Dear allstat members,
I have a question wrt transformations of the response variable in GLMs and
regression models in particular. Transformed response variables are often
used to deal with model assumption violations. The parameters of this model
provide the effects of the explanatory variables on the transformed
response variable. If one wants to obtain their effects on the original
response variable, a back-transformation has to be carried out in which the
reverse transformation is applied to both sides of the model equation.
However, this changes the interpretation of the parameters. E.g. when a
logarithmic transformation was applied to the response variable, the
backtransformation yields a multiplicative model instead of an additive
model and the expected values on the basis of the model can no longer be
interpreted as contional means but only as conditional medians.
Can anyone provide me with references on this topic, i.e. on the issue of
model parameter interpretations after a back-transformation. I know that
most text books discuss this type of transformations but the
back-transformation and the interpretation of the parameters is usually not
discussed.
Thanks,
Jerry
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