Repeates Measures MANOVA for Time*Treatment Interactions
Jarrett Byrnes <redbeard at arrr.net> writes:
Dear R folk, First off I want to thank those of you who responded with comments for my R quick and dirty stats tutorial. They've been quite helpful, and I'm in the process of revising them. When it comes to repeated measures MANOVA, I'm in a bit of a bind, however. I'm beginning to see that all of the documentation is written for psychologists, who have a slightly different mind-set behind their experiments than, say, an ecologist, who is interested in the effects of time per se, and not just the effects of a treatment. For example, here's my dataset, say, looking at plant height in cm with and without fertilizer Treatment, Time1, Time2, Time3, Time4, Time5 Fertilizer, 1, 4, 8, 10, 12 Control,1,2,3,4,5 Fertilizer,1,8,10,12,20 Control,1,3,5,6,6 Fertilizer,2,5,10,20,25 Control,1,2,4,4,4 Clearly there is a time*treatment interaction (just eyeballing the dataset) My question is, how does one set this up using the anova.mlm approach so that in the end I can write up a table that says Treatment Time Time*Treatment I can see from ?anova.mlm how one would get the Treatment effect using something like response<-with(my.data, rbind(Time1, Time2, Time3, Time4, Time5))
cbind() would be more like it
mlmfit<-lm(response~1) mlmfit0<-update(mlmfit, ~0) anova(mlmfit, mlmfit0, X = ~ Treatment, idata=my.data, test="Spherical")
No... idata is the *intra*-block structure, so it should just be your five times. I'm somewhat baffled that you're getting away with supplying a data frame that doesn't have the right number of rows, but maybe that's because you're supplying the transposed matrix as a response. Try mlmfit <- lm(response ~ Treatment) mlmfit1 <- lm(response ~ 1) mlmfit0 <- lm(response ~ 0) Then anova.mlm(mlmfit, mlmfit1, X=~1, test="Spherical") tests whether time contrasts depend on treatment, which is the time*treatment effect. anova.mlm(mlmfit, mlmfit1, M=~1) is the test for overall treatment effect and anova.mlm(mlmfit1, mlmfit0, X=~1, test="Spherical") is the test for overall time effect. (If Time1 is a pre-randomization baseline measurement you should consider including it as a covariate, but that is another matter)
Although this yields the result that, after correction, it's not significant - perhaps due to the low DF from this simple example -- Analysis of Variance Table Model 1: response ~ 1 Model 2: response ~ 1 - 1 Contrasts orthogonal to ~Treatment Greenhouse-Geisser epsilon: 0.3565 Huynh-Feldt epsilon: 0.4982 Res.Df Df Gen.var. F num Df den Df Pr(>F) G-G Pr H-F Pr 1 4 0.43167 2 5 1 0.50937 3.7939 4 16 0.02356 0.09620 0.06966 -- But, I still want to get my time and time*treatment interactions - what would be the appropriate anova statements here? Thanks so much, and hopefully this will resolve the confusion both for myself and for LOTS of other ecology types! -Jarrett ---------------------------------------- Jarrett Byrnes Population Biology Graduate Group, UC Davis Bodega Marine Lab 707-875-1969 http://www-eve.ucdavis.edu/stachowicz/byrnes.shtml
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