[R] summary.lme and anova question

[Peter Dalgaard]

Christoph Scherber wrote:
> Dear all,
>
> Thanks to Brian Ripley for pointing this out. If I understand it
> correctly, this would mean that looking at the parameter estimates,
> standard errors and P-values in summary.lme only makes sense if no
> interaction terms are present?

Yes and no. What it means is that the interpretation of parameter
estimates is parameterization-dependent and non-trivial. Consider a
simple 2x2 design

       A
    0  |  1
------------
B 0| a | b |
   ---------
  1| c | d |
------------

(make sure to view that in a fixed-width font)

Parametrization with treatment contrasts has the "A" effect as  (b - a),
the "B" effect as (c - a) and the "A:B" effect as ((d - a) - ((c - a) +
(b - a) = (d - c) - (b - a) = (d - b) - (c - a)). Without the assumption
that the latter term is zero, you end up with "main effects" that really
only refer to  subsets of data

> My conclusion would then be that it is better to rely on the
> anova.lme() output when assessing the significance of terms in the
> model (rather than looking at the P-values from summary.lme).
>
> Is that correct? Because in most books (e.g. Crawley, "The R book"),
> the P values from summary.lme are used to assess the significance of
> terms.

No! The point is that if you have interactions in the model, either
interpret them or get rid of them (if non-significant). Main effects
just don't make sense in that case. Well, you can (and there are those
who do) _define_ them, e.g., as ((b-a)+(d-c))/2, but it is not obvious
what that means if you are averaging two terms known to be significantly
different.

-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
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