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題名 多群體試題反應理論樹狀模型之統計推論與應用
Statistical Inference and Applications of a Multiple-group Item Response Theory Tree Model
作者 楊承鑫
Yang, Cheng-Xin
貢獻者 張育瑋
Chang, Yu-Wei
楊承鑫
Yang, Cheng-Xin
關鍵詞 貝氏估計
差異試題功能
試題反應樹狀模型
遺失值
spike-and-slab 先驗分佈
Bayesian estimation
Differential item functioning
Item Response Theory tree model
Missing data
Spike-and-slab priors
日期 2022
上傳時間 1-八月-2022 17:15:40 (UTC+8)
摘要 本研究將文獻上的一個試題反應理論樹狀模型推廣至可以處理多群體的模型，可以同時考慮問卷或成就測驗中的群體差異與遺失值的效應。有別於大多數差異試題功能檢驗的研究需要先尋找定錨題再偵測具差異試題功能的題目，以在成就測驗中去掉這類的題目進而達到測驗的公平性，本研究透過貝氏估計搭配使用 spike-and-slab 先驗分佈 (Ishwaran 與 Rao 2005; Rockova 與 George 2018) 在特定參數，並使用吉氏採樣與 Metroplis-Hastings 演算法等計算技巧，可以同時完成差異試題功能的檢驗與模型的參數估計。本文亦將呈現對於提出模型建議的估計流程，並以模擬研究展現參數估計的不偏性與均方根誤差，及差異試題功能檢驗的成效。最後將本文提出的方法應用至一筆實際資料。
In the current study, we extend an Item Response Theory tree model with four end nodes (TR4) in the literature to accommodate group difference. The extended model takes the group difference and missing data in questionnaire or achievement test into consideration. Different from most of present differential item functioning (DIF) studies where one has to select anchor items and then detect DIF items, we achieve DIF detection and parameter estimation simultaneously through applying some spike-and-slab priors (Ishwaran and Rao 2005; Rockova and George 2018) in full Bayesian inference. The suggested estimation procedure for the Multiple-group TR4 model is presented. Simulation studies are conducted to illustrate the validation of the proposed estimation procedure and the efficiency of DIF detection. The proposed method is further applied to a real data set for illustration.
參考文獻 Candell, G. L., & Drasgow, F. (1988). An iterative procedure for linking metrics and
assessing item bias in item response theory. Applied Psychological Measurement,
12, 253-260.
Casella, G., & Berger, R. L. (2002). Statistical Inference. the United State of America:
Brooks/Cole Cengage Learning.
Castillo, I., Schmidt-Hieber, B., & Vaart, A. V. D. (2015). Bayesian Linear Regression
With Sparse Priors. The Annuals of Statistics, 43, 1986-2018.
Chang, Y.-W., Hsu, H.-J., & Tsai, R.-C. (2021). An item response tree model with notall-distinct end nodes for non-response modelling. British Journal of Mathematical
and Statistical Psychology, 74, 487-512.
Chang, Y.-W., & Tu, J.-Y. (2022).Bayesian Estimation for an Item Response Tree Model
for Nonresponse Modeling. Metrika. Published online.
Chen, S. M., Bauer, D. J., Belzak, W. M., & Brandt, H. (2022). Advantages of Spike and
Slab Priors for Detecting Differential Item Functioning Relative to other Bayesian
Regularizing Priors and Frequentist Lasso. Structural Equation Modeling: A Multidiscriplinary Journal, 29, 122-139.
Debeer, D., Janssen, R., & De Boeck, P. (2017). Modeling skipped and not-reached items
using IRTrees. Journal of Educational Measurement, 54, 333–363.
Gelman, A., Carlin, J. B., Rubin, D. B., & Stern, H. S. (2004). Bayesian data analysis. New York: Chapman and Hall.
Gelman, A., & Rubin, D. B. (1992). Inference from Iterative Simulation Using Multiple
Sequences. Statistical Science, 7, 457-511.
George, E. I., & McCulloch, R. E. (1993). Variable Selection Via Gibbs Sampling. Journal of the American Statistical Association, 88, 881-889.
Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their
applications. Biometrika, 57, 97–109.
Ishwaran, H., & Rao, J. S. (2000). Baysian nonparametric MCMC for large variable
selection problems. Unpublished manuscript.
Ishwaran, H., & Rao, J. S. (2005). Spike and Slab Variable Selection: Frequentist and
Bayesian Strategies. The Annals of Statistics, 33, 730-773.
Lempers, F. B. (1971). Posterior probabilities of alternative linear models. Rotterdam
University Press.
Li, H.-H., & Stout, W. (1996). A New Procedure For Detection of Crossing DIF. Psychometrika, 61, 647-677.
Lord, F. (1952). A theory of test scores. Psychometric Monograph. VA：Psychometric
Corporation.
Millsap, R. E. (2011). Statistical Approaches to Measurement Invariance. New York:
Routledge.
