[R] Contrast anova multi factor

[peter dalgaard]

> 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 José 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 José Marques-Azevedo
>> Ph.D. Candidate in Ecology
>> Dept. Plant Biology, Institute of Biology
>> University of Campinas - UNICAMP
>> Campinas, São Paulo, Brazil
>> 
>>        [[alternative HTML version deleted]]
>> 
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> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com