I responded to a question on RADSTATS asking about transformations, andhave now been faced with the type of basic question that a good student
should raise and a good teacher should be able to answer. I offer my
response below, but would be grateful for comments, additions or
references from (send to me). Since I have not asked his permission, I
have removed the questioner's name, but will circulate a summary and also
make sure my interrogator is informed.
--On 30 June 2002 <[log in to unmask]> wrote (personal email):
>> ... various books and papers on generalized linear models, which use
>> error distributions from the exponential family, of which Gaussian is
>> just one. The manual for GLIM (Payne et al) is perhaps as good as any
>> primer, or McCullagh and Nelder's book for a more theoretical approach.
--response from X was:
> Thanks, I'm aware of these, but I haven't explicitely seen a debate
> between using power transformations and using techniques based on
> non-gaussian distributions. Does it exist?
RAR's response: The question makes me realise that for twenty years I have
taken it as axiomatic that modelling with stated assumptions was "better"
than using an approximation based on other assumptions+normality. One
argument has been that the older methods were employed simply because the
mathematics was more tractible with hand calculations and tables.
Another has been the elegance of GLMs in dispelling the morass of
terminology surrounding all the alternative specific techniques.
Thirdly, has been the assumption that modelling gives better insight into
the generating mechanisms, getting away from the idea of data analysis as
no more than an exercise in arithmetic (to the "research cycle"). But I
cannot point to specific evidence that we get "better" answers, only to
examples used, which might be considered anecdotal.
Allan
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