How to compute contrast where there are interaction terms in the linear model?
On Fri, Dec 4, 2009 at 12:18 PM, Charles C. Berry <cberry at tajo.ucsd.edu> wrote:
On Fri, 4 Dec 2009, Peng Yu wrote:
On Tue, Dec 1, 2009 at 4:04 PM, Charles C. Berry <cberry at 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? 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?
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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Charles C. Berry ? ? ? ? ? ? ? ? ? ? ? ? ? ?(858) 534-2098 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?Dept of Family/Preventive Medicine E mailto:cberry at tajo.ucsd.edu ? ? ? ? ? ? ? UC San Diego http://famprevmed.ucsd.edu/faculty/cberry/ ?La Jolla, San Diego 92093-0901