Study questions

1. Define what is meant by a mixed model. Think of an example of a set of data that might be suitable for analysis as a mixed model. Illustrate the data structure and explain which effects you would define as random terms in the model.

2. Write down the statistical model for a balanced split-plot design and decide whether it falls into the category of a mixed model or not. Similarly consider a hierarchical or nested model without any fixed effects. Does this come under the definition of a mixed model?

3. Before REML procedures were available, statistical analysis of hierarchical data sets was often undertaken in two stages: first, least squares analysis of variance to estimate fixed effects, then a nested analysis of variance, with the data corrected for fixed effects to estimate random effects at each layer in the hierarchy. What do you think are the advantages of REML over this approach? Describe an example when correcting data for fixed effects may still be useful (see, for example Case Study 2). Describe how you would 'correct' the data.

4. Run GenStat with fixed effects for BREED (lamb breed), SEX, AGEWEAN, DL and DQ: a) with YEAR also as a fixed effect, b) YEAR as a fixed effect and RAM_ID and EWE_ID added as random effects and c) YEAR, RAM_ID and EWE_ID added as random effects. Compare the parameters obtained for BREED in the three outputs. Comment on how and why they vary and suggest which model you would use to report the results. Discuss the premise that year can be assumed to be a random effect.