本研究針對連續型資料中可能存在的結構性異質性，提出三區制門檻邊界迴歸模型及其估計演算法TBR3-WSVM。既有門檻邊界迴歸模型雖能根據共變量學習分割邊界，但大多僅適用於兩區制；多重門檻變化平面模型雖可處理多區制，通常仍要求各邊界彼此平行。為克服上述限制，本研究將樣本空間劃分為三個具有不同迴歸關係的區域，並允許三條門檻邊界具有不同方向且共享一個共同交界。估計方面，本文以加權支援向量機為基礎，透過疊代式兩階段程序估計三條邊界及各區域的迴歸係數。模擬結果顯示，TBR3-WSVM在線性、高維及經特徵展開的非線性邊界情境下皆具有良好的估計、分類與預測表現。實證分析顯示，所提出的方法能從UCISeeds小麥種子資料中辨識出與真實品種相符的子群結構，並從CapitalBikeshare單車租用資料中揭示不同氣象條件下的用車異質性。

This study proposes a three-regime threshold boundary regression model and its estimation algorithm, TBR3-WSVM, to address structural heterogeneity in continuous data. Although existing threshold boundary regression models can learn partitioning boundaries from covariates, they are generally limited to two regimes. Multiple change-plane models can accommodate multiple regimes but typically require the boundaries to be parallel. To overcome these limitations, the proposed model partitions the sample space into three regions with distinct regression relationships and allows the three threshold boundaries to have different orientations while sharing a common intersection. For estimation, TBR3-WSVM employs a two-stage iterative procedure based on weighted support vector machines to estimate the three boundaries and the regression coefficients within each region. Simulation results demonstrate satisfactory estimation, classification, and prediction performance under linear, high-dimensional, and nonlinear boundary settings constructed through feature expansion. Empirical analyses further show that the proposed method identifies subgroup structures consistent with the true varieties in the UCI Seeds dataset and reveals heterogeneity in bicycle usage under different weather conditions in the Capital Bikeshare dataset.

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