elementary method functions for multiple imputation with mice

Summary:

This is an idea for a "new developer friendly" project.
mice (Multivariate Imputation by Chained Equations) package
https://cran.r-https://cran.r-project.org/package=mice
allows user defined elementary imputation methods. It would be quite easy to make functions which would allow use of rstanarm, too.

Description:

Implement Stan versions of elementary imputation methods

• mice.impute.stan.norm
• mice.impute.stan.logreg
• mice.impute.stan.polr
• mice.impute.stan.2l.norm
• mice.impute.stan.2lonly.norm
  based on the corresponding existing functions (without .stan in the name). The existing norm function uses a fixed conjugate prior and analytic posterior, logreg uses glm.fit, polr uses a function from MASS package, and 2l functions use Gibbs sampling. rstanarm would provide more flexibility on priors and better inference.

Start by reading the existing mice.impute.norm, mice.impute.logreg, mice.impute.polr, mice.impute.2l.norm, and mice.impute.2lonly.norm methods named in the issue, along with the corresponding rstanarm modeling approach. The work is complete when Stan-based versions of all five named mice.impute.stan.* functions support the stated imputation methods with configurable priors and inference.