  In Japan, the Housing and Land Survey (HLS) provides municipality-level
grouped data on household incomes. Although these data can be used for
effective local policymaking, their analyses are hindered by several
challenges, such as limited information attributed to grouping, the presence of
non-sampled areas, and the very low frequency of implementing surveys. To
address these challenges, we propose a novel grouped-data-based spatio-temporal
finite mixture model to model the income distributions of multiple spatial
units at multiple time points. A unique feature of the proposed method is that
all the areas share common latent distributions and that the mixing proportions
that include the spatial and temporal effects capture the potential area-wise
heterogeneity. Thus, incorporating these effects can smooth out the quantities
of interest over time and space, impute missing values, and predict future
values. By treating the HLS data with the proposed method, we obtain complete
maps of the income and poverty measures at an arbitrary time point, which can
be used to facilitate rapid and efficient policymaking with fine granularity.
