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Re: st: Log Transform Justification


From   "Clive Nicholas" <clivelists@googlemail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Log Transform Justification
Date   Mon, 27 Aug 2007 14:31:02 +0100

Bilal Hossain wrote:

> In my PhD project, I was having problem to have a good model with
> Thikonov Regularization in inverse problem. I checked the data and
> try to get a good distribution of the data set.  I did log transform
> of raw data and run the model with transformed data. The model that I
> get is fantastic. Now I am happy to put the model, however, I think I
> have to justify the data transformation. So how can I justify?

Like Phil, I would say that's hard to answer your query properly if
you don't show us _exactly_ what you did. Also like Phil, I'll reply
using first principles, adding to his comments.

The main justification for log-transforming your dependent variable is
pretty straightforward: if your variable is a proportional, normalized
measure ranging from 0 to 1, a regression model may predict values
that lie outside that range, which wouldn't make any sense, since you
can't have >100% or <0%, for instance. Another problem is that an
independent variable has a lot less impact on the extreme margins of
such a dependent variable than it does at its centre.

Thus, you log-transform (LT) the variable, transforming the scale from
0-1 to minus infinity-plus infinity. You now have an unbounded scale
this is _linear_ in the coefficients. I fit models using LT variables
in Stata all the time, and I always use -glm- to fit them, adding
-logit- as the -link()- option. You should find that -glm- suits your
requirements in this regard.

-- 
Clive Nicholas

[Please DO NOT mail me personally here, but at
<clivenicholas@hotmail.com>. Thanks!]

"Courage is going from failure to failure without losing enthusiasm."
-- Winston Churchill
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