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

box.cox.var(y)

Arguments

Details

The constructed variable is defined as y[log(y/y') -1], where 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 jfox@mcmaster.ca

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. (1997) Applied Regression, Linear Models, and Related Methods. Sage.

See Also

boxcox, box.cox, box.cox.powers, box.cox.axis, av.plots

Examples

mod <- lm(interlocks + 1 ~ assets, data=Ornstein)
mod.aux <- update(mod, . ~ . + box.cox.var(interlocks + 1))
summary(mod.aux)
## Call:
## lm(formula = interlocks + 1 ~ assets + box.cox.var(interlocks + 
##     1), data = Ornstein)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -23.189  -6.701   0.541   6.773  12.051 
## 
## Coefficients:
##                               Estimate Std. Error t value Pr(>|t|)
## (Intercept)                  1.461e+01  5.426e-01  26.920   <2e-16
## assets                      -7.142e-05  5.119e-05  -1.395    0.164
## box.cox.var(interlocks + 1)  7.427e-01  4.136e-02  17.956   <2e-16
## 
## Residual standard error: 7.247 on 245 degrees of freedom
## Multiple R-Squared: 0.7986,     Adjusted R-squared: 0.797 
## F-statistic: 485.7 on 2 and 245 degrees of freedom,     p-value:     0 
av.plots(mod.aux, "box.cox.var(interlocks + 1)")