BoxTidwell.glm {glmtoolbox}

Box-Tidwell transformations in Generalized Linear Models

Description

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

Usage

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

Arguments

object

an object of the class glm.

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.

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,

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.lm

Examples

###### Example 1: Skin cancer in women
data(skincancer)
fit1 <- glm(cases ~ age + city, offset=log(population), family=poisson(log), data=skincancer)
AIC(fit1)
BoxTidwell(fit1, transf= ~ age)
fit1 <- update(fit1,formula=. ~ I(age^(-1/2)) + city)
AIC(fit1)

###### Example 3: Gas mileage
data(Auto, package="ISLR")
fit3 <- glm(mpg ~ horsepower + weight, family=inverse.gaussian(log), data=Auto)
AIC(fit3)
BoxTidwell(fit3, transf= ~ horsepower + weight)
fit3 <- update(fit3,formula=. ~ I(horsepower^(-1/3)) + weight)
AIC(fit3)

###### Example 4: Advertising
data(advertising)
fit4 <- glm(sales ~ TV + radio, family=gaussian(log), data=advertising)
AIC(fit4)
BoxTidwell(fit4, transf= ~ TV)
fit4 <- update(fit4,formula=. ~ I(TV^(1/10)) + radio)
AIC(fit4)

###### Example 5: Leukaemia Patients
data(leuk, package="MASS")
fit5 <- glm(ifelse(time>=52,1,0) ~ ag + wbc, family=binomial, data=leuk)
AIC(fit5)
BoxTidwell(fit5, transf= ~ wbc)
fit5 <- update(fit5,formula=. ~ ag + I(wbc^(-0.18)))
AIC(fit5)