Mixed Effect Models and Hierarchical Models

Ask yourself the following questions. If you need some background, look up material on "mixed effects","hierarchical models" in .

In a typical (simple) ANOVA model the errors are assumed to be independent. Why? When does it break down?
I have data from 5 adults in a study regarding a particular response. Do the adults have an effect on my results? How do I consider the effect of the adult in the study? Is it even possible?
I have data from 5 adults in a study with a particular response being measured at weekly intervals for 3 weeks for each adult. Let the data be {X11,X12,X13,X21,X22,X23,.....,X51,X52,X53} Are X11,X12,X13 correlated? Why or why not?
Can I think of another hypothetical case where the data might have a correlation structure as above?

When do we usually think in terms of factor analysis? Devise an example to convince yourself. Remember a factor is latent - "you have no primary data corresponding to it".
What are ways we can think of grouping factors? Is it by how large they are? Is it by their variance? But variance not a measure with respect to another factor. Then is it by their correlation? What if we are even sure about about the dependence structure of the factors within themselves and maybe some observed data.

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