On Fri, 4 Dec 2009, Peng Yu wrote:
On Fri, Dec 4, 2009 at 12:18 PM, Charles C. Berry <cbe...@tajo.ucsd.edu> wrote:
On Fri, 4 Dec 2009, Peng Yu wrote:
On Tue, Dec 1, 2009 at 4:04 PM, Charles C. Berry <cbe...@tajo.ucsd.edu>
wrote:
On Tue, 1 Dec 2009, Peng Yu wrote:
Could somebody recommend some textbook how to compute contrast when
there are interactions terms? "Applied Linear Regression Models"
(book) mentioned contrast, but I cannot extend it to the case where
there are interaction terms.
Textbook? Schmextbook!
You have the power of R at your fingertips!
Use it to explore concepts you are trying to wrap your brain around!
df <- expand.grid(x1=1:20,x2=factor(letters[1:2]))
vanilla <- model.matrix(~0+poly(x1,degree=3), df )
matplot(row( vanilla) , vanilla, type='b')
inter <- model.matrix(~0+poly(x1,degree=3):x2, df )
matplot(row( inter ) , inter, type='b')
I don't understand. Where the contrast is?
I don't understand what polynomial contrasts are. Would you please
help me understand?
Look at the graphs, please. They are linear basis functions for
polynomials. Construct a third order polynomial in x <- 1:20 (say) then
fit it with poly( x , degree=1), poly ( x, degree =2 ) , ..., poly( x,
degree=19 ). Compare the predict() ed values of each to the actual
polynomial. Study the coefficients.
May I ask you the following question to understand contrasts in a
simpler examples?
In the following example, I fit formula Y~x1+x2 and Y~x1*x2.
For Y~x1+x2, I understand that coefficients(afit)['x1b'] is the
contrast between the factor mean of a and the factor mean of b.
But for Y~x1*x2, since there are the interaction terms, I'm not sure
if it makes sense to compare the levels of a and b. Would you please
let me know what coefficients(afit)['x1b'] means in this case?
Well, it is literally the coefficient of
model.matrix(afit)[, 'x1b' ]
and you can see from inspection of that matrix where it figures in.
And/or you can do some plots like:
repl1 <- aframe$x3==1 # just one replicate
matplot( 1:sum(repl1),
predict(afit)[repl1] +
outer(model.matrix(afit)[repl1,'x1b'],-1:1),
pch="-o+")
to get a sense of how that coefficient affects the means of the different
groups.
As to what it 'means', in many discussions one does not mention that
coefficient nor test it if interactions that involve it are present. Its
status is much like the intercept in the main effects only model in the
sense that it is not of much interest by itself, but its absence ( \equiv
setting its coefficient to zero) usually implies an unwanted and unnatural
constraint.
Chuck
n=3
aframe=expand.grid(x1=c('a','b'),x2=c('u','v','w'),x3=1:n)
set.seed(0)
Y=rnorm(dim(aframe)[[1]])
aframe=cbind(aframe,Y)
afit=aov(Y~x1+x2, aframe)
coefficients(afit)
(Intercept) x1b x2v x2w
-0.14740700 -0.27974772 1.00234567 -0.01278949
afit=aov(Y~x1*x2, aframe)
coefficients(afit)
(Intercept) x1b x2v x2w x1b:x2v x1b:x2w
-0.27108992 -0.03238187 0.61269558 0.74790937 0.77930018 -1.52139771
The numbered curves are the terms of polynomial contrasts.
See
?poly
?contr.poly
and note
all( contr.poly(5) == poly(1:5,degree=4) )
BTW, what does 'schmextbook' mean?
Well, repeating a word and prepending 'schm' (in place of the initial
consonant sound, if any) is a slang idiom for asserting low regard for the
idea expressed by the word.
As in 'Birthday-Schmirthday' when moaning about getting older:
http://www.berkeleydailyplanet.com/issue/2009-01-29/article/32134?headline=First-Person-Birthday-Schmirthday-Whinings-on-Mortality
or 'Middle-schmiddle' which expresses low regard for the 'middle' policy,
see
http://aussiethule.blogspot.com/2006/03/olmerts-middle-schmiddle.html
Or 'Nilsson-Schmilsson', a self-deprecating title for an album by Harry
Nilsson:
http://en.wikipedia.org/wiki/Nilsson_Schmilsson
Or 'textbook-schmextbook', in which I express the idea that a textbook
really isn't needed.
Chuck
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PLEASE do read the posting guide
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Charles C. Berry (858) 534-2098
Dept of Family/Preventive
Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Charles C. Berry (858) 534-2098
Dept of Family/Preventive Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
______________________________________________
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
