(Updated: July 22 2017 21:38)
Errata
- The top row of the table on p. 21 of Missing Data should read ‘not MAR’ instead of ‘not MCAR’. Thanks to John Fox.
Issues
- In Bayes: Things that can go wrong, note that the under-dispersion problem discussed in the “Unbounded likelihoods” section occurs not infrequently (in my experience) with real data. Consider what might happen if you use a mixed model with different raters rating individuals. Sometimes raters will self-calibrate based on the sample thus producing less variability than expected in the mean ratings. For example differences in mean grades between sections of the same course may show much less variation than expected through the random distribution of students among sections, which, if violated, would tend to produce even more variability between sections. The reasons for reduced variability is likely to be that instructors, deliberately or not, adjust grades to achieve a target distribution. A study of British judges in the last three centuries showed that the rate at which they sentenced defendants to capital punishment varied between judges, in each time period, less than expected by chance assignment of defendants, suggesting a tendency to meet an implicit quota. All these examples may exhibit non-convergence using a standard mixed model. Thanks to Camilla Griffiths for raising a question about a data set that might exhibit this kind of structure.