Re: multiple linear regression

On Wed, 14 May 2008 09:07:34 -0700 (PDT), wallisjon@xxxxxxxxx wrote:

[snip, previous]

Hi Ray,

Thank you for that very clear explanation. I'm begining to see how I
can work this out from first principles rather than relying on the
trial-and-error approach that I have been adopting.

I have read arguments that dummy variables should not be standardized.
I think the concern was that by dividing by their standard deviation,
it rendered the interpretation of the dummy variable difficult. But
that aside, everything I have read seems to advise coding dummy
variables as 0 and 1.

Nobody divides dummy variables by their SDs, that I
am aware of. Most computer programs provide the "standardized
regression coefficients" as a by-product, and call that "beta" as
opposed to "b".

Centering a dummy makes the main effect of the dummy
harder to interpret. Centering the dummy values when computing
the interaction takes care of the interpretation problem, too.
Looking at the tests on main effect *before* entering the
interaction terms (and not, after) also avoids the distortion of
the main effect by the interaction coding.


But, if I understand this correctly, if we center x1, but leave x2 as
0 and 1, aren't we in some sense decreasing the likelihood of seeing a
significant effect of x1 (unless b3 is zero I guess, which in practice
seems unlikely)? What's so special about dummy variables that they
should not be centered (if indeed that advice is correct)?

Especially for "polynomial regression", the program itself
will use dummy variables that are centered and scored to
achieve the same weight for each term.

Programs that provide computation of interactions generally
provide information (hard to read) on what is indicated by
each separate term. When you do it yourself, you have to
figure it out for yourself -- and centering usually makes that
easier. (Concerning another post - I don't know what they
do in economics; there are some geniuses working there, and
there also are some flat-out statistical idiots.)

--
Rich Ulrich

http://www.pitt.edu/~wpilib/index.html
.

Relevant Pages

  • Re: multiple linear regression
    ... everybody uses dummy variables of 0 and 1. ... Centering is important to interpreting the main effects, ... Centering will not change the interaction coefficient, ... and centering x2 will change the main effect coefficient of x1, ...
    (sci.stat.consult)
  • Re: multiple linear regression
    ... everybody uses dummy variables of 0 and 1. ... Centering is important to interpreting the main effects, ... Centering will not change the interaction coefficient, ... and centering x2 will change the main effect coefficient of x1, ...
    (sci.stat.consult)
  • Re: multiple linear regression
    ... it rendered the interpretation of the dummy variable difficult. ... Nobody divides dummy variables by their SDs, ... Centering a dummy makes the main effect of the dummy ... Thank you to everybody for their advice in this thread - its really ...
    (sci.stat.consult)