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.

翻译：在日本，住房与土地调查（HLS）提供了市级层面的家庭收入分组数据。尽管这些数据可用于制定有效的地方政策，但其分析面临若干挑战，例如分组造成的信息有限、存在未抽样区域以及调查实施频率极低。为应对这些挑战，我们提出了一种新颖的基于分组数据的时空有限混合模型，用于对多个空间单元在多个时间点上的收入分布进行建模。该方法的一个独特优势在于，所有区域共享共同的潜在分布，而包含空间和时间效应的混合比例则捕捉了区域间的潜在异质性。因此，纳入这些效应可以对时间与空间维度的目标量进行平滑、对缺失值进行插补，并对未来值进行预测。通过将HLS数据应用于所提出方法，我们获得了任意时间点上的收入与贫困度量完整地图，这可用于支持细粒度、高效且迅速的政策制定。