Dear Spencer, > -----Original Message----- > From: Spencer Graves [mailto:spencer.gra...@prodsyse.com] > Sent: April-03-11 11:07 AM > To: Krishna Kirti Das > Cc: John Fox; r-help@r-project.org > Subject: Re: [R] Unbalanced Anova: What is the best approach? > > Hi, Krishna: > > > <in line> > > On 4/3/2011 7:35 AM, Krishna Kirti Das wrote: > > Thank you, John. > > > > Yes, your answers do help. For me it's mainly about getting familiar > > with the "R" way of doing things. > > > > Thus your response also confirms what I suspected, that there is no > > explicit user-interface (at least one that is widely used) in terms of > > functions/packages that represents an unbalanced design in the same > > way that aov would represent a balanced one. Analyzing balanced and > > unbalanced data are obviously possible, but with balanced designs via > > aov what has to be done is intuitive within the language but > > unintuitive for unbalanced designs. > > Intuition is subject to one's background and expectations. If you > think in terms of a series of nested hypotheses, then the standard R anova > is very intuitive. I never use aov, because it's not intuitive to me and > not very general. 'aov' is only useful for a balanced design with normal > independent errors with constant variance. The real world is rarely so > simple. The 'aov' algorithm was wonderful over half a century ago, when > all computations were done by hand or using a mechanical calculator (e.g., > an abacus or a calculator with gears). > Unbalanced designs were largely impractical because of computational > difficulties. There were many procedures for imputing missing values for > a design that was "almost balanced". > > > I encourage you to think in terms of alternative sequences of > nested hypotheses, including the implications of A being significant by > itself, but not with B already present, except that the A:B interaction is > or is not significant.
So-called type-II tests do exactly that -- that is, obey the principle of marginality; they are maximally powerful if the higher-order term(s) to which a particular term is marginal are 0. Best, John > > > I did notice that this question gets asked several times and in > > slightly different ways, and I think the lack of an interface that > > represents an unbalanced design in the same way aov represents > > balanced designs is why the question will probably keep getting asked > again. > > > > I had mentioned nlme and lme4 because I saw in some of the discussions > > that using those were recommended for working with unbalanced designs. > > And specifying random effects with zero variance, for example, would > > probably serve my purposes. > > I'd be surprised if nlme or lme4 changes what I wrote above. > > > Hope this helps. > Spencer > > > Thank you for your help. > > > > Sincerely, > > > > Krishna > > > > On Sun, Apr 3, 2011 at 7:28 AM, John Fox<j...@mcmaster.ca> wrote: > > > >> Dear Krishna, > >> > >> Although it's difficult to explain briefly, I'd argue that balanced > >> and unbalanced ANOVA are not fundamentally different, in that the > >> focus should be on the hypotheses that are tested, and these are > >> naturally expressed as functions of cell means and marginal means. > >> For example, in a two-way ANOVA, the null hypotheses of no > >> interaction is equivalent to parallel profiles of cell means for one > >> factor across levels of the other. What is different, though, is that > >> in a balanced ANOVA all common approaches to constructing an ANOVA > >> table coincide. > >> > >> Without getting into the explanation in detail (which you can find in > >> a text like my Applied Regression Analysis and Generalized Linear > >> Models), so-called type-I (or sequential) tests, such as those > >> performed by the standard anova() function in R, test hypotheses that > >> are rarely of substantive interest, and, even when they are, are of > >> interest only by accident. So-called type-II tests, such as those > >> performed by default by the > >> Anova() function in the car package, test hypotheses that are almost > >> always of interest. Type-III tests, which the Anova() function in car > >> can perform optionally, require careful formulation of the model for > >> the hypotheses tested to be sensible, and even then have less power > >> than corresponding type-II tests in the circumstances in which a test > would be of interest. > >> > >> Since you're addressing fixed-effects models, I'm not sure why you > >> introduced nlme and lme4 into the discussion, but I note that Anova() > >> in the car package has methods that can produce type-II and -III Wald > >> tests for the fixed effects in mixed models fit by lme() and lmer(). > >> > >> Your question has been asked several times before on the r-help list. > >> For example, if you enter terms like "type-II" or "unbalanced ANOVA" > >> in the RSeek search engine and look under the "Support Lists" tab, > >> you'll see many hits -- e.g., > >> <Mhttps://stat.ethz.ch/pipermail/r-help/2006-August/111927.html>. > >> > >> I hope this helps, > >> John > >> > >> -------------------------------- > >> John Fox > >> Senator William McMaster > >> Professor of Social Statistics > >> Department of Sociology > >> McMaster University > >> Hamilton, Ontario, Canada > >> http://socserv.mcmaster.ca/jfox > >> > >> > >> > >>> -----Original Message----- > >>> From: r-help-boun...@r-project.org > >>> [mailto:r-help-boun...@r-project.org] > >>> On Behalf Of Krishna Kirti Das > >>> Sent: April-03-11 3:25 AM > >>> To: r-help@r-project.org > >>> Subject: [R] Unbalanced Anova: What is the best approach? > >>> > >>> I have a three-way unbalanced ANOVA that I need to calculate (fixed > >>> effects plus interactions, no random effects). But word has it that > >>> aov() is good only for balanced designs. I have seen a number of > >>> different recommendations for working with unbalanced designs, but > >>> they seem to differ widely (car, nlme, lme4, etc.). So I would like > >>> to know what is > >> the > >>> best or most usual way to go about working with unbalanced designs > >>> and extracting a reliable ANOVA table from them in R? > >>> > >>> [[alternative HTML version deleted]] > >>> > >>> ______________________________________________ > >>> R-help@r-project.org 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. > >> > > [[alternative HTML version deleted]] > > > > ______________________________________________ > > R-help@r-project.org 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. > > > > > -- > Spencer Graves, PE, PhD > President and Chief Operating Officer > Structure Inspection and Monitoring, Inc. > 751 Emerson Ct. > San José, CA 95126 > ph: 408-655-4567 ______________________________________________ R-help@r-project.org 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.
