| bcTransform {Transform} | R Documentation |
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)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. |
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.
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 |
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.
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