Re: st: logit transformation of RHS variable

[David Hoaglin <dchoaglin@gmail.com>]

Many people try to add a quadratic term, almost by reflex, but (as you
note) many types of nonlinearity are not well approximated by
quadratics (or higher-degree polynomials).

If you have enough data, you can replace that RHS variable (x) with a
set of predictor variables that may help you to find a suitable
functional form.  Split the range of x into intervals, take one of
them as the reference category (perhaps one at the middle of the
range), and create a dummy (i.e., 0/1) variable for each of the other
intervals.  Use those dummy variables in your model, in place of x.
Then plot the resulting coefficients against the midpoints of the
corresponding intervals, and consider what functions of x the pattern
is compatible with.

Incidentally, the logit transformation of x is log[x/(1 - x)].
Rewriting it as log(x) - log(1 - x) shows that the logit is a member
of the family of "folded powers."  The folded square root is sqrt(x) -
sqrt(1 - x).

David Hoaglin

On Wed, Jan 4, 2012 at 6:21 PM, Raymond Lim <rl2240@columbia.edu> 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?
>
> Some alternatives may be
> 1. Add a quadratic term, but this doesn't get the S-shape representing
> "easier to go from 0 to .10; harder to go from .80 to .90"
> 2. Add a lag term to control for value in the previous period (yes,
> this is panel data).
>
> Thanks!
> -Raymond
> ---
> Raymond Lim
> Research Coordinator
> Columbia Business School - Finance & Economics Division
> RL2240@columbia.edu
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