There were several earlier messages, and then
I thought Don Burrill said most of what needed to be said --
On 20 Dec 1999 22:43:52 -0800, [EMAIL PROTECTED] (Donald F.
Burrill) wrote:
>
> For openers, I quote from Pedhazur (2nd edition), p 329 (summary for
> Chapter 9), so that we're all on the same wavelength, more or less:
> "... Regardless of the coding method used, the results of the
> overall analysis are the same. ..."
> (This is the point that other respondents and I had in mind when we
> were questioning your interpretation of Pedhazur.)
> Continuing a few sentences later:
> "... The coding methods do differ in the properties of their
> regression equations. A brief summary ... follows. ..."
> After the summaries of each method, the final paragraph:
> "Which method of coding one chooses depends on one's purpose and
> interest. [For one purpose], dummy coding is the preferred
> method. Orthogonal coding is most efficient [for another
> purpose]. It was shown, however, that the different types of
> multiple comparisons ... can be easily performed [with] effect
> coding. Consequently, effect coding is generally the preferred
> method of coding categorical variables."
>
> Burke Johnson had written:
>
> << 1. I agree with Joe that the term "dummy" in dummy coding is a rather
[ snip, various details.]
Later Don recommended constructing dummies for the Interactions in
such a manner so that they would be orthogonal to the main effects, in
order to reduce confusion of confounded interpretations; that bit of
advice received a minor criticism from someone else who pointed out
that you should never be trying to interpret *those* coefficients in
the first place.
Well, I agree with both Don and the critic. I create my interactions
as orthogonal, or approximately orthogonal -- in the old days, your
program was too likely to blow up if you did not get rid of all the
numerical problems you could, whenever you could. Further, if I
happen to look at the wrong listing, it will still have numbers that
are in the right range, and PROBABLY right. Finally, it may be a
cheap piece of consistency, but it gives me one less item that I have
to explain to the non-statisticians who look at various results.
Like the critic, though, I never want to interpret the coded main
effects in any regression that has also included the interactions.
- I would not mind receiving guidance on this final point. It is
*conceivable* to use codings so that the coefficients and tests for
main effects do have meaning when the interaction is included in a
regression. If it is what I remember seeing in an ANOVA text many
years ago, the weights and coefficients can be constructed to take
into account the Ns of the cells (more complicated than -1,0,1).
I believe: The test that this gives you for main effects is either
exactly the same as some other way of constructing the problem, or it
is considered obsolete. The construction that I like is Searle's
partitioning of sums of squares, usually in a hierarchy: (A), (B|A),
(AB|A,B) for instance.
Today, Burke Johnson sent an SPSS-worked example to Don B., with a CC:
to me, since I had posted earlier. The example was supposed to show
that different codings give different results. The example shows that
the total SS and test is always the same. And the example shows that
different codings can give you different results for coefficients and
tests when you look at Main effects when Interactions are already in
the equation -- which is entirely consistent with what Don and I (I
think) have both said, i.e., those effects should be presumed to be
uninterpretable -- so the illustration just heightens the question of
whether those effects are *ever* interpretable, since the
inconsistency proves that they are not strictly interpretable for most
sets of coefficients.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
