[R] type III Sum Sq in ANOVA table - Howto?

Peter Dalgaard BSA p.dalgaard at biostat.ku.dk
Fri Mar 7 08:39:01 CET 2003

Thomas Lumley <tlumley at u.washington.edu> writes:

> I think this is a bug, since it doesn't happen if factor1 isn't a factor,
> and leaving aside any question about Type III SS it seems to make it
> impossible to fit the model
>    lm(vardep~factor2+factor1:factor2)
> While this model isn't terribly often useful, it is sometimes.

Hmm... no ... and yes. There are some useful models, but you cannot
specify them unambiguously with model formulas. At least to my way of
thinking, the only useful way of thinking of interaction terms is that
f1:f2 describes an arbitrary pattern of means in the f1 x f2
crosstable, and the rest is just R/S being helpful in removing known
aliased effects. So f1 + f2 + f1:f2 is the same model as f2 + f1:f2 is
the same as f1:f2.

If you try to make any other sense of f2 + f1:f2  you get into
parametrization dependent models. The absense of f1 in the model could
mean no average effect of f1 or no effect of f1 at the first level of
f2 corresponding to "sum" or "treatment" contrasts. The former model
is basically what a usual Type III test would do and as several have
pointed out, the interpretation is tenuous at best. The latter model,
I agree is useful sometimes ("no difference at baseline" is a viable
hypothesis in randomised trials, e.g.) but you need to work harder to
specify it. 

   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

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