### Course Topics

This course will discuss what mixed models are, why they are called "mixed" models, what is a "random factor", and why. The primary focus will be for the researcher to understand when he or she should be thinking about a mixed effects model. The course will also talk briefly about what is a hierarchical model and why they are the obvious choice of modelers in most cases. This will be followed by an example that explicitly defines a hierarchical structure. The concepts will be explained almost wholly through examples in SAS or in R.

The course will be open for questions and discussion at the end. Feel free to ask questions specific to your research and enquire if your data will benefit from a hierarchical structure, or specifically if a mixed model will be appropriate for your research questions.

### Before you show up:

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

• What is a linear model?
• What is an additive effects model?
• What is a fixed effect?
• 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 if "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 unsure about about the dependence structure of the factors within themselves and maybe some observed data?