Mitchell, T. J., & Beauchamp, J. J. (1988). Bayesian Variable Selection in Linear Regression. Journal of the American Statistical Association, 32, 1023-1032
OECD (2014). PISA 2012 Technical Report.
Park, D. G., & Lautenschlager, G. J. (1990). Improving IRT item bias detection with
iterative linking and ability scale purification. Applied Psychological Measurement,
14, 163-173.
Rockova, V., & George, E. (2018). The Spike-and-Slab LASSO. Journal of the American
Statistical Association, 113, 431-444.
Shealy, R., & Stout, W. (1993). A model-based standardization approach that separate
true bias/DIF from group ability differences and detects test bias/DIF as well as item
bias/DIF. Psychometrika, 58, 159-194.
Stark, S., Chernyshenko, O. S., & Drasgow, F. (2006). Detecting differential item functioning with confirmatory factor analysis and item response theory: Toward a unified strategy. Journal of Applied Psychology, 91, 1292-1306.
Xu, X., & Ghosh, M. (2015). Bayesian Variable Selection and Estimation for Group
Lasso. Bayesian Analysis, 10, 909-936.
描述 碩士
國立政治大學
統計學系
109354015
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109354015
資料類型 thesis
dc.contributor.advisor 張育瑋zh_TW
dc.contributor.advisor Chang, Yu-Weien_US
dc.contributor.author (作者) 楊承鑫zh_TW
dc.contributor.author (作者) Yang, Cheng-Xinen_US
dc.creator (作者) 楊承鑫zh_TW
dc.creator (作者) Yang, Cheng-Xinen_US
dc.date (日期) 2022en_US
dc.date.accessioned 1-八月-2022 17:15:40 (UTC+8)-
dc.date.available 1-八月-2022 17:15:40 (UTC+8)-
dc.date.issued (上傳時間) 1-八月-2022 17:15:40 (UTC+8)-
dc.identifier (其他 識別碼) G0109354015en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141007-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 109354015zh_TW
dc.description.abstract (摘要) 本研究將文獻上的一個試題反應理論樹狀模型推廣至可以處理多群體的模型，可以同時考慮問卷或成就測驗中的群體差異與遺失值的效應。有別於大多數差異試題功能檢驗的研究需要先尋找定錨題再偵測具差異試題功能的題目，以在成就測驗中去掉這類的題目進而達到測驗的公平性，本研究透過貝氏估計搭配使用 spike-and-slab 先驗分佈 (Ishwaran 與 Rao 2005; Rockova 與 George 2018) 在特定參數，並使用吉氏採樣與 Metroplis-Hastings 演算法等計算技巧，可以同時完成差異試題功能的檢驗與模型的參數估計。本文亦將呈現對於提出模型建議的估計流程，並以模擬研究展現參數估計的不偏性與均方根誤差，及差異試題功能檢驗的成效。最後將本文提出的方法應用至一筆實際資料。zh_TW
dc.description.abstract (摘要) In the current study, we extend an Item Response Theory tree model with four end nodes (TR4) in the literature to accommodate group difference. The extended model takes the group difference and missing data in questionnaire or achievement test into consideration. Different from most of present differential item functioning (DIF) studies where one has to select anchor items and then detect DIF items, we achieve DIF detection and parameter estimation simultaneously through applying some spike-and-slab priors (Ishwaran and Rao 2005; Rockova and George 2018) in full Bayesian inference. The suggested estimation procedure for the Multiple-group TR4 model is presented. Simulation studies are conducted to illustrate the validation of the proposed estimation procedure and the efficiency of DIF detection. The proposed method is further applied to a real data set for illustration.en_US
dc.description.tableofcontents 第 一 章 緒 論 . . . . . . . . . . . . . . . . . . . . . . 1
第 二 章 Multiple−Group TR4 模 型 . . .. . . . . . . . . . 4
2.1 定錨題與差異試題功能 . . . . . . . . . . . 9
2.2 MG−TR4 模型之概似函數 . . . . . . . . . . 11
第 三 章 貝 氏 估 計 . . . . . . . . . . . . . . . 13
3.1 Spike-and-slab 先驗分佈 . . . . . . . . . . . 13
3.2 先驗分佈設定. . . . . . . . . . . . . . . . . . . 15
3.3 貝氏估計流程. . . . . . . .. . . . . . . . . . . 20
第 四 章 模 擬 研 究 . . . . . . . . . . . . . . . . . 26
4.1 模擬設定 . . . . . . . . .. . . . . . . . . . . . 26
4.2 模擬結果 . . . . . . . . . . . .. . . . . . . . . 27
第 五 章 實 際 資 料 分 析. . . . . . . . . .. . . . . . 32
5.1 資料與資料前置處理. . . . . . . . . . . . . 32
5.2 資料分析 . . . . . . . . . . . . . . . . . . . . 33
第 六 章 結 論 與 建 議 . . . . . . . . . . . . . . . . . 38
參考文獻..............................39
附 錄. . . . .. . . . . . . . . . . . . . . 42
附錄 A 第二層參數之先驗分佈設定 . .42
附錄 B 第二層參數之全條件 . . . . . . . . . . . . . 43		zh_TW
dc.format.extent 746227 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109354015en_US
dc.subject (關鍵詞) 貝氏估計zh_TW
dc.subject (關鍵詞) 差異試題功能zh_TW
dc.subject (關鍵詞) 試題反應樹狀模型zh_TW
dc.subject (關鍵詞) 遺失值zh_TW
dc.subject (關鍵詞) spike-and-slab 先驗分佈zh_TW
dc.subject (關鍵詞) Bayesian estimationen_US
dc.subject (關鍵詞) Differential item functioningen_US
dc.subject (關鍵詞) Item Response Theory tree modelen_US
dc.subject (關鍵詞) Missing dataen_US
dc.subject (關鍵詞) Spike-and-slab priorsen_US
dc.title (題名) 多群體試題反應理論樹狀模型之統計推論與應用zh_TW
dc.title (題名) Statistical Inference and Applications of a Multiple-group Item Response Theory Tree Modelen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Candell, G. L., & Drasgow, F. (1988). An iterative procedure for linking metrics and
assessing item bias in item response theory. Applied Psychological Measurement,
12, 253-260.
