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
[[alternative HTML version deleted]]
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 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 > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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.[[alternative HTML version deleted]]
?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 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
>>
>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
>> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
>> 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.
>
>
>
[[alternative HTML version deleted]]
> 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 >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> 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. > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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.-- 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