博碩士論文 962405002 詳細資訊




以作者查詢圖書館館藏 以作者查詢臺灣博碩士 以作者查詢全國書目 勘誤回報 、線上人數:11 、訪客IP:34.204.191.31
姓名 陳婉貞(Wan-chen Chen)  查詢紙本館藏   畢業系所 統計研究所
論文名稱 複合概似函數有效性之探討
(Efficiency of the Composite Likelihood)
相關論文
★ 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
檔案 [Endnote RIS 格式]    [Bibtex 格式]    [相關文章]   [文章引用]   [完整記錄]   [館藏目錄]   至系統瀏覽論文 ( 永不開放)
摘要(中) 近年來,複合概似函數方法 (Composite Likelihood) 引起高度關注。原因在於複合概似函數方法對於分析不易獲得聯合分布函數的相關性資料,既便利又有效。無庸置疑的,多維常態分配經常被當作建構複合概似函數的核心模式。
本論文納入多維負二項分配為核心模式來建構複合概似函數,對於相關性資料的迴歸分析,證明此核心模式所建構的複合概似函數相較於多維常態分配是更好的選擇。此外,多維負二項複合概似函數方法亦能得到更有效的迴歸參數估計量。
集群內相關性的估計對於改善有效性是有助益的。本文最後,根據錯誤的模型假設(如用二項分配模式配適相關二元資料或多項分配模式配適相關的有序資料)所導致Bartlett第二等式錯誤的性質,提出一個估計集群內相關性的新方法。此方法可應用於如:邏吉斯迴歸模型、對數迴歸模型、比例勝算迴歸模型或其他適當的連結函數,且可利用有提供naïve及sandwich共變異數矩陣的統計軟體來簡單的執行此估計方法。
摘要(英) The method of composite likelihood (CL) has attracted a lot of attentions in recent years. This expedient method is convenient for analyzing correlated data whose joint distribution is difficult to model or unattainable. Without surprises, multivariate normal has been the sole model utilized to fabricate composite likelihood functions
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.
關鍵字(中) ★ 複合概似函數
★ 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
關鍵字(英) ★ Composite likelihood
★ Multivariate negative binomial distribution
★ Fisher information matrix
★ Bartlett’s second identity
★ clustered data
★ Correlation coefficient
論文目次 Contents
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
參考文獻 References
1. Agresti, A. (2002). Categorical Data Analysis(2nd edn). Wiley, Hoboken.
2. Andersen, E. W. (2004). Composite likelihood and two-stage estimation in family studies. Biometrics, 5, 15–30.
3. Bartlett, M. S. (1953). Approximate confidence intervals. Biometrika, 40, 12–19.
4. Besag, J. E. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion). Journal of the Royal Statistical Society Series B, 34, 192–236.
5. Bellio, R. and Varin, C. (2005). A pairwise likelihood approach to generalized linear models with crossed random effects. Statistical Modelling, 5, 217–227.
6. Birnbaum, L. S., Harris, M. W., Stocking, L. M., Clark, A. M., and Morrissey, R. E. (1989). Retinoic acid selectively enhances teratogenesis in C57BL/6N mice. Toxicology and Applied Pharmacology, 98, 487–500.
7. Birnbaum, L. S., Morrissey, R. E., and Harris, M. W. (1991). Teratogenic effects of 2,3,7,8-tetrabromodibenzo-p-dioxin and three polybrominated dibenzofurans in C57BL/6N mice. Toxicology and Applied Pharmacology, 107, 141–192.
8. Blizzard, L. and Hosmer, D. W. (2006). Parameter estimation and goodness-of-fit in log binomial regression. Biometrical Journal, 48, 5–22.
9. Chatelain, F., Lambert-Lacroix, S., and Tourneret, J.-Y. (2008). Pairwise likelihood estimation for multivariate mixed poisson models generated by gamma intensities. Statistics and Computing, 19, 283–301.
10. Chen, J.J., Kodell, R.L., Howe, R.B., and Gaylor, D.W. (1991). Analysis of Trinomial Responses from Reproductive and Developmental Toxicity Experiments. Biometrics, 47, 1049–1058.
