Modeling $t$-distributed Data

In addition to the common multivariate normal imputation model, ${\mathfrak{A}melia}$ can also impute under the assumption that the data is distributed multivariate-$t$ (Little 1988, Lange et al. 1989). Setting _AMemt=1 replaces the EM portion of EMis with an ECME algorithm (Liu 1994, Liu and Rubin 1994) that also estimates the degrees of freedom parameter, while the importance sampling is modified to sample from the $t$-distribution also. Computation details are given in Honaker, Katz, and King (2000). As a general technique, users should check the final value of the degrees of freedom parameter. If this value is greater than around 30, the data should not be considered $t$-distributed, and the multivariate normal model should be employed. This value is stored in the buffer as dffin and can be read using the amread command:

_AMemt=1;
buff=amelia(dataset);
df=vread(buff,"dffin");

Also stored in the buffer are vectors of weights from which $t$-based regressions can be conducted, by using these weights in weighted least squares. The vector wfin is the value of the weights at the maximum of the likelihood found by the ECME algorithm, while the vector weightn is the vector of weights to be used with the nth imputed dataset. These weights are only valid though if all the variables in the imputation model are in the analysis model, otherwise they may need to be recalculated, or an explicit $t$-based regression conducted.