Case Study 4: Mixed model analysis for the estimation of components of genetic variation in lamb weaning weight

Study questions

Choose model b) in Question 4. Write a short report including a description of the statistical analysis (with the statistical model expressed algebraically) and a summary of the results.
Explain what is meant by fixed and random effects. Give an example of a split-plot design. Describe the random effects that feature in its analysis. Why can these random effects be estimated by a conventional least squares analysis of variance so that REML is not necessary in this case?
Yields from a number of plots are missing in a split-plot design. Describe two alternative ways of analysing the data and say when you think one method is preferable to the other.
What do you understand by 'heritability'? The formula for calculating an estimate of heritability from a number of offspring nested within sires is 4s_s² / (s_s² + s_e²), where s_s² is the variance component among sires and s_e² is the error or residual component. Calculate the heritability estimate from the REML output and also its standard error. A heritability estimate lies between 0 and 1. Comment on the result you get.