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RE: st: Log Transform Justification


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Log Transform Justification
Date   Tue, 28 Aug 2007 12:56:09 +0100

Some confusion here between logarithms and logits? 

Nick 
n.j.cox@durham.ac.uk 

Clive Nicholas

> 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.

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