## 5.7 Exercises

Allison and Cicchetti (1976) investigated the interrelationship between sleep, ecological and constitutional variables. They assessed these variables for 39 mammalian species. The authors concluded that slow-wave sleep is negatively associated with a factor related to body size. This suggests that large amounts of this sleep phase are disadvantageous in large species. Also, paradoxical sleep was associated with a factor related to predatory danger, suggesting that large amounts of this sleep phase are disadvantageous in prey species.

Allison and Cicchetti (1976) performed their analyses under complete-case analysis. In this exercise we will recompute the regression equations for slow wave (“nondreaming”) sleep (hrs/day) and paradoxical (“dreaming”) sleep (hrs/day), as reported by the authors. Furthermore, we will evaluate the imputations.

Exercise 5.1 (Complete-case analysis) Compute the regression equations (1) and (2) from the paper of Allison and Cicchetti (1976) under complete-case analysis.

Exercise 5.2 (Imputation) The mammalsleep data are part of the mice package. Impute the data with mice() under all the default settings. Recalculate the regression equations (1) and (2) on the multiply imputed data.

Exercise 5.3 (Traces) Inspect the trace plot of the MICE algorithm. Does the algorithm appear to converge?

Exercise 5.4 (More iterations) Extend the analysis with 20 extra iterations using mice.mids(). Does this affect your conclusion about convergence?

Exercise 5.5 (Distributions) Inspect the data with diagnostic plots for univariate data. Are the univariate distributions of the observed and imputed data similar? Can you explain why they do (or do not) differ?

Exercise 5.6 (Relations) Inspect the data with diagnostic plots for the most interesting bivariate relations. Are the relations similar in the observed and imputed data? Can you explain why they do (or do not) differ?

Exercise 5.7 (Defaults) Consider each of the seven default choices from Section 6.1 in turn. Do you think the default is appropriate for your data? Explain why.

Exercise 5.8 (Improvement) Do you have particular suggestions for improvement? Which? Implement one (or more) of your suggestions. Do the results now look more plausible or realistic? Explain. What happened to the regression equations?

Exercise 5.9 (Multivariate analyses) Repeat the factor analysis and the stepwise regression. Beware: There might be pooling problems.