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Re: st: logit transformation of RHS variable


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: logit transformation of RHS variable
Date   Thu, 5 Jan 2012 09:12:33 +0000

In generalized linear models, loglog, cloglog and logc are sometimes
used as link functions. I see no reason why they couldn't be used as
transformations on the RHS, as you seek a transformation asymmetric on
(0,1). At worst you need a nested function call such as -log(-log(x)).
 Note that exact values of 0 or 1 can be problematic for these
transformations. Naturally you would end up needing to explain such
transformations.

Nick

On Thu, Jan 5, 2012 at 1:25 AM, Brendan Halpin <brendan.halpin@ul.ie> wrote:
> On Wed, Jan 04 2012, Raymond Lim wrote:
>
>> Hello Statalisters,
>> I have an independent variable that I believe that needs to be
>> transformed because it's bounded between 0 and 1, and it's easier to
>> go from 0 to .10 than say .80 to .90. My question is, can I use a
>> logit transformation on this RHS variable (new_x = x / (1 - x)? Or are
>> logits usually for LHS variables only?
>
> I'd read the logit transformation as suggesting it is harder rather than
> easier to go from 0 to 0.1 than from 0.8 to 0.9. In log-odds 0 is
> -infinity and 0.1 is log(0.1111) or about -2.2, whereas 0.8 to 0.9 is
> 1.4 to 2.2. The logit makes it hard to move at both extremes, but easy
> around 0.5.
>
> It may be that the "fractional logit model" may be what you need:
>
> glm y x1 x2 ... , family(binomial) link(logit) robust
>
> Googling "fractional logit" gets
> www.maartenbuis.nl/presentations/UKsug06.pdf as the first hit. Maarten
> may have more to say himself, but I would imagine he is currently
> asleep!
>
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