yjTransform {Transform}

Yeo- Johnson Transformation for Normality

Description

yjTransform performs Yeo- Johnson transformation for normality of a variable and provides graphical analysis.

Usage

yjTransform(data, lambda = seq(-3,3,0.01), plot = TRUE, alpha = 0.05, 
  verbose = TRUE)

Arguments

data

a numeric vector of data values.

lambda

a vector which includes the sequence of candidate lambda values. Default is set to (-3,3) with increment 0.01.

plot

a logical to plot histogram with its density line and qqplot of raw and transformed data. Defaults plot = TRUE.

alpha

the level of significance to check the normality after transformation. Default is set to alpha = 0.05.

verbose

a logical for printing output to R console.

Details

Denote y the variable at the original scale and y' the transformed variable. The Yeo-Johnson power transformation is defined by:

y' = \left\{ \begin{array}{ll} \frac{(y+1)^\lambda-1}{\lambda} \mbox{ , if $\lambda \neq 0, y \geq 0$} \cr \log(y+1) \mbox{ , if $\lambda = 0, y \geq 0$} \cr \frac{(1-y)^{2-\lambda}-1}{\lambda-2} \mbox{ , if $\lambda \neq 2, y < 0$} \cr -\log(1-y) \mbox{ , if $\lambda = 2, y < 0$} \end{array} \right.

Value

A list with class "yj" containing the following elements:

method

method to estimate Yeo-Johnson transformation parameter

lambda.hat

estimate of Yeo-Johnson transformation parameter

statistic

Shapiro-Wilk test statistic for transformed data

p.value

Shapiro-Wilk test p.value for transformed data

alpha

level of significance to assess normality

tf.data

transformed data set

var.name

variable name

Author(s)

Muge Coskun Yildirim, Osman Dag

References

Asar, O., Ilk, O., Dag, O. (2017). Estimating Box-Cox Power Transformation Parameter via Goodness of Fit Tests. Communications in Statistics - Simulation and Computation, 46:1, 91–105.

Yeo, I.K., Johnson, R.A. (2000). A New Family of Power Transformations to Improve Normality or Symmetry. Biometrika, 87:4, 954–9.

Examples

data <- cars$dist

library(Transform)
out <- yjTransform(data)
out$lambda.hat # the estimate of Yeo- Johnson parameter based on Shapiro-Wilk test statistic 
out$p.value # p.value of Shapiro-Wilk test for transformed data 
out$tf.data # transformed data set