[R] TukeyHSD changes if I create interaction term

[Andrew Robinson]

Dear R community,

I'm trying to understand this behavior of TukeyHSD.  My goal is to obtain 
defensible, labelled multiple comparisons of an interaction term.

Firstly, if I plot the TukeyHSD from the model that calculates its own 
interactions, then the y-axis labels appear to be reflected on their median 
when compared to the text output of the TukeyHSD statement.  The labels are 
integers.

Secondly, if I provide an interaction term for the model, to try to coerce 
TukeyHSD to label the comparisons, then the multiple comparison outcome is 
quite different, as is the output from coefficients().  It must be using a 
different parameterization, because the anova statements that summarize the 
model are identical.  

However, if two different parameterizations give rise to two different sets of 
multiple comparisons, how ought we choose between them?

The following snippet illustrates.   

=======================================================================

data(warpbreaks)
warpbreaks$WT <- interaction(warpbreaks$wool, warpbreaks$tension)

summary(fm1 <- aov(breaks ~ wool * tension, data = warpbreaks))
summary(fm2 <- aov(breaks ~ wool + tension + WT, data = warpbreaks))

summary(fm1) #  Identical
summary(fm2) #  Identical

coefficients(fm1) #  Different
coefficients(fm2) #  Different

TukeyHSD(fm1, "wool:tension") 

# (1) My first concern is that the y-axis labels seem to be reflected
#     in their median. 

plot(TukeyHSD(fm1, "wool:tension")) # Labels are upside down?

# (2) My second concern is that the estimates and intervals are 
#     different from fm2

TukeyHSD(fm2, "WT") 

=======================================================================

I would appreciate any advice.  

Andrew
-- 
Andrew Robinson                      Ph: 208 885 7115
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