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Re: st: visual guide to variable transformations?


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: visual guide to variable transformations?
Date   Thu, 7 Jun 2012 16:56:08 -0400

Hi, Lloyd.

Quite a lot has been written about transformations, including their
role in regression modeling.  I'll have to look for material that
approaches "a visual guide."

For now, I would like to correct the misimpression that, after
transformation, the data on an independent variable should resemble a
normal distribution.  I would not transform an independent variable
for that reason.

In the context of a regression model, the main aim in transforming an
independent variable is to promote linearity of the relation between
the dependent variable and the independent variable (as you describe
for Figure 1d).  Promoting linearity is also an important aim in
transforming the dependent variable.  Also, if the model involves more
than one independent variable, transforming the dependent variable may
make the contributions of the independent variables more nearly
additive (i.e., reduce or remove interactions among the independent
variables).

Another reason for transforming the dependent variable is to make
residual variability more nearly constant across the range of that
variable.  One usually checks on this by making various plots of
residuals.

Choosing transformations often requires thought.  It should not be
reduced to a simple rule.  The transformations need to make sense in
the context of the data.

David Hoaglin

On Thu, Jun 7, 2012 at 3:10 PM, Lloyd Dumont <lloyddumont@yahoo.com> wrote:
> Hello, Stalisters.
>
> Does anyone know of a visual guide to variable transformations?  I have seen many decent verbal exlanations of whether, when, and specifically how to transform variables.  But, is there a single resource that shows which transformation is appropriate when.  For example, something like...
>
> When an indep variable is distributed as it is in Figure 1a and is related to the dep var as shown here in Figure 1b, then you should use the _____ transformation.  Then, the transformed indep variable will be displayed as in Figure 1c (which I imagine will almost always be something like a normal distribution) and the relationship between the transformed variable and the dep var will be as displayed in Figure 1d (which I imagine will almost always be linear).
>
> Of course, it all gets a little more complicated if we start talking about transforming the dep var, though this sort of transformation could also easily be displayed and explained visually.
>
> Does anyone know of such a resource?  If not, why not?

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