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| Title: | 無母數多元邏輯斯迴歸之spline估計與節點選取
Nonparametric Multinomial Logistic Regression Spline Estimation and Knots Selection |
| Authors: | 張軼棣
Chang, I-Ti |
| Contributors: | 黃子銘
黃佳慧
Huang, Tzee-Ming
Huang, Chia-Hui
張軼棣
Chang, I-Ti |
| Keywords: | 樣條
樣條邏輯斯迴歸
節點
變數篩選
B-spline
Spline Logistic Regression
Knots
Variable Selection |
| Date: | 2024 |
| Issue Date: | 2024-08-05 14:00:39 (UTC+8) |
| Abstract: | 樣條函數的靈活性在於節點位置和數量作為自由變數，使得其在配適過程中具有多樣的功能。本研究深入探討樣條邏輯斯迴歸(spline logistic regression)中的兩種邏輯斯函數，致力於建立在不同節點配置下的對比效果。為了提升模型選擇的效率，我們對傳統的AIC向後選取法(backward AIC)進行了改良，特別適用於樣條邏輯斯迴歸。
我們的改良方法不僅能夠同時針對不同邏輯斯函數下的節點進行篩選，同時透過優化參數和變數篩選方法，相較於傳統AIC向後選取法，獲得更為優越的效果。此外，本研究進一步模擬了不同初始節點下的篩選效果，並使用ISE(integrated squared error)的平均值來評估各種情況下的模型配適效果。這項模擬的結果有助於更全面地理解不同初始節點配置對模型性能的影響，並提供對於節點選擇的方向。整體而言，本研究綜合運用不同方法，致力於提升樣條邏輯斯迴歸的節點選擇和估計效能。
The flexibility of spline functions lies in the freedom to choose the positions and number of knots, which endows them with diverse capabilities during the fitting process. This study delves into two different logistic functions within spline logistic regression, aiming to establish a comparative analysis under various knot configurations. To enhance the efficiency of model selection, we have improved the traditional backward AIC method, making it particularly suitable for spline logistic regression.
Our improved method not only allows for the simultaneous selection of knots under different logistic functions but also achieves superior performance compared to the traditional backward AIC method through parameter optimization and variable selection techniques. Additionally, this study simulates the selection effect under different initial knot configurations and uses the mean integrated squared error (ISE) to evaluate the model fitting performance in various scenarios. The simulation results contribute to a more comprehensive understanding of how different initial knot configurations affect model performance and provide guidance on knot selection. Overall, this research integrates various approaches to enhance knot selection and estimation efficiency in spline logistic regression. |
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Gazi University Journal of Science, vol. 35, no. 2, pp. 716–729, 2022.
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A Simplex Method for Function Minimization,
The Computer Journal,
vol. 7, Issue 4, pp. 308–313, January 1965.
F. Bessaoud, J.-P. Daures and N. Molinari.
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Computer Methods and Programs in Biomedicine,
vol. 77, no. 1, pp. 1-9, January 2005.
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Comparing measures of model selection for penalized splines in Cox models,
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vol. 53, no. 7, pp. 2605-2616, May 15, 2009. |
| Description: | 碩士
國立政治大學
統計學系
111354029 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0111354029 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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