boxcoxmeta {AID} R Documentation

## Ensemble Based Box-Cox Transformation via Meta Analysis for Normality of a Variable

### Description

boxcoxmeta performs ensemble based Box-Cox transformation via meta analysis for normality of a variable and provides graphical analysis.

### Usage

boxcoxmeta(data, lambda = seq(-3,3,0.01), nboot = 100, 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. nboot a number of Bootstrap samples to estimate standard errors of lambda estimates. lambda2 a numeric for an additional shifting parameter. Default is set to lambda2 = 0. 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 nonpositive 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 "boxcoxmeta" containing the following elements:

 method name of method lambda.hat estimate of Box-Cox Power transformation parameter lambda2 additional shifting parameter result a data frame containing the result alpha the level of significance to assess normality. tf.data transformed data set var.name variable name

### Author(s)

Muhammed Ali Yilmaz, Osman Dag

### References

Yilmaz, M. A., Dag, O. (2022). Ensemble Based Box-Cox Transformation via Meta Analysis. Journal of Advanced Research in Natural and Applied Sciences, 8:3, 463–471.

### Examples

library(AID)
data(textile)

out <- boxcoxmeta(textile[,1])
out$lambda.hat # the estimate of Box-Cox parameter out$tf.data # transformed data set



[Package AID version 2.9 Index]