# Re: st: Standard normal Depvar

 From Evans Jadotte To statalist@hsphsun2.harvard.edu Subject Re: st: Standard normal Depvar Date Fri, 07 Aug 2009 16:23:17 +0200

```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

> 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.
```

```
```> 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.
```

```
```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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