11. Cox, D. R. and Reid, N. (2004). A note on pseudolikelihood constructed from marginal densities. Biometrika, 91, 729–737.
12. Crowder, M. J., 1978. Beta-binomial ANOVA for proportions. Journal of the Royal Statistical Society. Series C, 27, 34–37.
13. de Leon, A. R. (2005). Pairwise likelihood approach to grouped continuous model and its extension. Statistics and Probabilities Letters, 75, 49–57.
14. de Leon, A. R. and Carriere, K. C. (2007). General mixed-data model: extentsion of general location and grouped continuous models. The Canadian Journal of Statistics, 35, 533–548.
15. Fearnhead, P. and Donnelly, P. (2002). Approximate likelihood methods for estimating local recombination rates. Journal of the Royal Statistical Society Series B, 64, 657–680.
16. Gennings, C., Carter Jr., W.H., and Martin, B.R. (1994). Drug interactions between morphine and marijuana. In: Lange, N., Ryan, L., Billard, L., Brillinger, D., Conquest, L., Greenhouse, J. (Eds.), Case Studies in Biometry. Wiley, New York, 429–451.
17. Godambe, V. P. (1960). An optimum property of regular maximum likelihood estimation. The Annals of Mathematical Statistics, 31, 1208–1211.
18. Hadgu , A. and Koch , G. ( 1999 ). Application of generalized estimating equations to a dental randomized clinical trial . J. Biopharmaceut. Statist., 9, 161 – 178 .
19. He, W. and Yi, G. Y. (2011). A pairwise likelihood method for correlated binary data with/without missing observations under generalized partially linear single-index models. Statistica Sinica, 21, 207–229.
20. Heindel, J. J., Price, C. J., Field, E. A., Marr, M. C., Myers, C. B., Morrissey, R. E., and Schwetz, B. A. (1992). Developmental toxicity of boric acid in mice and rats. Fundamental and Applied Toxicology, 18, 266–277.
21. Joe, H. and Lee, Y. (2009). On weighting of bivariate margins in pairwise likelihood. Journal of Multivariate Analysis, 100, 670–685.
22. Kuk, A. Y. and Nott, D. J. (2000). A pairwise likelihood approach to analyzing correlated binary data. Statistics & Probability Letters, 47, 329–335.
23. Kuk, A. Y. C. (2007). A hybrid pairwise likelihood method. Biometrika, 94, 939–952.
24. Lee, Y. (2004). Estimating intraclass correlation for binary data using extended quasi-likelihood. Statistical Modeling, 4, 113–126.
25. Liang, K.Y., Zeger, S.L., and Qaqish, B. (1992). Multivariate regression analyses for categorical data. Journal of the Royal Statistical Society, Series B, 54, 3–40.
26. Lindsay, B. G. (1988). Composite likelihood methods. Contemp. Math., 80, 221–239.
27. Lindsay, B. G., Yi, G. Y., and Sun, J. (2011). Issues and strategies in the selection of composite likelihoods. Statistica Sinica, 21, 71–105.
28. Mardia, K. V., Hughes, G., and Taylor, C. C. (2007). Efficiency of the pseudolikelihood for multivariate normal and von Mises distributions. Research reports, Department of Statistics, University of Leeds.
29. McCullagh, P. (1980). Regression models for ordinal data. Journal of the Royal Statistical Society, Series B, 42, 109–142.
30. McCullagh, P. (1983). Quasi-likelihood functions. Annals of Statistics, 11, 59–67.
31. McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, London: Chapman and Hall.
32. Molenberghs, G. and Lesaffer, E. (1994). Marginal modelling of correlated ordinal data using a multivariate Plackett distribution. Journal of the American Statistical Association, 89, 633–644.
33. Molenberghs, G. and Verbeke, G. (2005). Models for Discrete Longitudinal Data. Springer:New York.
34. Parner, E. T. (2001). A composite likelihood approach to multivariate survival data. Scandinavian Journal of Statistics, 28, 295–302.
