
lambda: Numeric. It is recycled to the same length as y if necessary.
derivative: Non-negative integer. The default is the ordinary function evaluation, otherwise the derivative with respect to lambda.
epsilon: Numeric and positive value. The tolerance given to values of lambda when comparing it to 0 or 2.
inverse: Logical. Return the inverse transformation?

Details

The Yeo-Johnson transformation can be thought of as an extension of the Box-Cox transformation. It handles both positive and negative values, whereas the Box-Cox transformation only handles positive values. Both can be used to transform the data so as to improve normality. They can be used to perform LMS quantile regression.

Value

The Yeo-Johnson transformation or its inverse, or its derivatives with respect to lambda, of y.

References

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

Yee, T. W. (2004). Quantile regression via vector generalized additive models. Statistics in Medicine, 23, 2295–2315.

Author

Thomas W. Yee

Note

If inverse = TRUE then the argument derivative = 0 is required.

Examples

y <- seq(-4, 4, len = (nn <- 200))
ltry <- c(0, 0.5, 1, 1.5, 2)  # Try these values of lambda
lltry <- length(ltry)
psi <- matrix(NA_real_, nn, lltry)
for (ii in 1:lltry)
  psi[, ii] <- yeo.johnson(y, lambda = ltry[ii])

if (FALSE) { # \dontrun{
matplot(y, psi, type = "l", ylim = c(-4, 4), lwd = 2,
        lty = 1:lltry, col = 1:lltry, las = 1,
        ylab = "Yeo-Johnson transformation", 
        main = "Yeo-Johnson transformation with some lambda values")
abline(v = 0, h = 0)
legend(x = 1, y = -0.5, lty = 1:lltry, legend = as.character(ltry),
       lwd = 2, col = 1:lltry) } # }