Transform (version 1.0)

bcTransform: Box-Cox Transformation for Normality

Description

bcTransform performs Box-Cox transformation for normality of a variable and provides graphical analysis.

Usage

bcTransform(data, lambda = seq(-3,3,0.01), lambda2 = NULL, plot = TRUE, 
  alpha = 0.05, verbose = TRUE)

Value

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

method

method to estimate Box-Cox transformation parameter

lambda.hat

estimate of Box-Cox Power transformation parameter

lambda2

additional shifting 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

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.

lambda2

a numeric for an additional shifting parameter. Default is set to lambda2 = NULL.

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.

Author

Muge Coskun Yildirim, Osman Dag

Details

Denote \(y\) the variable at the original scale and \(y'\) the transformed variable. The Box-Cox power transformation is defined by:

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

If the data include any non- positive observations, a shifting parameter \(\lambda_2\) can be included in the transformation given by:

$$y' = \left\{ \begin{array}{ll} \frac{(y + \lambda_2)^\lambda - 1}{\lambda} \mbox{ , if $\lambda \neq 0$} \cr log(y + \lambda_2) \mbox{ , if $\lambda = 0$} \end{array} \right.$$

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.

Box, G.E., Cox, D.R. (1964). An Analysis of Transformations. Journal of the Royal Statistical Society: Series B (Methodological), 26:2, 211--43.

Examples

data <- cars$dist

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