S3 Class

Objects of S3 class "boxcoxLm" are returned by the EnvStats function boxcox when the argument x is an object of class "lm". In this case, boxcox computes values of an objective function for user-specified powers, or computes the optimal power for the specified objective, based on residuals from the linear model.

Details

Objects of class "boxcoxLm" are lists that contain information about the "lm" object that was suplied, the powers that were used, the objective that was used, the values of the objective for the given powers, and whether an optimization was specified.

Methods

Generic functions that have methods for objects of class "boxcoxLm" include:
plot, print.

Value

The following components must be included in a legitimate list of class "boxcoxLm".

lambda: Numeric vector containing the powers used in the Box-Cox transformations. If the value of the optimize component is FALSE, then lambda contains the values of all of the powers at which the objective was evaluated. If the value of the optimize component is TRUE, then lambda is a scalar containing the value of the power that maximizes the objective.
objective: Numeric vector containing the value(s) of the objective for the given value(s) of $\lambda$ that are stored in the component lambda.
objective.name: character string indicating the objective that was used. The possible values are "PPCC" (probability plot correlation coefficient; the default), "Shapiro-Wilk" (the Shapiro-Wilk goodness-of-fit statistic), and "Log-Likelihood" (the log-likelihood function).
optimize: logical scalar indicating whether the objective was simply evaluted at the given values of lambda (optimize=FALSE), or instead the optimal power transformation was computed within the bounds specified by lambda (optimize=TRUE).
optimize.bounds: Numeric vector of length 2 with a names attribute indicating the bounds within which the optimization took place. When optimize=FALSE, this contains missing values.
eps: finite, positive numeric scalar indicating what value of eps was used. When the absolute value of lambda is less than eps, lambda is assumed to be 0 for the Box-Cox transformation.
lm.obj: the value of the argument x provided to boxcox (an object that must inherit from class "lm").
sample.size: Numeric scalar indicating the number of finite, non-missing observations.
data.name: The name of the data object used for the Box-Cox computations.

Note

Since objects of class "boxcoxLm" are lists, you may extract their components with the $ and [[ operators.

Author

Steven P. Millard (EnvStats@ProbStatInfo.com)

Examples

  # Create an object of class "boxcoxLm", then print it out.

  # The data frame Environmental.df contains daily measurements of 
  # ozone concentration, wind speed, temperature, and solar radiation
  # in New York City for 153 consecutive days between May 1 and 
  # September 30, 1973.  In this example, we'll plot ozone vs. 
  # temperature and look at the Q-Q plot of the residuals.  Then 
  # we'll look at possible Box-Cox transformations.  The "optimal" one 
  # based on the PPCC looks close to a log-transformation 
  # (i.e., lambda=0).  The power that produces the largest PPCC is 
  # about 0.2, so a cube root (lambda=1/3) transformation might work too.

  # Fit the model with the raw Ozone data
  #--------------------------------------
  ozone.fit <- lm(ozone ~ temperature, data = Environmental.df) 

  # Plot Ozone vs. Temperature, with fitted line 
  #---------------------------------------------
  dev.new()
  with(Environmental.df, 
    plot(temperature, ozone, xlab = "Temperature (degrees F)",
      ylab = "Ozone (ppb)", main = "Ozone vs. Temperature"))
  abline(ozone.fit) 

  # Look at the Q-Q Plot for the residuals 
  #---------------------------------------
  dev.new()
  qqPlot(ozone.fit$residuals, add.line = TRUE) 

  # Look at Box-Cox transformations of Ozone 
  #-----------------------------------------
  boxcox.list <- boxcox(ozone.fit) 
  boxcox.list 
#> 
#> Results of Box-Cox Transformation
#> ---------------------------------
#> 
#> Objective Name:                  PPCC
#> 
#> Linear Model:                    ozone.fit
#> 
#> Sample Size:                     116
#> 
#>  lambda      PPCC
#>    -2.0 0.4286781
#>    -1.5 0.4673544
#>    -1.0 0.5896132
#>    -0.5 0.8301458
#>     0.0 0.9871519
#>     0.5 0.9819825
#>     1.0 0.9408694
#>     1.5 0.8840770
#>     2.0 0.8213675
  #Results of Box-Cox Transformation
  #---------------------------------
  #
  #Objective Name:                  PPCC
  #
  #Linear Model:                    ozone.fit
  #
  #Sample Size:                     116
  #
  # lambda      PPCC
  #   -2.0 0.4286781
  #   -1.5 0.4673544
  #   -1.0 0.5896132
  #   -0.5 0.8301458
  #    0.0 0.9871519
  #    0.5 0.9819825
  #    1.0 0.9408694
  #    1.5 0.8840770
  #    2.0 0.8213675

  #----------

  # Clean up
  #---------
  rm(ozone.fit, boxcox.list)

S3 Class "boxcoxLm"