Re: st: Standard normal Depvar

[Evans Jadotte <evans.jadotte@uab.es>]

Nick Cox wrote:
> I am glad we agree that exponentiation, meaning exp(), preserves 
> ranks. Sorry, but I don't understand what you want otherwise. Nor it 
> seems do Maarten Buis, Austin Nichols or Martin Weiss.
>
> I suggest that you try again with a fuller explanation, together with 
> examples.
>
> Nick
>
> Evans Jadotte wrote:
>
> > You did not read my earlier mail apologizing for my mind lapsus. I was
> > thinking about squaring all variables when I mentioned the re-ranking
> > issue. Evidently exponentiation preserves ranks. Also, as Austin
> > mentioned that the exercise I want to carry out does not make sense, it
> > has been applied many time in papers published from refereed journals
> > and was proposed the time by: Amemiya (1977) The ML
> > Estimator............ /Econometrica 45:955-68/.
> > Many thanks again for the feedback.
>
> Nick Cox wrote:
>
> > > To echo Austin Nichols, your assertion about exponentiation and 
> > > change of rank is quite incorrect. Think of a plot of exp(x) and you 
> > > will see that it is a monotonic function with any real as argument 
> > > and so rank reversal will not occur.
> > >
> > > Also, to expand on my earlier comment, only linear transforms will 
> > > map normals to normals.
>
> Evans Jadotte wrote:
>
> > > > Thanks Nick. However, exponentiation will result in a re-ranking of
> > > > individuals, which I must avoid. For instance, someone with a 
> > > score -5
> > > > compared with one whose score is 4, the former will end up being 
> > > ranked
> > > > higher than the latter after exponentiating. I need to preserve the
> > > > ranks and normality after transforming.
>
> Nick Cox wrote:
>
> > > > > Exponentiation will get you all positives. After that many options 
> > > > > are open.
>
> Evans Jadotte wrote:
>
> > > > > > Nick Cox wrote:
> > > > > > > This produces zero or positive values.
> > > > > > >
> > > > > > > Less pedantically, if the variable is already standard normal, 
> > > > > > > why does it need transforming?
>
>
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Hello Nick,

   Sorry for my being terse (and also the typos and missed words). What
   I am trying to do is the three-step feasible generalized least
   squares (proposed by Amemiya, 1977), which is not a problem /per
   se/. My only issue is on how to transform a  /y/, which is N(0,1), 
   in the first step in order to have strictly positive  xb^ while
   preserving normality. I did not put examples since it would be too
   cumbersome in the mail and would probably waste your time.


Many thanks,

Evans
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