I would appreciate it if someone could explain the results of the
example from the aov() help file. The output given below is different
from book
Venables and Ripley - MASS
The results In R1.5.1 (Under windows) is as follows:
> N <- c(0,1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,1,0,0)
> P <- c(1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0)
> K <- c(1,0,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0,1,1,1,0,1,0)
> yield <- c(49.5,62.8,46.8,57.0,59.8,58.5,55.5,56.0,62.8,55.8,69.5,55.0,
+ 62.0,48.8,45.5,44.2,52.0,51.5,49.8,48.8,57.2,59.0,53.2,56.0)
> npk <- data.frame(block=gl(6,4), N=factor(N), P=factor(P),
+ K=factor(K), yield=yield)
>
> ( npk.aov <- aov(yield ~ block + N*P*K, npk) )
Call:
aov(formula = yield ~ block + N * P * K, data = npk)
Terms:
block N P K
N:P N:K P:K
Sum of Squares 343.2950 189.2817 8.4017 95.2017 21.2817 33.1350
0.4817
Deg. of Freedom 5 1 1 1
1 1 1
Residuals
Sum of Squares 185.2867
Deg. of Freedom 12
Residual standard error: 3.929447
1 out of 13 effects not estimable
Estimated effects may be unbalanced
> summary(npk.aov)
Df Sum Sq Mean Sq F value Pr(>F)
block 5 343.30 68.66 4.4467 0.015939 *
N 1 189.28 189.28 12.2587 0.004372 **
P 1 8.40 8.40 0.5441
0.474904
K 1 95.20 95.20 6.1657 0.028795 *
N:P 1 21.28 21.28 1.3783 0.263165
N:K 1 33.13 33.13 2.1460 0.168648
P:K 1 0.48 0.48 0.0312
0.862752
Residuals 12 185.29 15.44
---
Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` '
1
> coefficients(npk.aov)
(Intercept) block2 block3 block4 block5 block6
51.8250000 3.4250000 6.7500000 -3.9000000 -3.5000000 2.3250000
N1 P1 K1 N1:P1 N1:K1 P1:K1
9.8500000 0.4166667 -1.9166667 -3.7666667 -4.7000000 0.5666667
The output for the ANOVA table is exactly the same as in Venables and
Ripley MASS page 177, but the values of the coefficients are different.
Also if
alias(npk.aov) is used,as in the book, a different result is also obtained :
Model :
yield ~ block + N + P + K + N:P + N:K + P:K + N:P:K
Complete :
(Intercept) block2 block3 block4 block5 block6
N1 P1 K1 N1:P1 N1:K1 P1:K1
N1:P1:K1 0.25 0.25 0.25
-0.25 -0.25 -0.25 0.50 0.50 0.50
Can someone explain why this is different from the book MASS.
I also have a more general question in relation to the coefficient
terms. Why are there more than one coefficint for the blocking factor. I
want to construct a normal probability plot of effects and since the
ANOVA table gives me one block term, why are are more than one
coefficient term for blocks. Is there another way to extract the
regression coefficients? I don't understand why there are more than one
blocking coefficient .
Also in this analysis the block coefficients are from block2 to block 6,
whereas we have block1 to block5 in MASS.
Another point is that at the end of the ANOVA (summary) table the
warning "Estimated effects may be unbalanced" (aslo different from the
book) . In this case, should aov() be used or should I refit the model
with , say lme() ?
Thanks
Peter
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On Tue, 6 Aug 2002, Peter Ho wrote:> I would appreciate it if someone could explain the results of the > example from the aov() help file. The output given below is different > from book > Venables and Ripley - MASSYou forgot to set the the contrasts! -- Brian D. Ripley, ripley at stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272860 (secr) Oxford OX1 3TG, UK Fax: +44 1865 272595 -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
> From: Peter Ho [mailto:peter at esb.ucp.pt] > > I would appreciate it if someone could explain the results of the > example from the aov() help file. The output given below is different > from book > Venables and Ripley - MASS >[snipped]> > The output for the ANOVA table is exactly the same as in Venables and > Ripley MASS page 177, but the values of the coefficients are > different.I believe this is in the FAQ. By default Splus uses the Helmert contrasts for factors. R uses the "treatment contrasts", which are the differences between the 1st and all other levels of the factor (most likely easier to interpret than the Helmert contrast). I guess that's the reason the coefficients in R are labelled "block2" through "block6". [snipped]> > I also have a more general question in relation to the coefficient > terms. Why are there more than one coefficint for the > blocking factor. I > want to construct a normal probability plot of effects and since the > ANOVA table gives me one block term, why are are more than one > coefficient term for blocks. Is there another way to extract the > regression coefficients? I don't understand why there are > more than one > blocking coefficient .Sorry to be frank--- where did you learn your linear model / ANOVA? For a factor with k levels, there are k-1 contrasts, and thus k-1 coefficients. The entry in the ANOVA table encompasses all these coefficients. (Notice there are 6 blocks, so 5 df for the block term in the ANOVA table, and 5 coefficients for block).> Also in this analysis the block coefficients are from block2 > to block 6, > whereas we have block1 to block5 in MASS.See above.> Another point is that at the end of the ANOVA (summary) table the > warning "Estimated effects may be unbalanced" (aslo different > from the > book) . In this case, should aov() be used or should I refit > the model > with , say lme() ?MASS, up to the 3rd edition, is totally based on Splus, and R is *not* Splus. You should not expect the output to be identical to that degree. That's almost like asking all vendors of C compilers to use exactly the same set of error messages! I'd suggest you get more familiar with aov (and linear model formulations) before you wet your feet with lme, or risk being drown.> Thanks > > PeterAndy ------------------------------------------------------------------------------ Notice: This e-mail message, together with any attachments, contains information of Merck & Co., Inc. (Whitehouse Station, New Jersey, USA) that may be confidential, proprietary copyrighted and/or legally privileged, and is intended solely for the use of the individual or entity named on this message. If you are not the intended recipient, and have received this message in error, please immediately return this by e-mail and then delete it. ============================================================================= -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.- r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html Send "info", "help", or "[un]subscribe" (in the "body", not the subject !) To: r-help-request at stat.math.ethz.ch _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._