### 博碩士論文 962405002 詳細資訊

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(Efficiency of the Composite Likelihood)

 ★ 不需常態假設與不受離群值影響的選擇迴歸模型的方法 ★ 用卜瓦松與負二項分配建構非負連續隨機變數平均數之概似函數 ★ 強韌變異數分析 ★ 用強韌概似函數分析具相關性之二分法資料 ★ 利用Bartlett第二等式來估計有序資料的相關性 ★ 相關性連續與個數資料之強韌概似分析 ★ 不偏估計函數之有效性比較 ★ 一個分析相關性資料的新方法-複合估計方程式 ★ (一)加權概似函數之強韌性探討 (二)影響代謝症候群短期發生及消失的相關危險因子探討 ★ 利用 Bartlett 第二等式來推論模型假設錯誤下的變異數函數 ★ (一)零過多的個數資料之變異數函數的強韌推論 (二)影響糖尿病、高血壓短期發生的相關危險因子探討 ★ 一個分析具相關性的連續與比例資料的簡單且強韌的方法 ★ 時間數列模型之統計推論 ★ 決定分析相關性資料時統計檢定力與樣本數的普世強韌法 ★ 檢定DNA鹼基替換模型的新方法 - 考慮不同DNA鹼基間的相關性 ★ 針對名目、個數與有序資料迴歸係數統計檢定力計算的普世強韌法

In this thesis we incorporate the multivariate negative binomial distribution as the core model to build up composite likelihoods. We will show that using the negative binomial model to formulate a composite likelihood might be a better choice for regression analysis of general correlated data. The negative binomial-based composite likelihood (NB-CL) will be demonstrated to be more efficient than the usual normal-based composite likelihood (NM-CL).
To further improve the efficiency, a sensible estimation of the intra cluster correlation (ICC) is often beneficial for this purpose. To this end, we introduce a new tool for inference making for ICC between correlated binary data and correlated ordinal data. The creation of this method is founded upon the violation of Bartlett’s second identity when adopting the binomial distributions to model cluster binary data and the multinomial distributions to model cluster ordinal data. The new methodology applies to any sensible link functions that connect the success probability and covariates. One can easily implement the procedure by using any statistical software providing the naïve and the sandwich covariance matrices for regression parameter estimates.

★ 多維負二項分配
★ 費雪訊息
★ Bartlett’s 第二等式
★ 集群資料
★ 相關係數

★ Multivariate negative binomial distribution
★ Fisher information matrix
★ Bartlett’s second identity
★ clustered data
★ Correlation coefficient

Abstract………………………………………………………………………… ii
Contents…………………………………………………………………… iv
List of Figures…………………………………………………………… vi
List of Tables………………………………………………………………… vii
1 Introduction………………………………………………………………… 1
2 Reviews on robust likelihood and composite likelihood methods……………3
2.1 Robust likelihood method……………………………………… 3
2.2 Composite likelihood method…………………………………… 5
3 Efficiency and robustness of the composite likelihood method……………………8
3.1 Introduction…………………………………………………………… 8
3.2 The performance of MPLEs of group means………………… 9
3.2.1 Multivariate normal working model………………………… 9
3.2.2 Multivariate negative binomial working model……… 13
3.3 The robust variance matrices for MLEs and MPLEs–Regression scenario……………17
3.3.1 Variance matrix under multivariate normal working model…………………………17
3.3.2 Variance matrix under multivariate negative binomial working model……………20
3.4 Simulation studies…………………………………………………… 22
3.5 Examples…………………………………………………………………… 30
3.6 Concluding remarks.………………………………………………… 35
4 Estimation of intra-cluster correlation coefficient for binary data………………37
4.1 Introduction…………………………………………………………… 37
4.2 The variance of the score and the expected Fisher information………………38
4.2.1 Model-based expected Fisher information……………… 39
4.2.2 Variance of the score…………………………………………… 39
4.3 Estimation of intra-cluster correlation coefficient…40
4.4 Simulation studies………………………………………………………43
4.5 Examples………………………………………………………………………52
4.5.1 Boric Acid Data…………………………………………………………52
4.5.2 Weil-Williams Toxicology Data…………………………………52
4.5.3 Crowder’s Germination Data………………………………………53
4.5.4 Cleft Palate Data………………………………………………………53
4.6 Conclusions…………………………………………………………………54
5 Estimation of intra-cluster correlation coefficient for ordinal data..........55
5.1 Introduction……………………………………………………………55
5.2 The variance of the score and the expected Fisher information…………………56
5.2.1 Model-based expected Fisher information matrix…58
5.2.2 Variance matrix of the score functions………………… 58
5.3 Estimation of intra-cluster correlation coefficient…59
5.4 Simulation studies…………………………………………………61
5.5 Examples…………………………………………………………………65
5.5.1 NTP Ethylene Glycol Study…………………………………65
5.5.2 Hydroxyurea data…………………………………………………65
5.6 Conclusions……………………………………………………………66
6 Concluding remarks……………………………………………………67
References……………………………………………………………………68
Appendix A……………………………………………………………………72
Appendix B……………………………………………………………………76

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