In response to a comment of mine:
> Incidentally, I'd strongly recommend constructing interaction variables
> that are orthogonal at least to their own main effects (and lower-order
> interactions, when there are any), and possibly orthogonal to some or all
> of the apparently irrelevant other predictors. Else correlations between
> the interaction variables and other variables can, sometimes, be horribly
> confusing; especially with the "quantitative" (non-categorical)
> variables, whose products with other such variables are likely to be
> strongly (positively) correlated with the original variables merely
> because the original variables tend to be always positive and sometimes
> far from zero -- thus inducing what I've elsewhere called "spurious
> multicollinearity".
Frank E Harrell Jr wrote:
> This I do not understand. I don't see the point in testing main
> effects in the presence of interaction effects (unlike the pooled main
> effect + interaction effect tests which are completely invariant to
> coding). So I don't see why coding matters. -Frank Harrell
Sorry if I have confused two issues. The remark quoted is not related to
the coding of variables; it applies generally. As to "testing main
effects in the presence of interactions", in a factorial analysis of
variance one tests main effects and all possible interactions in the
presence of each other; and it is standard advice not to attempt to
interpret main effects (or for that matter lower-order interactions) in
the presence of significant interaction(s), at least until one has made
some sense out of the interaction(s) (or, better, out of the pattern of
main effects & interactions).
But in a balanced factorial ANOVA things are unambiguous in two
ways: (1) the apparent significance of individual sources of variation
does not depend on the order of their entry into the model; (2) the
significance of any particular source does not depend on the presence or
absence of other sources. Both of these are due to the orthogonality
inherent in a balanced design. When the predictors are correlated, as is
usual in regression and in unbalanced ANOVAs, neither of these is true.
Constructing interactions to be orthogonal to their main effects and to
lower-order interactions, as recommended above, means at least that one's
ability to detect main effects is not bollixed up by including the
interaction terms in the analysis. It also means that if any interaction
term is significant, one can believe that one is indeed looking at an
interaction effect, and not at an artifact arising from inadvertent
correlation between the interaction variable and its main effects.
I take it that one first looks for the patterns of main effects
and interactions that must be taken into account in the eventual
restricted model; then one attempts to interpret the model. At this
point coding matters, because the meaning one can attribute to any
particular coefficient will depend on the coding of the variable. It
follows that one may choose to revise the coding, to facilitate or
simplify the interpretation.
There is one other sense in which "coding matters", although this
may be a bit off-topic from the original thread. Consider an experiment
in which the subjects are of two sexes, and the experimental treatments
are mediated by experimenters, who also are of two sexes. Whatever else
is going on, there is a 2x2 subdesign representing (sex of Subject) by
(sex of Experimenter). One may code both variables, for example, so that
0 = male and 1 = female. Then if the data show a difference between
cases where subject and experimenter are of the same sex and cases where
they are of opposite sexes, that's an interaction effect. But if one had
coded (0 = male and 1 = female) for Subjects, and (0 = same sex as
Subject and 1 = opposite sex from Subject) for Experimenters, then the
effect just described is a main effect of the Experimenter sex variable.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
