  Missing values with mixed data types is a common problem in a large number of
machine learning applications such as processing of surveys and in different
medical applications. Recently, Gaussian copula models have been suggested as a
means of performing imputation of missing values using a probabilistic
framework. While the present Gaussian copula models have shown to yield state
of the art performance, they have two limitations: they are based on an
approximation that is fast but may be imprecise and they do not support
unordered multinomial variables. We address the first limitation using direct
and arbitrarily precise approximations both for model estimation and imputation
by using randomized quasi-Monte Carlo procedures. The method we provide has
lower errors for the estimated model parameters and the imputed values,
compared to previously proposed methods. We also extend the previous Gaussian
copula models to include unordered multinomial variables in addition to the
present support of ordinal, binary, and continuous variables.
