Contrast anova multi factor
On 26 Apr 2015, at 17:30 , Thierry Onkelinx <thierry.onkelinx at inbo.be> wrote: Dear Mario, The interpretation is the same: the average at the reference situation which is the group that has f1 == "f1 level1" and f2 == "f2 level1".
A little more precisely: It is the estimate of the expected value at the reference situation. In a balanced two-way design, this can be worked out explicitly: It is the average of the first row + the average of the first column - the total average. E.g.
library(ISwR) lm(hr~subj+time, heart.rate)
Call:
lm(formula = hr ~ subj + time, data = heart.rate)
Coefficients:
(Intercept) subj2 subj3 subj4 subj5 subj6
94.917 18.000 -5.750 -8.000 30.500 6.500
subj7 subj8 subj9 time30 time60 time120
-22.000 -16.000 11.500 -4.000 -5.444 -4.222
with(heart.rate, tapply(hr, subj, mean))
1 2 3 4 5 6 7 8 9 91.50 109.50 85.75 83.50 122.00 98.00 69.50 75.50 103.00
with(heart.rate, tapply(hr, time, mean))
0 30 60 120 96.55556 92.55556 91.11111 92.33333
with(heart.rate, mean(hr))
[1] 93.13889
91.5+96.55556 - 93.13889
[1] 94.91667 In an unbalanced design, the calculation of the intercept gets a bit lost in matrix-calculus land; there is no simple formula, but it is still an estimate of the same thing. - Peter D
Best regards, ir. Thierry Onkelinx Instituut voor natuur- en bosonderzoek / Research Institute for Nature and Forest team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance Kliniekstraat 25 1070 Anderlecht Belgium To call in the statistician after the experiment is done may be no more than asking him to perform a post-mortem examination: he may be able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher The plural of anecdote is not data. ~ Roger Brinner The combination of some data and an aching desire for an answer does not ensure that a reasonable answer can be extracted from a given body of data. ~ John Tukey 2015-04-26 17:12 GMT+02:00 Mario Jos? Marques-Azevedo <mariojmaaz at gmail.com> :
Hi all,
I am doing anova multi factor and I found different Intercept when model
has interaction term.
I have the follow data:
set.seed(42)
dt <- data.frame(f1=c(rep("a",5),rep("b",5)),
f2=rep(c("I","II"),5),
y=rnorm(10))
When I run
summary.lm(aov(y ~ f1 * f2, data = dt))
The Intercept term is the mean of first level of f1 and f2. I can confirm
that with:
tapply(dt$y, list(dt$f1, dt$f2), mean)
I know that others terms are difference of levels with Intercept.
But I do not know what is Intercept when the model do not have interaction
term:
summary.lm(aov(y ~f1 + f2, data = dt))
I know that I can create a specific contrast table, by I would like
understand the default R output.
I read contrast sub-chapter on Crawley 2012 (The R book) and in his example
the Intercept is different when model has or not interaction term, but he
explain that Intercept is mean of first level of the factors.
Best regards,
Mario
.............................................................
Mario Jos? Marques-Azevedo
Ph.D. Candidate in Ecology
Dept. Plant Biology, Institute of Biology
University of Campinas - UNICAMP
Campinas, S?o Paulo, Brazil
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