conditional independence in repeated measures design How the responses are independent when conditioned on random effect in repeated measure analysis (linear mixed model)?
 A: The model has them as independent when you condition on the random effect. It's an assumption, just like independence in fixed effects regression is an assumption; in some situations it will be a very good approximation to reality.
The (possibly) surprising part is how that conditional independence produces dependence when taken unconditionally (i.e. when you don't condition on the random effect).
Consider performance of students of age 14 in some subject at different schools on a series of tests of similar difficulty.
Imagine we have one class from each school. The underlying mean scores on the tests in the two classes differ (for a variety of reasons). For students within a class, imagine their scores are independent. 
So if you look in class A you have independence between student scores and if you look in class B you also have independence (and they're also independent if you compare one student from each school. 
Now imagine you didn't know about the different means, and stack up the students for both classes (class A then class B), to treat them as one large group. 
Now we compute the correlations in scores across pairs of students.
Now when you check the scores, you notice there's correlation between student's scores - a randomly chosen pair of scores from the top half of the list (and similarly for the bottom half) seem more similar than a pair taken from the top and bottom halves. That is, the first 25 scores seem more similar to each other than they are to the rest. They're correlated (i.e. you have intra-class correlation). The random effects that produce the underlying class-means causes this dependence when considered unconditionally.

