Hi,

This topic has been discussed in several posts in this list before, but I
could not completely understand if there was a clear answer. Also, I
searched the books (Pinheiro, Faraway and Zuur) I could not reach a
conclusion. I guess I am missing some point here :) so I am sorry for
recover this topic again.
I will start by providing an example code and then put my questions, as
clear as possible.

Following the code provided in previous posts (see for example):
http://markmail.org/message/lhtols3t5wrleewc
using another dataset, for example:

            # Example to ask the list
            data(iris)
            kk=data.frame(stack(iris[,1:3]),sp=rep(iris$Species),
subject=rep(1:dim(iris)[1],3))
            summary(kk)
            require(nlme)
            kk2=lme(values~ind*sp, kk, weights = varIdent(form= ~ 1|ind),
random=~1|subject)
            kk2
            anova(kk2) #all factors are significant.

            # Calculate model predictions    and plot it ==== this is from
Ben's code
                newdat <- expand.grid(ind=levels(kk$ind), sp=levels(kk$sp))
                newdat$pred <- predict(kk2, newdat, level = 0)

                Designmat <- model.matrix(eval(eval(kk2$call$fixed)[-2]),
newdat[-3])
                predvar <- diag(Designmat %*% kk2$varFix %*% t(Designmat))
                newdat$SE <- sqrt(predvar)
                newdat$SE2 <- sqrt(predvar+kk2$sigma^2)

                #install.packages("ggplot2")
                library(ggplot2)
                pd <- position_dodge(width=0.4)
                ggplot(newdat,aes(x=ind, y=pred, colour=sp))+
                geom_point(aes(x=kk$ind,y=kk$values, colour=kk$sp),
size=.3, shape=2, position=pd)+
                geom_point(position=pd)+
                geom_linerange(aes(ymin=pred-2*SE2,
ymax=pred+2*SE2),col="red", position=pd)+
                geom_errorbar(aes(ymin=pred-2*SE, ymax=pred+2*SE),
col="black", width=.1, position=pd)

So, we can see the actual points, the SE and SE2 modelled and respective
means, I think.
My questions are:
What is exactly the SE and SE2 (how do we call it in an article legend, for
example) and how can these be interpreted?
Can we consider that when the 'lines' do not overlap the species (or
varieties) are different?
The SE2 are larger than the actual data in setosa/Petal.Length and overlap
in the remaining variaties--- how can these show significant differences
than?

I think I am getting confused or I am missing something important, because
the results do not appear congruent in my head.

Any help will be much appreciated,

All the best,
Marta

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