Heterogeneity Exploration for Multi-Response Regression

Understanding treatment heterogeneity plays a key role in many contemporary applications arising from different areas. Although there is a growing literature on subgroup analysis based on the heterogeneous univariate regression model, little work has been done for the heterogeneous multi-response re...

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Bibliographic Details
Published inCommunications in mathematics and statistics Vol. 13; no. 4; pp. 845 - 861
Main Authors Wu, Jie, Gao, Wenjie, Dong, Ruipeng, Zheng, Zemin
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2025
Springer Nature B.V
Subjects
Heterogeneity
Mathematics
Mathematics and Statistics
Regression models
Statistics
Subgroups
Subgroup analysis
62H30
Oracle property
Multi-response
62H12
Penalized least squares
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Summary:Understanding treatment heterogeneity plays a key role in many contemporary applications arising from different areas. Although there is a growing literature on subgroup analysis based on the heterogeneous univariate regression model, little work has been done for the heterogeneous multi-response regression model. In contrast to the existing methods which are based on subject-specific intercepts, we introduce a heterogeneous multi-response regression method which allows the coefficients for treatment variables to be subject-dependent with unknown grouping information, thus applicable to a wider range of situations. Moreover, we provide an efficient algorithm based on concave pairwise fusion penalization and establish the oracle property of the proposed estimator. The effectiveness of the suggested method is demonstrated through simulation examples and an empirical study.
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ISSN:2194-6701
2194-671X
DOI:10.1007/s40304-023-00342-w