Introduction to robust transformations
in linear regression
Several analyses of regression datasets can be improved by using a transformation
of the response, rather than the original response itself, in the analysis of the
data. More specifically the transformation may improve the approximate normality
or the homogeneity of the errors. In a lot of examples there are physical reasons
why a transformation might be expected to be helpful. For instance if the response
is a non negative variable, cannot be subject
to additive errors of constant variance.
In this part of the toolbox we consider the parametric family of power transformations
introduced by Box and Cox (1964). A full discussion is given by Atkinson Riani (2000).
Given that the estimated transformation and related test statistic may be sensitive
to the presence of one, or several, outliers, we use the forward search to see how
the estimates and statistics evolve as we move through the ordered data. As the
user will see, influential observations may only be evident for some transformations
of the data. Since observations that appear as outlying in untransformed data may
not be outlying once the data have been transformed, and vice versa, we employ the
forward search on data subject to various transformations, as well as on untransformed
data.