結構方程模型下時間序列資料與縱貫性資料之貝氏分析

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：30

、訪客IP：18.219.8.25

姓名

王義富(Yi-Fu Wang) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

結構方程模型下時間序列資料與縱貫性資料之貝氏分析
(Bayesian Structural Equation Modeling of Time Series Data and Longitudinal Data)

相關論文

★ 具Box-Cox轉換之逐步加速壽命實驗的指數推論模型	★ 多元反應變數長期資料之多變量線性混合模型
★ 多重型 I 設限下串聯系統之可靠度分析與最佳化設計	★ 應用累積暴露模式至單調過程之加速衰變模型
★ 串聯系統加速壽命試驗之最佳樣本數配置	★ 破壞性加速衰變試驗之適合度檢定
★ 串聯系統加速壽命試驗之最佳妥協設計	★ 加速破壞性衰變模型之貝氏適合度檢定
★ 加速破壞性衰變模型之最佳實驗配置	★ 累積暴露模式之單調加速衰變試驗
★ 具ED過程之兩因子加速衰退試驗建模研究	★ 逆高斯過程之完整貝氏衰變分析
★ 加速不變原則之偏斜-t過程	★ 花蓮地區地震資料改變點之貝氏模型選擇
★ 颱風降雨量之統計迴歸預測	★ 花蓮地區地震資料之長時期相關性及時間-空間模型之可行性

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]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

結構方程模式(Structural Equation Modeling, SEM) 是一個在社會學與心理學中極為廣用的分析方法，用以探討觀測值與潛在因素間其各自相依關係的一個重要工具，因此眾多的套裝軟體相繼而生。然而若資料型態不符合SEM 模型的假設，便不能進行SEM 的分析研究，儘管擁有與SEM 模型類似的模型構念。因此本文先基於SEM 模型的貝氏分析，提出一具時間序列的SEM 模型，使其也能充分的應用在時間序列的資料中。另外也對此模型加以提升改進，加入相關性的元素，讓模型更能滿足較多樣化的資料。此外，針對縱貫性資料之SEM模型分析，我們將採用隨機效果 (random effect) 的概念於SEM 模型中，使其充分的解釋資料既有的相關性。在實例分析中，具時間序列的SEM 模型對歐洲、亞洲以及美洲實際股價指數進行配適與預測，皆獲得不錯的解釋及準確的預測結果，另一方面，具縱貫性的SEM 模型對於我們所考慮的青少年左右眼資料之分析，亦有著相當良好的配適能力及解釋程度。最後，我們考慮在 SEM 模型之貝氏分析中，加入混合先驗分佈 (Mixture prior)來完成模型選擇問題，並對模型中之反應變數及隨機變數進行篩選，藉由剔除模型中不必要的關連性，來降低模型之參數個數，挑選出一具解釋力且較簡化之SEM模型。

摘要(英)

Structural equation models (SEM) have been extensively used in behavioral, social, and psychological research to model relations between latent variables and observations. Most softwares for fitting SEM rely on frequentist methods. However, traditional models and softwares are not appropriate to analyze dependent observations such as the time-series data and multidimensional longitudinal data. We first introduce a structural equation model with time series feature via Bayesian approach with the aid of the Markov chain Monte Carlo method. Bayesian inference as well as prediction of the proposed time series structural equation model will be developed which can also reveal certain unobserved relationship among the observations. The approach is successfully employed using real Asian, American and European stock return data. Moreover, we consider to deal with the multidimensional longitudinal myopia data with correlation between both eyes. Myopia is becoming a significant public health problem, affecting more and more people. Motivated by the increase in the number of people affected by this problem, the primary focus is to utilize mathematical methods to gain further insight into their relationship with myopia. Accordingly, utilizing multidimensional longitudinal myopia data with correlation between both eyes, a Bayesian structural equation model including random effects is developed. Four observed factors, including intraocular pressure, anterior chamber depth, lens thickness and axial length, are considered. The results indicate that the genetic effect has much greater influence on myopia than the environmental effects. We also consider to apply the model selection problem with mixture prior to the SEMs. To put the reasonable mixture prior on the specific parameter which describes the doubting relationship in the SEMs, the model posterior probability can be computed via the MCMC iterations and viewed as a Bayesian model selection criterion. An advantage of the method using mixture priors is that it can automatically identify the predictors having non-zero fixed effect coefficients or non-zero random effects variance in the MCMC procedure. Specifically, we will focus on the multidimensional longitudinal myopia data to reduce the dimensionality of the parameter space and to select the simpler model.

