Other Algorithms

Although we recommend the default EMis algorithm, ${\mathfrak{A}melia}$ for Gauss also includes the ability to impute using three Monte Carlo Markov Chain (MCMC) algorithms -- IP, SIP, and VIP. IP (imputation-posterior) and SIP (stacked IP) are discussed in the literature (Schafer, 1997); VIP (vectorized IP), our creation, is a vectorized version of IP that is faster in modern programming languages but produces imputations that are more dependent. Although the algorithms generate different Markov chains, they converge asymptotically (in the iteration number) to the same distribution. Of course, monitoring and detecting MCMC convergence is somewhat an art form, and requires knowledge from the time series and MCMC literatures. We provide some graphic diagnostic procedures in the Gauss version of Amelia; see amgraph (Section 10.4), but we do not recommend that you use these procedures unless you feel confident evalutating MCMC convergence. EMis produces the same answers as these algorithms (when they are run sufficiently long and used correctly), and it does so in less time and without any special expertise in time series models or MCMC algorithms. Both versions of Amelia also allow the non-MCMC algorithms EM and EMs. EM ignores estimation uncertainty, EMs is only appropriate when you have a large number of observations relative to parameters.