Casella, G., & Berger, R. L. (2002). Statistical Inference. the United State of America:
Brooks/Cole Cengage Learning.
Castillo, I., Schmidt-Hieber, B., & Vaart, A. V. D. (2015). Bayesian Linear Regression
With Sparse Priors. The Annuals of Statistics, 43, 1986-2018.
Chang, Y.-W., Hsu, H.-J., & Tsai, R.-C. (2021). An item response tree model with notall-distinct end nodes for non-response modelling. British Journal of Mathematical
and Statistical Psychology, 74, 487-512.
Chang, Y.-W., & Tu, J.-Y. (2022).Bayesian Estimation for an Item Response Tree Model
for Nonresponse Modeling. Metrika. Published online.
Chen, S. M., Bauer, D. J., Belzak, W. M., & Brandt, H. (2022). Advantages of Spike and
Slab Priors for Detecting Differential Item Functioning Relative to other Bayesian
Regularizing Priors and Frequentist Lasso. Structural Equation Modeling: A Multidiscriplinary Journal, 29, 122-139.
Debeer, D., Janssen, R., & De Boeck, P. (2017). Modeling skipped and not-reached items
using IRTrees. Journal of Educational Measurement, 54, 333–363.
Gelman, A., Carlin, J. B., Rubin, D. B., & Stern, H. S. (2004). Bayesian data analysis. New York: Chapman and Hall.
Gelman, A., & Rubin, D. B. (1992). Inference from Iterative Simulation Using Multiple
Sequences. Statistical Science, 7, 457-511.
George, E. I., & McCulloch, R. E. (1993). Variable Selection Via Gibbs Sampling. Journal of the American Statistical Association, 88, 881-889.
Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their
applications. Biometrika, 57, 97–109.
Ishwaran, H., & Rao, J. S. (2000). Baysian nonparametric MCMC for large variable
selection problems. Unpublished manuscript.
Ishwaran, H., & Rao, J. S. (2005). Spike and Slab Variable Selection: Frequentist and
Bayesian Strategies. The Annals of Statistics, 33, 730-773.
Lempers, F. B. (1971). Posterior probabilities of alternative linear models. Rotterdam
University Press.
Li, H.-H., & Stout, W. (1996). A New Procedure For Detection of Crossing DIF. Psychometrika, 61, 647-677.
Lord, F. (1952). A theory of test scores. Psychometric Monograph. VA：Psychometric
Corporation.
Millsap, R. E. (2011). Statistical Approaches to Measurement Invariance. New York:
Routledge.
Mitchell, T. J., & Beauchamp, J. J. (1988). Bayesian Variable Selection in Linear Regression. Journal of the American Statistical Association, 32, 1023-1032
OECD (2014). PISA 2012 Technical Report.
Park, D. G., & Lautenschlager, G. J. (1990). Improving IRT item bias detection with
iterative linking and ability scale purification. Applied Psychological Measurement,
14, 163-173.
Rockova, V., & George, E. (2018). The Spike-and-Slab LASSO. Journal of the American
Statistical Association, 113, 431-444.
Shealy, R., & Stout, W. (1993). A model-based standardization approach that separate
true bias/DIF from group ability differences and detects test bias/DIF as well as item
bias/DIF. Psychometrika, 58, 159-194.
Stark, S., Chernyshenko, O. S., & Drasgow, F. (2006). Detecting differential item functioning with confirmatory factor analysis and item response theory: Toward a unified strategy. Journal of Applied Psychology, 91, 1292-1306.
Xu, X., & Ghosh, M. (2015). Bayesian Variable Selection and Estimation for Group
Lasso. Bayesian Analysis, 10, 909-936.		zh_TW
dc.identifier.doi (DOI) 10.6814/NCCU202200971en_US