Notice the degrees of freedom as well in the different models. With factors A and B, the 2 models:
A + B + A:B And A + A:B Are actually the same overall model, just different parameterizations (you can also see this by using x=TRUE in the call to lm and looking at the x matrix used). Testing if the main effect A should be in the model given that the interaction is in the model does not make sense in most cases, therefore the notation gives a different parameterization rather than the generally uninteresting test. -- Gregory (Greg) L. Snow Ph.D. Statistical Data Center Intermountain Healthcare greg.s...@imail.org 801.408.8111 > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r- > project.org] On Behalf Of Paul Gribble > Sent: Friday, February 27, 2009 11:01 AM > To: r-help@r-project.org > Subject: [R] testing two-factor anova effects using model comparison > approach with lm() and anova() > > I wonder if someone could explain the behavior of the anova() and lm() > functions in the following situation: > > I have a standard 3x2 factorial design, factorA has 3 levels, factorB > has 2 > levels, they are fully crossed. I have a dependent variable DV. > > Of course I can do the following to get the usual anova table: > > > anova(lm(DV~factorA+factorB+factorA:factorB)) > Analysis of Variance Table > > Response: DV > Df Sum Sq Mean Sq F value Pr(>F) > factorA 2 7.4667 3.7333 4.9778 0.015546 * > factorB 1 2.1333 2.1333 2.8444 0.104648 > factorA:factorB 2 9.8667 4.9333 6.5778 0.005275 ** > Residuals 24 18.0000 0.7500 > > This is perfectly satisfactory for my situation, but as a pedagogical > exercise, I wanted to demonstrate the model comparison approach to > analysis > of variance by using anova() to compare a full model that contains all > effects, to restricted models that contain all effects save for the > effect > of interest. > > The test of the interaction effect seems to be as I expected: > > > fullmodel<-lm(DV~factorA+factorB+factorA:factorB) > > restmodel<-lm(DV~factorA+factorB) > > anova(fullmodel,restmodel) > Analysis of Variance Table > > Model 1: DV ~ factorA + factorB + factorA:factorB > Model 2: DV ~ factorA + factorB > Res.Df RSS Df Sum of Sq F Pr(>F) > 1 24 18.0000 > 2 26 27.8667 -2 -9.8667 6.5778 0.005275 ** > > As you can see the value of F (6.5778) is the same as in the anova > table > above. All is well. > > However, if I try to test a main effect, e.g. factorA, by testing the > full > model against a restricted model that doesn't contain the main effect > factorA, I get something strange: > > > restmodel<-lm(DV~factorB+factorA:factorB) > > anova(fullmodel,restmodel) > Analysis of Variance Table > > Model 1: DV ~ factorA + factorB + factorA:factorB > Model 2: DV ~ factorB + factorA:factorB > Res.Df RSS Df Sum of Sq F Pr(>F) > 1 24 18 > 2 24 18 0 0 > > upon inspection of each model I see that the Residuals are identical, > which > is not what I was expecting: > > > anova(fullmodel) > Analysis of Variance Table > > Response: DV > Df Sum Sq Mean Sq F value Pr(>F) > factorA 2 7.4667 3.7333 4.9778 0.015546 * > factorB 1 2.1333 2.1333 2.8444 0.104648 > factorA:factorB 2 9.8667 4.9333 6.5778 0.005275 ** > Residuals 24 18.0000 0.7500 > > This looks fine, but then the restricted model is where things are not > as I > expected: > > > anova(restmodel) > Analysis of Variance Table > > Response: DV > Df Sum Sq Mean Sq F value Pr(>F) > factorB 1 2.1333 2.1333 2.8444 0.104648 > factorB:factorA 4 17.3333 4.3333 5.7778 0.002104 ** > Residuals 24 18.0000 0.7500 > > I was expecting the Residuals in the restricted model (the one not > containing main effect of factorA) to be larger than in the full model > containing all three effects. In other words, the variance accounted > for by > the main effect factorA should be added to the Residuals. Instead, it > looks > like the variance accounted for by the main effect of factorA is being > soaked up by the factorA:factorB interaction term. Strangely, the > degrees of > freedom are also affected. > > I must be misunderstanding something here. Can someone point out what > is > happening? > > Thanks, > > -Paul > > -- > Paul L. Gribble, Ph.D. > Associate Professor > Dept. Psychology > The University of Western Ontario > London, Ontario > Canada N6A 5C2 > Tel. +1 519 661 2111 x82237 > Fax. +1 519 661 3961 > pgrib...@uwo.ca > http://gribblelab.org > > [[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. ______________________________________________ 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.
