Box-Cox power transformation for Linear Models

A utility helping finding lamda to transform y-->y^lamda to best fit multiple linear regression ...

Description

Helps choose a Box-Cox power transformation for a multivariate linear regression.

Assume you are looking at the residuals of [b,bint,r] = regress(y,X) and it seems a transformation is in place. Use:
boxcoxlm(y,X) to find the best lambda for a Box-Cox power transformation (y^lambda, or log(y) for lambda=0)

The function will also plot the Maximum Log-Likelihood as a function of lambda, and a 95% confidence region for the best value of lambda

More control can be obtained using:

[LambdaHat,LambdaInterval]=boxcoxlm(y,X,PlotLogLike,LambdaValues,alpha)

which allows ommiting the plot, a different region or precision, and a different alpha value for the confidence interval

• MATLAB release: MATLAB 7.1.0 (R14SP3)

[Elisabeth O´neil]

 

[Corey Yanofsky]

 

[B]

the function for LogLH is
LogLike(end+1)=-0.5*n*log(VarHat)+(Lambd-1)*SigmaLogY;

but this seems to be in consistent with Draper and Box (1969)
which lacks teh 0.5 but includes the term:
-(2sig)^-1 * sum(Zi-MUi)^2
where:
Zi = (YLambdai - 1)/lambda
MUi = "the mean specified by the relevant linear model"

Any explanation? Do you have a reference for this equation?

Thank you.