Thank you for your reply. The WoodEnergy example helped a lot. I
understand now that it is inappropriate to make all pairwise comparisons
with an interaction present and better to make comparisons between levels of
one factor within a constant level of the second factor. As I understand it,
the solution in the WoodEnergy example is to produce separate ANOVAs for
each type of wood and then perform the multiple comparisons between stove
types within each wood type. This makes a lot of sense. For my data, I'm
using glm.nb and if I run the model separately for each level of "site," it
estimates a different theta for each which I immagine is a problem. Is this
ok, or do I need to find a way to use the coefficients from the full model
with the interaction to compare levels of clipping within fixed levels of
site?
-Eric Scott
On Mon, Mar 15, 2010 at 3:49 PM, RICHARD M. HEIBERGER <r...@temple.edu>wrote:
> In addtition to the example I mentioned previously,
> demo("MMC.WoodEnergy-aov", "HH")
>
> Please also see
> demo("MMC.WoodEnergy", "HH")
>
> In this example, since anova(energy.aov.4),
> shows that the Wood factor and Stove:Wood interaction are significant,
> all possible pairwise comparisons of the 12 Stove:Wood terms are not
> interpretable. Only comparisons of Stoves within each of the Woods is
> interpretable. These estimates are shown with both tables and graphs.
> Since the covariate is also significant, it is necessary to pick a
> reference
> value for the comparisons.
>
> Here is a simplification of the WoodEnergy example to ignore the covariate.
> The 66 pairwise comparisons that TukeyHSD provides for the interaction
> effect are not interpretable. The significant interaction and one
> significant
> main effect together are an indicator that
> main effects and interactions are not interpretable.
> Only simple effects of one factor within
> a constant level of the other factor are interpretable.
>
> > energy.aov.4b <- aov(Energy ~ Stove*Wood + Stove:Wood,
> + data=energy)
> > anova(energy.aov.4b)
> Analysis of Variance Table
> Response: Energy
> Df Sum Sq Mean Sq F value Pr(>F)
> Stove 2 0.007 0.003 0.0078 0.9923
> Wood 3 274.768 91.589 209.0130 < 2.2e-16 ***
> Stove:Wood 6 34.570 5.762 13.1483 3.781e-10 ***
> Residuals 76 33.303 0.438
> ---
> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> > energy.aov.4b.HSD <- TukeyHSD(energy.aov.4b)
> > sapply(energy.aov.4b.HSD, dim)
> Stove Wood Stove:Wood
> [1,] 3 6 66
> [2,] 4 4 4
> >
>
>
>
>
> About a year after I wrote this example, Torsten extended glht to permit
> an option of averaging over other factors and covariates. I need to revise
> the WoodEnergy example to use that option.
>
> Rich
>
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