boxCoxVariable: Constructed Variable for Box-Cox Transformation

In car: Companion to Applied Regression

Constructed Variable for Box-Cox Transformation

Description

Computes a constructed variable for the Box-Cox transformation of the response variable in a linear model.

Usage

boxCoxVariable(y)

Arguments

y	response variable.

Details

The constructed variable is defined as y[\log(y/\widetilde{y}) - 1], where \widetilde{y} is the geometric mean of y.

The constructed variable is meant to be added to the right-hand-side of the linear model. The t-test for the coefficient of the constructed variable is an approximate score test for whether a transformation is required.

If b is the coefficient of the constructed variable, then an estimate of the normalizing power transformation based on the score statistic is 1 - b. An added-variable plot for the constructed variable shows leverage and influence on the decision to transform y.

Value

a numeric vector of the same length as y.

Author(s)

John Fox [e-mail]

References

Atkinson, A. C. (1985) Plots, Transformations, and Regression. Oxford.

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations. JRSS B 26 211–246.

Fox, J. (2016) Applied Regression Analysis and Generalized Linear Models, Third Edition. Sage.

Fox, J. and Weisberg, S. (2019) An R Companion to Applied Regression, Third Edition, Sage.

See Also

boxcox, powerTransform, bcPower

Examples

mod <- lm(interlocks + 1 ~ assets, data=Ornstein)
mod.aux <- update(mod, . ~ . + boxCoxVariable(interlocks + 1))
summary(mod.aux)
# avPlots(mod.aux, "boxCoxVariable(interlocks + 1)")

car documentation built on Sept. 27, 2024, 9:06 a.m.