## 9.5 Exercises

Exercise 9.1 (Contingency table) Adapt the micemill() function for the walking data so that it prints out the contingency table of $$Y_\mathrm{A}$$ and $$Y_\mathrm{B}$$ of the first imputation at each iteration. How many statements do you need?
Exercise 9.2 (Pool) Find out what the variance of Kendall’s $$\tau$$ is, and construct its 95% confidence intervals under multiple imputation. Use the auxiliary function pool.scalar() for pooling.
Exercise 9.3 (Covariates) Calculate the correlation between age and the items A and B under two imputation models: one without covariates, and one with covariates. Which of the correlations is higher? Which solution do you prefer? Why?
Exercise 9.4 (Heterogeneity) Kendall’s $$\tau$$ in the source E is 0.57 (cf. Section 9.4.4). The average of the sampler is slightly lower (Figure 9.10). Adapt the micemill() function to calculate the $$\tau$$-values separately for the three sources. Which population has the lowest $$\tau$$-values?
Exercise 9.5 (Sample size) Repeat the previous exercise, but with the samples for A and B taken 10 times as large. Does the sample size have an effect on convergence? If so, can you come up with an explanation? (Hint: Think of how $$\tau$$ is calculated.)
Exercise 9.6 (True values) For sample B, we do actually have the data on Item A from sample E. Calculate the “true” value $$\theta_\mathrm{BA}$$, and compare it with the simulated values. How do these values compare? Should these values be the same? If they are different, what could be the explanations? How could you reorganize the walking data so that no iteration is needed?