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研究生： 陳冠宏
Chen, Kuan-Hung
論文名稱： Bayesian evaluation of inequality constrained hypotheses of means for ordered categorical data
Bayesian evaluation of inequality constrained hypotheses of means for ordered categorical data
指導教授： 蔡蓉青
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2016
畢業學年度： 104
語文別： 英文
論文頁數： 33
中文關鍵詞： 貝氏估計 、貝氏因子 、不等限制假說 、有序分類數據
英文關鍵詞： Bayesian estimation, Bayes factor, inequality constrained hypotheses, ordered categorical data
DOI URL： https://doi.org/10.6345/NTNU202204572
論文種類： 學術論文
相關次數： 點閱：97  下載：10 
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    • 本研究利用了多群組離散型驗證性因素分析模型來分析多群組的有序分類數據，主要目的在於利用貝氏估計在最小限制式的條件下，來估計模型中的閾值、潛在因子的平均與變異數等參數，我們利用了資料擴張與Gibbs抽樣的方式來估計這些參數的聯合分配。並利用貝氏因子來檢驗潛在因子的平均是否滿足不等限制的假說。而藉由模擬與實徵資料的分析，貝氏因子已被驗證在檢驗不等限制的假說上是可行的。

    The main purpose of this study is to use Bayesian estimation and Bayes factor to test for inequality constrained hypotheses of means for ordered categorical data among multiple groups using categorical confirmatory factor analysis model. Joint Bayesian estimates of the thresholds, the factor scores and the structural parameters subjected to some minimal identification constraints are obtained by using data augmentation and Gibbs sampling. By the simulation and real data analysis, Bayes factor is shown useful in testing hypotheses involving inequality constraints of means for ordered categorical data.

    Contents 1 Introduction. . . 5 2 Model description. . . 6 3 Bayesian estimation. . . 6 3.1 Joint prior distribution. . . 8 3.2 Conditional distributions of parameters. . . 9 3.2.1 Y(g)'s conditional distribution. . . 9 3.2.2 mu(g)'s conditional distribution. . . 10 3.2.3 F(g)'s conditional distribution. . . 10 3.2.4 Lambda(g)'s conditional distribution. . . 11 3.2.5 phi(g)(-1)'s conditional distribution. . . 12 3.2.6 alpha (g)'s conditional distribution. . . 13 3.3 Identi ability constraints. . . 13 3.4 Convergence of Gibbs sampler. . . 13 4 Bayes factor. . . 14 5 Simulation. . . 15 5.1 Simulation setting. . . 15 5.1.1 parameters for data generation. . . 15 5.1.2 parameters of the prior distributions. . . 16 5.1.3 starting values. . . 16 5.2 Results. . . 17 6 Real data. . . 20 7 Discussion. . . 30 8 Conclusion. . . 31 References. . . 32

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