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Re: st: Using natural logs on RHS of maximum likelihood models


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Using natural logs on RHS of maximum likelihood models
Date   Tue, 26 Mar 2013 22:18:50 -0400

Dear Sam,

Before anyone can make a constructive suggestion, you need to share
more information on the details of your model.  Maximum likelihood is
a method of estimating the parameters in a model.  It applies to a
very wide range of models, some of which have a dichotomous (0, 1)
outcome variable.  Is your model a logistic regression (logit) model,
a probit model, or another type entirely?  Please be specific.

Your question about the predictor variables does not have any single,
simple answer.  The aim is usually to express each predictor variable
in a form that appropriately captures its relation to the outcome
variable (after adjusting for the contributions of the other predictor
variables).  Generically, we could write something like

g(y) = b0 + b1*f1(x1) + b2*f2(x2) + (more predictors)

The functions g, f1, f2, etc. may differ as needed, and common choices
include "leave it alone," take the logarithm, take the square root,
and "square it."  Part of your challenge in analyzing data is to make
appropriate choices of such functions.  For some classes of models,
people have developed a variety of diagnostic tools that help this
process.  Once you have explained more about your model and the
context of your data, I or someone else reading this list may be able
to recommend a book that discusses this and other steps in the
model-building process and shows how they work on actual sets of data.

I hope these comments are helpful.

Regards,

David Hoaglin

On Tue, Mar 26, 2013 at 5:19 PM, SAM MCCAW <sam2stata@gmail.com> wrote:
> Hello All,
>
> I am running a maximum likelihood model with a (0,1) categorical
> dependent variable.
>
> On the right hand side is better to use natural logs of non
> categorical variables or leave them as is as real numbers?
>
> Thanks a bunch.
>
> SAM
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