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A0525
Title: Spatio-temporal smoothing, interpolation and prediction of income distributions based on grouped data Authors:  Genya Kobayashi - Meiji University (Japan) [presenting]
Shonosuke Sugasawa - Keio University (Japan)
Yuki Kawakubo - Chiba University (Japan)
Abstract: In science, especially in social science, exact values of some characteristics of individuals are not directly observed, but values of interest are grouped or collapsed in such a way that only numbers of individuals who belong to groups are observed. This type of data is typically called grouped data and any analysis should address this grouped nature. A new methodology of mixture modelling for grouped data observed over multiple spatial units or clusters and time periods is developed. The main idea is that all clusters share the common latent distributions and potential cluster-wise heterogeneity is captured by the cluster-wise mixing proportions. To model the unknown cluster-wise mixing proportions, we employ the multinomial logistic functions that include spatial and temporal effects. The inclusion of these effects enables smoothing of quantities of interest over time and space, imputation of missing values and prediction of future values. Using Polya-gamma data augmentation, an efficient posterior computational algorithm via Gibbs sampling is developed. As a specific application of the proposed method, modelling of cluster-wise income distributions based on longitudinal grouped data is considered. The usefulness of the method is demonstrated through the simulated data and income survey data of Japan.