Doubt about nested aov output
On 9/8/05, Ken Knoblauch <knoblauch at lyon.inserm.fr> wrote:
Your response nicely clarifies a question that I've had for a long time, but which I've dealt with by giving each subject a unique label. Unless I'm missing something, both techniques should work as the toy example below gives exactly the same output in all 3 cases below (forgetting about the convergence problem). Would there be a reason to prefer labeling the levels one way or another or is it just a matter of convenience? library(lmer) y <- rnorm(15) cond <- gl(3, 5, 15) obs <- gl(15, 1) subj <- gl(5, 1, 15) dd <- data.frame(y = y, cond = cond, obs = obs, subj = subj) l1 <- lmer(y~cond + (1|cond:obs), dd) l2 <- lmer(y~cond + (1|cond:subj), dd) l3 <- lmer(y~cond + (1|obs), dd)
I prefer to have a grouping factor constructed with unique levels for each distinct unit. The only reason I mention constructions like Treatment:Rat in the original part of this thread is that data are often provided in that form. Reusing "subject" labels within another group is awkward and can be error prone. One of the data sets I examine in the MlmSoftRev vignette of the mlmRev package is called Exam and has student identifiers within schools. The student identifiers are not unique but the school:student combination should be. It isn't. These data have been analyzed in scores of books and articles and apparently none of the other authors bothered to check this. There are some interesting ramifications such as some of the schools that are classified as mixed-sex schools are likely single-sex schools because the only student of one of the sexes in that school is apparently mislabelled. BTW, in your example you have only one observation per level of 'obs' so you can't use obs as a grouping factor as this variance component would be completely confounded with the per-observation noise.
Douglas Bates a ??crit: The difference between models like lmer(Glycogen~Treatment+(1|Rat)+(1|Rat:Liver)) and lmer(Glycogen~Treatment+(1|Treatment:Rat)+(1|Treatment:Rat:Liver)) is more about the meaning of the levels of "Rat" than about the meaning of "Treatment". As I understood it there are three different rats labelled 1. There is a rat 1 on treatment 1 and a rat 1 on treatment 2 and a rat 1 on treatment 3. Thus the levels of Rat do not designate the "experimental unit", it is the levels of Treatment:Rat that do this. -- Ken Knoblauch Inserm U371 Cerveau et Vision Dept. of Cognitive Neuroscience 18 avenue du Doyen L??pine 69500 Bron France tel: +33 (0)4 72 91 34 77 fax: +33 (0)4 72 91 34 61 portable: +33 (0)6 84 10 64 10 http://www.lyon.inserm.fr/371/