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Subgroup analysis for heterogeneous additive partially linear models and its application to car sales data

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  • Liu, Lili
  • Lin, Lu

Abstract

As an extension of additive partially linear model, heterogeneous additive partially linear model contains the homogeneous linear components and subject-dependent additive components, but has no group information of subject-dependent additive components. Such a model is more flexible and efficient for addressing some special issues such as precision medicine and precision marketing. A polynomial spline smoothing is used to approximate the heterogeneous additive components, and then a new clustering method is developed to automatically identify subgroups. The procedure avoids solving coefficient vector in each iterative step as in regression clustering procedures. Thus, this approach is rapid and computationally stable even if the sample size is large. Based on the clustered heterogeneous additive components, consistent estimators of the homogeneous parameters and subgroup-specific additive components are further obtained. Moreover, n-consistency and asymptotic normality for the estimators of the parametric components are established. The simulation studies and real data analysis illustrate that the model and proposed clustering and estimation are effective in practice.

Suggested Citation

  • Liu, Lili & Lin, Lu, 2019. "Subgroup analysis for heterogeneous additive partially linear models and its application to car sales data," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 239-259.
    • Handle: RePEc:eee:csdana:v:138:y:2019:i:c:p:239-259
    DOI: 10.1016/j.csda.2019.04.011
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    References listed on IDEAS

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    Cited by:

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    2. Fang, Kuangnan & Chen, Yuanxing & Ma, Shuangge & Zhang, Qingzhao, 2022. "Biclustering analysis of functionals via penalized fusion," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Cai, Tingting & Li, Jianbo & Zhou, Qin & Yin, Songlou & Zhang, Riquan, 2024. "Subgroup detection based on partially linear additive individualized model with missing data in response," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    4. Veronica Distefano & Maria Mannone & Irene Poli, 2023. "Exploring Heterogeneity with Category and Cluster Analyses for Mixed Data," Stats, MDPI, vol. 6(3), pages 1-16, July.
    5. Zhang, Xiaochen & Zhang, Qingzhao & Ma, Shuangge & Fang, Kuangnan, 2022. "Subgroup analysis for high-dimensional functional regression," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    6. Mingyang Ren & Qingzhao Zhang & Sanguo Zhang & Tingyan Zhong & Jian Huang & Shuangge Ma, 2022. "Hierarchical cancer heterogeneity analysis based on histopathological imaging features," Biometrics, The International Biometric Society, vol. 78(4), pages 1579-1591, December.

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