The message from this cute little data set is very clear. Consider > fm <- aov(resp ~ A*B + A/C, mydata) > > drop1(fm, test = "F") Single term deletions
Model: resp ~ A * B + A/C Df Sum of Sq RSS AIC F value Pr(F) <none> 65.540 47.261 A:B 2 16.132 81.672 47.222 0.7384 0.5168 A:C 6 199.501 265.041 60.411 3.0440 0.1007 So neither of the non-marginal terms is significant. To address questions about the main effects the natural next step is to remove the interactions. By orthogonality you can safely cut a few corners and do both at once: > drop1(update(fm, .~A+B), test = "F") Single term deletions Model: resp ~ A + B Df Sum of Sq RSS AIC F value Pr(F) <none> 281.17 57.47 A 2 33.12 314.30 55.48 0.8246 0.4586 B 1 915.21 1196.38 81.54 45.5695 9.311e-06 There is a very obvious, even trivial, B main effect, but nothing else. All this becomes even more glaring if you take the unusal step of plotting the data. What sort of editor would overlook this clear and demonstrable message leaping out from the data in favour of some arcane argument about "types of sums of squares"? Several answers come to mind: A power freak, a SAS afficianado, an idiot. If you get nowhere with this editor, my suggestion, hard as it may seem, is that you do not submit to that kind of midnless idealogy and make fatuous compromises for the sake of immediate publication. If necessary, part company with that editor and find somewhere else to publish where the editor has some inkling of what statistical inference is all about. Bill Venables. -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Carsten Jaeger Sent: Tuesday, 10 July 2007 4:15 AM To: R help list Subject: [R] type III ANOVA for a nested linear model Hello, is it possible to obtain type III sums of squares for a nested model as in the following: lmod <- lm(resp ~ A * B + (C %in% A), mydata)) I have tried library(car) Anova(lmod, type="III") but this gives me an error (and I also understand from the documentation of Anova as well as from a previous request (http://finzi.psych.upenn.edu/R/Rhelp02a/archive/64477.html) that it is not possible to specify nested models with car's Anova). anova(lmod) works, of course. My data (given below) is balanced so I expect the results to be similar for both type I and type III sums of squares. But are they *exactly* the same? The editor of the journal which I'm sending my manuscript to requests what he calls "conventional" type III tests and I'm not sure if can convince him to accept my type I analysis. R> mydata A B C resp 1 1 1 1 34.12 2 1 1 2 32.45 3 1 1 3 44.55 4 1 2 1 20.88 5 1 2 2 22.32 6 1 2 3 27.71 7 2 1 6 38.20 8 2 1 7 31.62 9 2 1 8 38.71 10 2 2 6 18.93 11 2 2 7 20.57 12 2 2 8 31.55 13 3 1 9 40.81 14 3 1 10 42.23 15 3 1 11 41.26 16 3 2 9 28.41 17 3 2 10 24.07 18 3 2 11 21.16 Thanks a lot, Carsten ______________________________________________ R-help@stat.math.ethz.ch mailing list 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. ______________________________________________ R-help@stat.math.ethz.ch mailing list 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.