[R] Contrast anova multi factor

[Mario José Marques-Azevedo]

​Dear Thierry,

That is the problem. I read that interpretation is the same, but the
Intercept value of summary is different:

The mean of level "a" of f1 and level "I" of f2 (first level of each
factor) is 0.7127851.

When I run model with interaction term:

summary.lm(aov(y~f1*f2,data=dt))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   0.7128     0.2884   2.471   0.0484 *
f1b           1.0522     0.4560   2.307   0.0605 .
f2II         -0.6787     0.4560  -1.488   0.1872
f1b:f2II     -1.1741     0.6449  -1.821   0.1185

I check that Intercept is mean of level "a" of f1 and level "I" of f2.

But when I run the model without interaction term, the Intercept value is
different:

summary.lm(aov(y~f1+f2,data=dt))

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)   0.9476     0.2976   3.185   0.0154 *
f1b           0.4651     0.3720   1.251   0.2513
f2II         -1.2658     0.3720  -3.403   0.0114 *

I do not know what is Intercept value in this case. I expected that it is
mean of level "a" of f1 and level "I" of f2, but not.

Best regards,

Mario


On 26 April 2015 at 12:30, 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".
>
> 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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>
>
>

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