4.9 Exercises

Exercise 4.1 (MAR) Repeat Exercise 3.1 for a multivariate missing data mechanism.

Exercise 4.2 (Convergence) Figure 4.3 shows that convergence can take longer for very high amounts of missing data. This exercise studies an even more extreme situation.

  1. The default argument ns of the simulate() function in Section 4.5.7 defines six scenarios with different missing data patterns. Define a \(6 \times 4\) matrix ns2, where patterns \(R_2\) and \(R_3\) are replaced by pattern \(R_4 = (1,0,0)\). How many more missing values are there in each scenario?

  2. For the new scenarios, do you expect convergence to be slower or faster? Explain.

  3. Change the scenario in which all data in \(Y_1\) and \(Y_2\) are missing so that there are 20 complete cases. Then run slow2 <- simulate(ns = ns2, maxit = 50, seed = 62771) and create a figure similar to Figure 4.3.

  4. Compare your figure with Figure 4.3. Are there any major differences? If so, which?

  5. Did the figure confirm your idea about convergence speed you had formulated in (b)?

  6. How would you explain the behavior of the trace lines?
Exercise 4.3 (Binary data) Perform the simulations of Section 4.5.7 with binary \(Y_1\) and \(Y_2\). Use the odds ratio instead of the correlation to measure the association between \(Y_1\) and \(Y_2\). Does the same conclusion hold?