  In some contexts, mixture models can fit certain variables well at the
expense of others in ways beyond the analyst's control. For example, when the
data include some variables with non-trivial amounts of missing values, the
mixture model may fit the marginal distributions of the nearly and fully
complete variables at the expense of the variables with high fractions of
missing data. Motivated by this setting, we present a mixture model for mixed
ordinal and nominal data that splits variables into two groups, focus variables
and remainder variables. The model allows the analyst to specify a rich
sub-model for the focus variables and a simpler sub-model for remainder
variables, yet still capture associations among the variables. Using
simulations, we illustrate advantages and limitations of focused clustering
compared to mixture models that do not distinguish variables. We apply the
model to handle missing values in an analysis of the 2012 American National
Election Study, estimating relationships among voting behavior, ideology, and
political party affiliation.
