Dear Rene,
At least from the part of the data.frame attached to your mail, I assumed that C,D and E changed in identical ways (but maybe I got this wrong).
With your following combination of factors:
A (four levels) B (three levels) C (two levels) D (29 levels) with E (four replicates)
And assuming independence of the treatment levels, you should get
3 d.f. for A 2 d.f. for B 28 d.f. for D 3 d.f. for E ? residual d.f. (how big is total number of Y values?)
The problem arises if parts of treatments B,D and E are applied to the same subjects, e.g.
B D E Y 1 1 1 400 2 2 2 300 2 2 3 420 2 2 4 350 (etc)
then you immediately run into problems because treatments B and D (in this case) change in an identical way, i.e. the variances calculated for each level of B and D are the same; this is what causes the ´singularities´. Errors need to be independent, otherwise you will have order dependence in your analyses.
i.e. the output of your aov model will change depending on the sequence in which the terms A,B,C,D,E are entered.
Did I get this right? It would probably help to see the full dataset
Best wishes Christoph
Rene Eschen wrote:
Dear Christoph,
The reason for the "singularities" is that B, C and D are not independent (in fact, they´re identical in their factor levels, and hence in their effect on Y).
I do not understand this. You gave the correct levels for A, B and E, but I do not see how they are identical. They have different levels and different codings, or is it because A has the same number of levels as E, and E shares some of the coding with B?
René Eschen.
---
For this reason, only the effects of A, B and E can be estimated:
Df Sum Sq Mean Sq F value Pr(>F) A 3 302286 100762 7.9887 0.002396 **
B 1 422869 422869 33.5263 4.683e-05 ***
E 3 22281 7427 0.5888 0.632334 Residuals 14 176583 12613
A has 4 levels so there should be 3 d.f. (that´s correct in the table) B has 2 levels so there is only 1 d.f. (that´s also correct) E has 4 levels so there should be 3 d.f. (also O.K.)
In total, there are [(n=22)-(3)-(1)-(3)] -1 = 14 residual d.f., so that´s OK, too.
Hope this helps, Christoph
levels(A) [1] "0" "250" "500" "1000" > levels(B) [1] "1" "2" > levels(E) [1] "1" "2" "3" "4"
Rene Eschen wrote:
factorsHi all,
I'm using R 2.0.1. for Windows to analyze the influence of following
reasonon response Y:
A (four levels) B (three levels) C (two levels) D (29 levels) with E (four replicates)
The dataset looks like this: A B C D E Y 0 1 1 1 1 491.9 0 1 1 1 2 618.7 0 1 1 1 3 448.2 0 1 1 1 4 632.9 250 1 1 1 1 92.4 250 1 1 1 2 117 250 1 1 1 3 35.5 250 1 1 1 4 102.7 500 1 1 1 1 47 500 1 1 1 2 57.4 500 1 1 1 3 6.5 500 1 1 1 4 50.9 1000 1 1 1 1 0.7 1000 1 1 1 2 6.2 1000 1 1 1 3 0.5 1000 1 1 1 4 1.1 0 2 2 2 1 6 0 2 2 2 2 4.2 0 2 2 2 3 20.3 0 2 2 2 4 3.5 250 2 2 2 1 8.4 250 2 2 2 2 2.8
etc.
If I ask the following: summary(aov(Y~A+B+C+D+E))
R gives me this answer:
Df Sum Sq Mean Sq F value Pr(>F) A 3 135.602 45.201 310.2166 <2e-16 ***
B 2 0.553 0.276 1.8976 0.1512 C 1 0.281 0.281 1.9264 0.1659 D 25 92.848 3.714 25.4890 <2e-16 ***
E 3 0.231 0.077 0.5279 0.6634 Residuals 411 59.885 0.146
Can someone explain me why factor C has only 25 Df (in stead of 28, what I expected), and why this number changes when I leave out factors B or C (but not A)? Why do factors B and C (but again: not A) not show up in the calculation if they appear later in the formula than D?
When I ask summary.lm(aov(Y~A+B+C+D+E)), R tells me that three levels of D
were not defined because of "singularities" (what does this word mean?).
After checking and playing around with the dataset, I find no logical
for which levels are not defined. Even if I construct a "perfect" datasethttp://www.R-project.org/posting-guide.html
(balanced, no missing values) I never get the correct number of Df.
My other datasets are analyzed as expected using the similar function calls and similar datasets. Am I doing something wrong here?
Many thanks,
René Eschen.
___ drs. René Eschen CABI Bioscience Switzerland Centre 1 Rue des Grillons CH-2800 Delémont Switzerland +41 32 421 48 87 (Direct) +41 32 421 48 70 (Secretary) +41 32 421 48 71 (Fax)
http://www.unifr.ch/biol/ecology/muellerschaerer/group/eschen/eschen.html
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