Box-Cox Transformations for Linear Model

Wrapper function to the boxcox function; estimates the optimal parameter for the Box-Cox power transformation and then applies the appropriate power transformation to the outcome variable.

boxcox_transform(
  x,
  outcome = NULL,
  parameter_grid = seq(-3, 3, 0.01),
  output = TRUE
)

Arguments

x

Either

• A numeric vector of positive values;

• A data frame with an outcome variable and set of predictors for a linear regression.

outcome

An optional character string with the column name for the outcome variable in x. Otherwise, the first column in x is assumed to be the outcome variable.

parameter_grid

Vector specifying the grid of parameters to explore for maximum likelihood estimation.

output

Logical; if TRUE, returns the outcome variable following the power transformation.

Value

Either the maximum likelihood estimate for the power transformation parameter or a vector for the outcome variable following the transformation.

Details

The Box-Cox power transformation for a vector of positive values \(x\) and parameter \(\lambda\) is:

$$ f(x) = \frac{x^{\lambda} - 1}{\lambda}. $$

For \(\lambda = 0\), one simply uses the log transform.

Examples

# Simulate 100 values from the normal distribution
set.seed(3)
z <- rnorm(100)
# Transform the simulated values
x <- (z * .5 + 1)^(1 / .5)
# Maximum likelihood estimate for
# transformation parameter
boxcox_transform(x, output = FALSE)
#> [1] 0.44

# Histogram of x, transform of x, and
# original simulated values
layout(rbind(1, 2, 3))
hist(x)
hist(boxcox_transform(x))
hist(z)