Bill Shipley
2008-May-07 20:09 UTC
[R] solution to differences in sequential and marginal ANOVA using a mixed model
Yesterday I posted the following question to the help list. Thanks to John Fox (copied below) who pointed out the solution. Original question: I have come across a result that I cannot explain, and am hopingthat someone else can provide an answer. A student fitted a mixed model usingthe lme function: out<- lme(fixed=Y~A+B+A:B, random=~1|Site). Y is a continuous variable while A and B are factors. The data set is balanced with the same number of observations in each combination of A and B. There are two hierarchical levels: Site and plots nested in site. He tried two different ways of getting theANOVA table: anova(out) and anova(out, type="marginal"). Since the data were balanced, these two ways should (I think) give the same output since they correspond to Type I and III sums of squares in the SAS terminology. At least, this is the case with normal (i.e. not mixed) linear models. However, he finds very different results of these two types of ANOVA tables. Why? Response of John Fox: Dear Bill, I expect that the problem is in the contrasts that your student used for A and B, though I haven't thought specifically about the context of a mixed model. If he or she used the default contr.treatment(), then the contrasts for different factors (and the interaction) are not orthogonal in the row basis of the model matrix and hence are not orthogonal, even for balanced data. Using, e.g., contr.sum() should provide A, B, and A:B contrasts that are orthogonal to each other. Indeed, changing to an appropriate type of contrast did solve the problem! My problem was in forgetting that R uses treatment contrasts by default while SPLUS uses Helmert contrasts by default (which would have worked as well as sum contrasts). [[alternative HTML version deleted]]