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| 題名: | 具局部相關結構之貝氏試題反應理論模型
Bayesian Item Response Theory Model with Local Dependence |
| 作者: | 劉孟展
Liu, Meng-Chan |
| 貢獻者: | 張育瑋
Chang, Yu-wei
劉孟展
Liu, Meng-Chan |
| 關鍵詞: | 貝氏統計推論
Ising 模型
試題反應理論模型
擬概似函數
Bayesian inference
Ising model
Item response theory model
Pseudo likelihood |
| 日期: | 2025 |
| 上傳時間: | 2025-08-04 15:11:58 (UTC+8) |
| 摘要: | 傳統的試題反應理論(Item Response Theory; IRT)模型假設一位受試者在所有試題的反應是給定隨機效應參數下彼此獨立，稱為局部獨立，但是在現實應用上，這項假設很難滿足。文獻上已發展各式各樣更符合現實情況的IRT模型，以處理例如題組、多群體、限時測驗、受試者各異反應...等各種不滿足局部獨立假設時的局部相關。近年更新穎的做法是直接發展更一般化的局部相關之IRT模型，例如Chen et al. (2018) 提出的 FLaG-IRT 模型透過將Ising 模型引入試題反應理論模型中來描述一般化的局部相關。然而，該文獻提出使用proximal gradient-based方法求解最大概似估計量相當複雜，在模型進一步推廣時並不容易隨之推廣。本研究針對FLaG-IRT模型提出一套貝氏統計推論流程，讓模型中的許多參數能透過先驗分配彼此互相借用訊息，並且提供一個更簡潔的估計架構以利未來的模型推廣。然而，該模型具有無法直接處理的正規化函數(intractable normalizing functions) 之議題，本研究使用 variational Bayesian 方法 (Kim et al., 2024)，並搭配適當的擬概似函數解決該議題。透過模擬研究呈現本研究所提出之統計推論方法在各種模擬條件下之估計優勢，最後將該方法應用於兩筆實際資料上。
Traditional Item Response Theory (IRT) models assume that the responses to all items by one respondent are conditionally independent, conditional on random-effect parameters, and this is referred to as local independence. However, it is not easy that this assumption is fulfilled in practical applications. Various extensions of IRT models have been proposed in the literature to deal with local dependence (LD) structures arising from situations such as testlets, time limit tests, and different response strategies of individuals. In recent years, a more innovative approach involves directly developing general IRT models that account for local dependence. For example, Chen, Li, Liu, and Ying (2018) proposed the FLaG-IRT model, which incorporates the Ising model into IRT model to capture local dependence. However, their statistical inference relies on proximal gradient-based algorithm for maximum likelihood estimation, which is computationally complex and is difficult to be further generalized. The current study proposes a Bayesian inference for the FLaG-IRT model. The advantage of the Bayesian FLaG-IRT inference is to allow parameters to borrow information through prior distributions and to provide a more concise estimation structure that facilitates future model extensions. The main challenge of Bayesian FLaG-IRT inference is the intractable normalizing function issues, and we adopt variational Bayesian method (Kim, Bhattacharya & Maiti, 2024) with an appropriate pseudo likelihood to overcome this issue. Simulation studies are conducted to evaluate the performance of the proposed method under various conditions with two real data sets illustrating its practical utility. |
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| 描述: | 碩士
國立政治大學
統計學系
112354025 |
| 資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0112354025 |
| 資料類型: | thesis |
| 顯示於類別: | [統計學系] 學位論文
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