car (version 3.1-3)

boxCoxVariable: 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)

Value

a numeric vector of the same length as y.

Arguments

y

response variable.

Author

John Fox

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.

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)")