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    Title: 懲罰R平方對線性混合模型中重要變數選取之研究
    Variables selection for linear mixed models with Penalized R-squared statistics
    Authors: 吳書恆
    Wu, Shu-Heng
    Contributors: 黃佳慧
    Huang, Chia-Hui
    吳書恆
    Wu, Shu-Heng
    Keywords: 自動化模型選擇
    適合度
    線性混合模型
    精簡模型
    懲罰係數
    Automatic selection methods
    Goodness-of-fit
    Linear mixed model
    Parsimonious model
    Penalty coefficient
    Date: 2022
    Issue Date: 2022-08-01 17:14:31 (UTC+8)
    Abstract: 在時間相依共變量拆解後的線性混合模型 (linear mixed model) 中，已提出不同型式的R2統計量來評估隨機效果與固定效果的適合度 (goodness-of-fit)，然而在自動化選模方法中，這些統計量因過度擬合 (overfitting) 的問題而無法直接根據最大值來選擇較精簡模型
    (parsimonious model) 。本研究提出一個具有懲罰性質的R2統計量，此統計量懲罰項納入參數個數的考量，可抑制R2隨解釋變數增加而不斷膨脹的問題，並且可搭配自動化選模方式選擇隨機與固定效果的精簡模型。此外，因應使用者對模型精簡程度的需求，此統計量懲罰項含有懲罰係數，可彈性地調整懲罰的強度。當使用者並無特定的精簡程度，本研究亦提供網格搜索與給定容忍值的方式，以得出最佳的懲罰範圍與對應的精簡模型。透過資料模擬結果可發現懲罰R2選到精簡模型的效果較其他AIC統計量 (cAIC與mAIC) 佳，同時使用隨機效果與固定效果的懲罰R2亦不會影響各自選模的結果。在北卡羅來納州 (North Carolina) 犯罪資料的實證分析中，亦發現本研究所提出R2統計量在自動化選模中具有辨別重要變數的能力。
    In the Linear Mixed Model (LMM) after time dependent covariates decomposition, different types of R2 statistics have been proposed to evaluate the goodness-of-fit (GOF) of random effects and fixed effects. However, due to the overfitting issue, the maximum value of the statistics cannot be applied in the automatic selection methods. In this study, we propose a R2 statistic, which includes a penalty that discourages the inflation of R2 when extra regressors are added to the model. Therefore, the R2 statistic can select parsimonious model of random effects and fixed effects by automatic model selection. In addition, the penalty coefficient of the proposed R2 statistic can be flexibly adjusted based on researcher`s demand for model simplification. When researchers do not have a specific degree of simplification, we also provide two methods to obtain the optimal range of penalty coefficient and the corresponding parsimonious model. The simulation results showed that the effect of penalized R2 in finding parsimonious model is better than that of other AIC statistics (cAIC and mAIC), and using penalized R2 with both random effects and fixed effects simaltaneously does not affect the results of their model selection. In an empirical analysis of North Carolina crime data, we found that the proposed R2 statistic is able to identify significant variables which were also found in the original study.
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    Description: 碩士
    國立政治大學
    統計學系
    109354003
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0109354003
    Data Type: thesis
    DOI: 10.6814/NCCU202200673
    Appears in Collections:[Department of Statistics] Theses

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