Publication type
Journal Article
Authors
Publication date
October 6, 2026
Summary:
Individual-level time series data, such as longitudinal survey data, are increasingly used for policy evaluation. To infer the impact of a policy given such data, we propose a hierarchical Bayesian structural time series (HBSTS) model that extends the existing Bayesian structural time series model. Hierarchical Bayesian structural time series can accommodate multiple observations per time point by adding an extra layer to capture individual-level variation. It also uses a regularized horseshoe prior with a signal-adaptive variable selection algorithm. These extensions provide a more flexible and realistic framework for policy evaluation, and make inference less sensitive to the prior specification of the expected model size (i.e. the expected number of covariates included in the model that are predictive of outcomes). In simulation studies, HBSTS demonstrated greater robustness to misspecification of the expected model size and was more powerful in detecting putative intervention effects compared with BSTS. We apply our model to the UK Household Longitudinal Study to investigate the impact of a UK immigration policy reform. Our findings indicated that the policy led to psychological distress among individuals from Black Caribbean backgrounds, which was also observed in an earlier Bayesian interrupted time series analysis, though derived by comparing them with people from White backgrounds.
Published in
Journal of the Royal Statistical Society Series C: Applied Statistics
DOI
https://doi.org/10.1093/jrsssc/qlag054
ISSN
359254
Subjects
Notes
Online Early
© The Royal Statistical Society 2026.
Open Access
This is an open access article distributed under the terms of the Creative Commons CC BY license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Code: The application example used the main survey data from the UK Household Longitudinal Study available from https://www.understandingsociety.ac.uk/. The R code for simulation studies and empirical analyses is provided in Code_for_HBSTS.zip in the online supplementary material and is also available on the GitHub repository https://github.com/xwyu2021/Hierarchical-Bayesian-Structural-Time-Series-model.
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