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

In glmtoolbox: Set of Tools to Data Analysis using Generalized Linear Models

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 class 'lm'
BoxTidwell(
  object,
  transf,
  epsilon = 1e-04,
  maxiter = 30,
  trace = FALSE,
  digits = getOption("digits") - 2,
  ...
)

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. By default, epsilon is set to be 0.0001.
maxiter	an (optional) positive integer value indicating the maximum number of iterations. By default, maxiter is set to be 30.
trace	an (optional) logical indicating if should the record of iterations be printed. By default, trace is set to be FALSE.
digits	an (optional) integer value indicating the number of decimal places to be used.
...	further arguments passed to or from other methods.

Value

a list list with components including

marginal	a matrix with estimates and standard errors of the estimated powers, as well as the statistic 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,

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.

See Also

BoxTidwell.glm

Examples

###### 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)

glmtoolbox documentation built on Oct. 10, 2023, 9:06 a.m.