Concomitant Variable Mixture Models for Small Area Estimation: An Application to Estimating Regional ARPRs in Germany


SAE in welfare and wellbeing studies

Jan Pablo Burgard (University of Trier, Faculty IV - Economics, Economics and Social Statistics Department) (Speaker)
Charlotte Articus (Trier University)

A basic assumption of standard small area models is that the statistic of interest can be modelled through a mixed model with common fixed effects for all areas under study. When modelling poverty through a set of social indicators, it might, however, be more realistic to assume that the exploited relationship between response variable and covariates differs between different types of areas, i.e. urban and rural regions. Finite mixtures of small area models offer a flexible approach to account for this kind of heterogeneity without requiring an ex ante segmentation of areas: Besides improving estimation accuracy in the presence of latent subgroups, they yield subgroup-specific model parameters and a model-based probabilistic clustering of areas. The mixture model can be extended to include further covariates, sometimes called concomitant variables, to model the mixture weights. Given suitable covariates, this improves both clustering performance and estimation accuracy. It furthermore provides valuable insights into the segmentation of areas into subgroups and substantiates the estimation of a mixture of small area models in applications. In our talk, we present the respective mixture of small area models with concomitant variables and apply it to small area estimation of the at-risk-of-poverty rate in the German federal states Rhineland-Palladium and Saarland.

Keywords: ARPR, Concomitant Variable Mixture Models , SAE

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