BoxTidwell.lm: Box-Tidwell transformations in Normal Linear Models

Description

Computes the Box-Tidwell power transformations of the predictors in a normal linear model.

Usage

# S3 method for lm
BoxTidwell(
  object,
  transf,
  epsilon = 1e-04,
  maxiter = 30,
  trace = FALSE,
  digits = max(3, getOption("digits") - 2),
  ...
)

Value

a list list with components including

`marginal`	a matrix with estimates, standard errors, and 95 and the p-value of the Wald test to assess the hypothesis \(H_0:\tau=1\) versus \(H_1:\tau\neq 1\),

`omnibus`	a matrix with the statistic and the p-value of the Wald test for null hypothesis that all powers are 1,

Arguments

object: an object of the class lm.
transf: an one-sided formula giving the quantitative predictors that are candidates for transformation.
epsilon: an (optional) numerical value. If the maximum relative change in coefficients is less than epsilon, then convergence is declared. As default, epsilon is set to 0.0001.
maxiter: an (optional) positive integer value indicating the maximum number of iterations. By default, maxiter is set to 30.
trace: an (optional) logical indicating if should the record of iterations be printed. By default, trace is set to FALSE.
digits: an (optional) integer value indicating the number of decimal places to be used.
...: further arguments passed to or from other methods.

References

Box G.E.P., Tidwell P.W. (1962) Transformation of the independent variables. Technometrics 4, 531-550.

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

Examples

Run this code

###### Example 1: Hill races in Scotland
data(races)
fit1 <- lm(rtime ~ distance + cclimb, data=races)
AIC(fit1)
BoxTidwell(fit1, transf= ~ distance + cclimb)
fit1 <- update(fit1,formula=rtime ~ distance + I(cclimb^2))
AIC(fit1)

###### Example 2: Gasoline yield
fit2 <- lm(mpg ~ hp + wt + am, data=mtcars)
AIC(fit2)
BoxTidwell(fit2, transf= ~ hp + wt)
fit2 <- update(fit2,formula=mpg ~ log(hp) + log(wt) + am)
AIC(fit2)

###### Example 3: New York Air Quality Measurements
fit3 <- lm(log(Ozone) ~ Solar.R + Wind + Temp, data=airquality)
AIC(fit3)
BoxTidwell(fit3, transf= ~ Solar.R + Wind + Temp)
fit3 <- update(fit3,formula=log(Ozone) ~ log(Solar.R) + Wind + Temp)
AIC(fit3)

###### Example 4: Heat capacity of hydrobromic acid
data(heatcap,package="GLMsData")
fit4 <- lm(Cp ~ Temp, data=heatcap)
AIC(fit4)
BoxTidwell(fit4, transf= ~ Temp)
fit4 <- update(fit4,formula=Cp ~ I(Temp^5))
AIC(fit4)

###### Example 5: Age and Eye Lens Weight of Rabbits in Australia
data(rabbits)
fit5 <- lm(log(wlens) ~ age, data=rabbits)
AIC(fit5)
BoxTidwell(fit5, transf= ~ age)
fit5 <- update(fit5,formula=log(wlens) ~ I(age^(-1/3)))
AIC(fit5)