關鍵字(中)

★ 混合先驗分佈
★ 結構方程模型
★ 時間序列
★ 縱貫性資料

關鍵字(英)

★ mixture prior
★ time-series
★ longitudinal data
★ structural equation model

論文目次

1 Introduction. . . . . . . . . . . . . . . . . . . . . . 1
1.1 Background and Motivation . . . . . . . . . . . . . 1
1.2 Overview. . . . . . . . . . . . . . . . . . . . . . 5
2 Bayesian Analysis on Time Series Structural Equation
Models. . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Time Series Structural Equation Models. . . . . . . 7
2.2 Bayesian Analysis and Forecasts . . . . . . . . . . 9
2.3 Simulation Study and Application . . . . . . . . . 14
2.4 Discussion . . . . . . . . . . . . . . . . . . . . 18
3 Bayesian Analysis of the Structural Equation Models with Application to a Longitudinal Myopia Trial . . . . . . . 22
3.1 Data . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 Model Description. . . . . . . . . . . . . . . . . 24
3.3 Bayesian Inferences. . . . . . . . . . . . . . . . 29
3.4 Application: Myopia Trial. . . . . . . . . . . . . 33
3.5 Discussion . . . . . . . . . . . . . . . . . . . . 38
4 Bayesian Inference on the Structural Equation Model with Random Effects Using Mixture Priors. . . . . . . . . . . 41
4.1 Model Description. . . . . . . . . . . . . . . . . 42
4.2 Bayesian Inference . . . . . . . . . . . . . . . . 42
4.3 Simulation Study and Application . . . . . . . . . 47
4.4 Discussion . . . . . . . . . . . . . . . . . . . . 51
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . 52
References . . . . . . . . . . . . . . . . . . . . . . . 54

