  Imputation of data with general structures (e.g., data with continuous,
binary, unordered categorical, and ordinal variables) is commonly performed
with fully conditional specification (FCS) instead of joint modeling. A key
drawback of FCS is that it does not invoke an appropriate data augmentation
mechanism and as such convergence of the resulting Markov chain Monte Carlo
procedure is not assured. Methods that use joint modeling lack these drawbacks
but have not been efficiently implemented in data of general structures. We
address these issues by developing a new method, the so-called GERBIL
algorithm, that draws imputations from a latent joint multivariate normal model
that underpins the generally structured data. This model is constructed using a
sequence of flexible conditional linear models that enables the resulting
procedure to be efficiently implemented on high dimensional datasets in
practice. Simulations show that GERBIL performs well when compared to those
that utilize FCS. Furthermore, the new method is computationally efficient
relative to existing FCS procedures.
