Return to the data set concerning the yield of F3 wheat families in the presence of ryegrass, introduced in Exercise 3 in Chapter 3.

(a) Using mixed modelling, obtain an estimate of the mean yield of each of the F3 families, regarding ‘family’ as a fixed-effect term.

(b) Using mixed modelling and regarding ‘family’ as a random-effect term, obtain the following: (i) an estimate of the overall mean of the population of F3 families (ii) the BLUP for the effect of each family.

(c) From the output of the analysis performed in Part (b), obtain the following: (i) an estimate of the variance component for ‘family’ (ii) an estimate of the residual variance component. Obtain also the number of observations of each family.

(d) From the information obtained in Part (a)–(c), compare the relationship between the BLUPs and the estimates of family means obtained regarding ‘family’ as a fixed-effect term with that given in Equation 5.6.

(e) Obtain the shrunk mean for each family, and plot the shrunk means against the means obtained regarding ‘family’ as a fixed-effect term (the unadjusted means). The point representing one of the families deviates from the general relationship between these two types of mean.

(f) What is the distinguishing feature of this family?