參考文獻

Albert, J.H. and Chib, S. (1997). ayesian Test and Model Diagnostics in Conditionally Independent Hierarchical Models. Journal of the American Statistical Association; 92:916--925.
Angi, M.R., Clementi, M., Sardei, C., Piattelli, E. and Bisantis, C. (1993). Heritability of myopia refractive errors in identical and fraternal twins. Graefe's Archive for Clinical and Experimental Ophthalmology; 231:580--585.
Bentler, P.M. (1992). EQS : Structural equation program manual. Los Angeles: BMDP Statistical Software.
Bentler, P.M. and Wu, E.J.C. (2002). EQS6 for Windows user guide. Encino, CA: Multivariate Software.
Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis (2nd edn). Springer Verlag: New York.
Bollen, K.A. (1989). Structural Equations With Latent Variables. Wiley: New York.
Browne, M.W. (1974). Generalized least squares estimatiors in the analysis of covariance structures. South African Statistical Journal; 8:1--24.
Cagnone, S., Moustaki, I. and Vasdekis, V. (2009). Latent variable models for multivariate longitudinal ordinal responses. British journal of mathematical and statistical psychology; 62:401--415.
Carlin, B.P. and Louis, T.A. (2000). Bayes and Empirical Bayes Methods for Data Analysis (2nd edn). Chapman and Hall/CRC: New York.
Chen, C.J., Cohen, B.H. and Diamond, E.L. (1985). Genetic and environmental effects on the development of myopia in Chinese twin children. Ophthalmic Paediatrics and Genetics; 6:353--359.
Chen, Z. and Dunson, D.B. (2003). Random effect selection in linear mixed models. Biometrics; 59:762--769.
Clyde, M. and George, E.I. (2004). Model uncertainty. Statistical Science; 19:81--94.
Daniels, M.J. and Normand, S.L.T. (2006). Longitudinal profiling of health care units based on continuous and discrete patient outcomes. Biostatistics; 7:1--15.
Dunson, D.B. (2003). Dynamic latent trail models for multidimensional longitudinal data. Journal of the American Statistical Association; 98:555--563.
Dunson, D.B. (2007). Bayesian methods for latent trait modeling of longitudinal data. Statistical Methods in Medical Research; 16:399--415.
Gelman, A., Meng, X.L. and Stern, H. (1996). Posterior Predictive Assessment of Model Fitness via Realized Discrepancies(with discussion). Statistica Sinica; 6:733--807.
Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. On Pattern Analysis and Machine Intelligence; 6:721--741.
George, E.I. and McCulloch, R.E. (1997). Approaches for Bayesian variable selection. Statistica Sinica; 7:339--374.
Hammond, C.J., Snieder, H., Gilbert, C.E. and Spector, T.D. (2001). Genes and environment in refractive error: the twin eye study. Investigative Ophthalmology and Visual Science; 42:1232--1236.
Hoeting, J.A., Madigan, D., Raftery, A.E. and Volinsky, C.T. (1999). Bayesian Model Averaging: A Tutorial. Statistical Science; 14:382--417.
Joreskog, K.G. and Sorbom, D. (1986). LISREL VI : Analysis of linear structural relationships by maximum likelihood, instrumental variables, and least squares. Mooresville, IN: Scientific Software International.
Joreskog, K.G. and Sorbom, D. (1996). LISREL 8 : Structural equation modeling with the SIMPLIS command language. London: Scientific Software International.
Kinney, S.K. and Dunson, D.B. (2007). Fixed and Random Effects Selection in Linear and Logistic Models. Biometrics; 63:690--698.
Kline, R.B. (2005). Principles and Practice of Structural Equation Modeling (2nd edn). Guildford Press: New York.
Kuo, L. and Mallick, B. (1998). Variable Selection for Regression Models. Sankhy1a: The Indian Journal of Statistics, Series B; 60:65--81.
Lee, S.Y. (2007). Structural equation modeling: A Bayesian approach. Chichester, UK: Wiley.
Lyhne, N., Sjolie, A.K., Kyvik, K.O. and Green, A. (2001). The importance of genes and environment for ocular refraction and its determiners: a population based study among 20-45 year old twins. British Journal of Ophthalmology; 85:1470--1476.
Meng, X.L. (1994). Posterior Predictive p-Values. The Annals of Statistics; 22:1142--1160.
Muthen, B., Brown, C.H., Masyn, K., Jo, B., Khoo, S.T., Yang, C.C., Wang, C.P., Kellam, S.G., Carlin, J.B. and Liao, J. (2002). General growth mixture modeling for randomized preventive interventions. Biometrics; 3:459--475.
Muthen, L.K. and Muthen, B.O. (1998). MPLUS : The comprehensive modeling program for applied researchers user's guide. Los Angeles: Muthen & Muthen.
Palomo, J., Dunson, D.B. and Bollen, K. (2007). Bayesian structural equation modeling. Handbook of Latent Variable and Related Models. NORTH-HOLLAND; 1:163--188.
Pauler, D.K., Wakefield, J.C. and Kass, R.E. (1999). Bayes factors and approximations for variance component models. Journal of the American Statistical Association; 94:1242--1253.
Raykov, T. (2007). Longitudinal Analysis With Regressions Among Random Effects: A Latent Variable Modeling Approach. Structural Equation Modeling; 14:146--169.
Roy, J. and Lin, X.H. (2000). Latent variable models for longitudinal data with multiple continuous outcomes. Biometrics; 56:1047--1054.
Scheines, R., Hoijtink, H. and Boomsma, A. (1999). Bayesian Estimation and Testing of Structural Equation Models. Psychometrika; 64:37--52.
Shih, Y.F., Hsiao, C.K., Chen, C.J., Chang, C.W., Hung, P.T. and Lin, L.L.K. (2001). An intervention trial on efficacy of atropine and multi-focal glasses in controlling myopic progression. Acta Ophthalmological Scandinavica; 79:233--236.
So, M.K.P., Li, W.K. and Lam, K. (2002). A threshold stochastic volatility model. Journal of Forecasting; 21:473--500.
Taylor, S.J. (1982). Financial returns modeled by the product of two stochastic processes, a study of daily sugar prices 1961-79. In Anderson OD (ed.). In Time Series Analysis: Theory and Practice; 1:203--226. North-Holland: Amsterdam.
Teikari, J.M., Kaprio, J., Koskenvuo, M.K. and Vannas, A. (1988). Heritability estimate for refractive errors--a population-based sample of adult twins. Genetic Epidemiology; 5:171--181.
Teikari, J.M., O'Donnell, J., Kaprio, J. and Koskenvuo, M. (1991). Impact of heredity in myopia. Human Heredity; 41:151--156.
Zadnik, K., Mutti, D.O., Mitchell, G.L., Jones, L.A., Burr, D. and Moeschberger, M.L. (2004). Normal eye growth in emmetropic schoolchildren. Optometry and Vision Science; 81:819--828.

指導教授

樊采虹(Tsai-Hung Fan)

審核日期

2011-7-4

推文