Thanks Greg - that makes sense... that the test of the main effect of A is uninteresting if the AxB interaction is in the model
- but isn't that exactly what appears in the usual anova(fullmodel) output? A test of the main effect of A, a test of the main effect of B, and then a test of the interaction AxB? Is it simply the case that the lm() function was designed so as to circumvent the uninteresting test, even if the user asks for it? (which would be fine by me - I just want to understand what's happening when I use it). -Paul On Fri, Feb 27, 2009 at 1:30 PM, Greg Snow <greg.s...@imail.org> wrote: > 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. > -- 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.
