Regarding the Box-Cox transformation, it does have a shortcoming ...
- ... or two, such as the fact that transformation to (approximate)
normality is not assured, as was explained in the statistics
literature over 20 years ago. The Box-Cox transformation should
generally be used to satisfy the model assumptions (constant error
variance, normality) rather than to improve the fit of the model.
Transforming the components of the right-hand side is done to improve
model fit. When the Box-Cox transformation is used, the right-hand
side must be transformed the same way to preserve the quality of the
fit (i.e., the transform-both-sides approach should be used, as
illustrated in the Carroll and Ruppert research monograph that was