[R] type III Sum Sq in ANOVA table - Howto?
Liaw, Andy
andy_liaw at merck.com
Fri Mar 7 02:08:23 CET 2003
> From: Rolf Turner [mailto:rolf at math.unb.ca]
>
> Andy Liaw wrote:
>
> > The long(er) answer: think harder about what question(s)
> you want answered
> > (i.e., what hypotheses you really want to test, and test
> only those). The
> > model hierarchy says that a model should not have an
> interaction term
> > involving a factor whose main effect is not present in the
> model. Seen in
> > this light, the hypothesis you're trying to test involves
> a non-sensical
> > model.
>
> Not really. The hypothesis being tested by Type III sums of square
> may be suspected of not being of ``central interest'', but it is NOT
> (as is commonly believed) ``non-sensical''.
>
> Let us think about the 2-way ANOVA case, where one can actually
> understand what is going on. Let the population ***cell means*** be
> mu_ij (i = 1, ..., m, j = 1, ..., n) and forget about the confusing
> and misleading over-parameterized model.
>
> Testing for the significance of the ``row factor'' by Type III
> sums of squares (with interaction in the model of course) tests
>
> H_0: mu_{1.}-bar = mu_{2.}-bar = ... = mu_{m.}-bar
>
> I.e. that the means of the population cell means, over columns, are
> all equal. I.e. that ``when rows are averaged over columns'' there
> is no row effect.
>
> This could, at least conceiveably, be of interest. Note that the
> average is not a weighted average, saying that all columns are
> equally important. If all columns are NOT equally important (e.g.
> if an item randomly drawn from the population is more likely to
> ``come from'' column 1 than from column 2 etc.) then this hypothesis
> is less likely to be of interest.
>
> But it isn't nonsensical.
>
> It is true, however, that most of the time when people test things
> using Type III sums of squares they don't understand what they are
> really testing. But then (said he cynically) people don't understand
> what the hell they are really testing in most situations, not just
> in the context of Type III sums of squares.
>
> cheers,
>
> Rolf Turner
I'm sorry, but I still don't see sense of this argument. By including the
interaction term in the model, isn't it implied that the cells have
different means, and the structure isn't a simple row + column? Assuming
that being the case, what's the sense of "averaging" over columns (or rows)?
I can perhaps understand the utility of such "test" in an exploratory
setting, but fail to see how this can be valid test in a more rigorous
sense. Maybe I'm stuck too deep in the rut...
Cheers,
Andy
------------------------------------------------------------------------------
More information about the R-help
mailing list