35. Presnell, B. and Boos, D. D. (2004). The IOS test for model misspecification. Journal of the American Statistical Association, 99, 216–227.
36. Price, C. J., Kimmel, C. A., Tyl, R. W., and Marr, M. C. (1985). The developmental toxicity of ethylene glycol in rats and mice. Toxicology and Applied Pharmacology, 81, 113–127.
37. Qaqish, B. F. (2003). A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations. Biometrika, 90, 455–463.
38. Renard, D., Molenberghs, G., and Geys, H. (2004). A pairwise likelihood approach to estimation in multilevel probit models. Computational Statistics and Data Analysis, 44, 649–667.
39. Ridout, M. S., Demétrio, C. G. B., and Firth D. (1999). Estimating intraclass correlation for binary data. Biometrics, 55, 137–148.
40. Royall, R. M. (2000). On the probability of observing misleading statistical evidence(with discussion). Journal of the American Statistical Association, 95, 760–780.
41. Royall, R. M. and Tsou, T. S. (2003). Interpreting statistical evidence using imperfect models: robust adjusted likelihood functions. Journal of the Royal Statistical Society B, 65, 391–404.
42. Scheeringa, M. S. and Zeanah, C. H. (1995). Symptom expression and trauma variables in children under 48 months of age. Infant Mental Health Journal, 16, 259–270.
43. Shen, C.W., Tsou, T. S., and Balakrishnan, N. (2011). Robust likelihood inference for regression parameters in partially linear models. Computational Statistics & Data Analysis, 55, 1696–1714
44. Slaton, T. L., Piegorsch, W. W., and Durham, S. D. (2000). Estimation and Testing With Overdispersed Proportions Using the Beta-Logistic Regression Model of Heckman and Willis. Biometrics, 56, 125–133.
45. Stefanski, L. A. and Boos, D. D. (2002). The Calculus of M-Estimation. The American Statistician, 56, 29–38.
46. Tsou, T. S. and Shen, C.W. (2008). Parametric robust inferences for correlated ordinal data. Statistics in Medicine, 27, 3550–3562.
47. Tsou, T. S. (2005a). Robust inferences for the correlation coefficient – a parametric robust way. Comm. Stat.- Theor, Meth., 34, 147–162.
48. Tsou, T. S. (2005b). Inference of Variance Function-a parametric robust way. Journal of Applied Statistics, 32, 785–796.
49. Tsou, T. S. (2006). Parametric robust test for several variances with unknown underlying distributions. Metrika, 64, 333-349.
50. Varin, C. and Vidoni, P. (2005). A note on composite likelihood inference and model selection. Biometrika, 92, 519–528.
51. Varin, C., Host, G., and Skare, O. (2005). Pairwise likelihood inference in spatial generalized linear mixed models. Computational Statistics and Data Analysis, 49, 1173–1191.
52. Varin, C. (2008). On composite marginal likelihoods. Advances in Statistical Analysis, 9, 21–28.
53. Varin, C., Reid, N., and Firth, D. (2011). An overview of composite likelihood methods. Statistica Sinica, 21, 5–42.
54. Weil, C. S. (1970). Selection of the valid number of sampling units and a consideration of their combination in toxicological studies involving reproduction, teratogenesis or carcinogenesis. Food and Cosmetics Toxicology, 8, 177–182.
55. White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica, 82, 1–25.
56. Willams, D. A. (1975). The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity. Biometrics, 31, 949–952.
57. Yi, G. Y., Zeng, L., and Cook, R. J. (2011b). A robust pairwise likelihood method for incomplete longitudinal binary data arising in clusters. Canadian Journal of Statistics, 39, 34–51.
58. Zhao, Y. and Joe, H. (2005). Composite likelihood estimation in multivariate data analysis. The Canadian Journal of Statistics, 33, 335–356.
59. Zou, G. and Donner, A. (2004). Confidence Interval Estimation of the Intraclass Correlation. Biometrics, 60, 807–811.
指導教授 鄒宗山(Tsung-Shan Tsou) 審核日期 2013-10-3
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明