## 3.9 Exercises

Exercise 3.1 (MAR) Reproduce Table 3.1 and Table 3.2 for MARRIGHT, MARMID and MARTAIL missing data mechanisms of Section 3.2.4.

1. Are there any choices that you need to make? If so, which?

2. Consider the six possibilities to combine the missing data mechanism and missingness in $$x$$ or $$y$$. Do you expect complete-case analysis to perform well in each case?

3. Do the Bayesian sampling and bootstrap methods also work under the three MAR mechanisms?

Exercise 3.2 (Parameter uncertainty) Repeat the simulations of Section 3.2 on the whiteside data for different samples sizes.

1. Use the method of Section 3.2.3 to generate an artificial population of 10000 synthetic gas consumption observations. Re-estimate the parameter from the artificial population. How close are they to the “true” values?

2. Draw random samples from the artificial population. Systematically vary sample size. Is there some sample size at which norm.nob is as good as the Bayesian sampling and bootstrap methods?

3. Is the result identical for missing $$y$$ and missing $$x$$?

4. Is the result the same after including insulation status in the model?