Priors for High Missingness, Small $n$'s, or Large Correlations

When the data to be analyzed contain a high degree of missingness or very strong correlations among the variables, or when the number of observations is not much greater than $p(p+3)/2$ (where $p$ is the number of variables), results from your analysis model will be more dependent on the choice of the imputation model. This suggests more testing in these cases of alternative specifications under Amelia.

In addition, in these circumstances, we recommend adding a ridge prior will help with numerical stability by shrinking the covariances among the variables toward zero without changing the means or variances. The ridge prior can be implemented by setting the global _AMempri to a positive number. Including this prior is roughly equivalent to adding _AMempri artificial observations to the data set with the same means and variances as the existing data but with zero covariances. Thus, increasing the number at which _AMempri is set results in more shrinkage of the covariances thus putting more a priori structure on the estimation problem. In general, keep the value on this prior relatively small and increase it only when necessary.

${\mathfrak{A}melia}$ also has the capability to put strong informative priors on the parameters of the imputation model (see Section 10.1), but this option will not normally be used.