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題名：貝氏隱藏式類別分析統計法在數學科教育評量的應用
書刊名：臺中師院學報
作者：楊志堅 引用關係／劉湘川／楊志強 引用關係
作者(外文)：Yang, Chih-chien／Liu, Hsin-chuan／Yang, Chih-chiang
出版日期：1999
卷期：13
頁次：頁1-13
主題關鍵詞：Latent class analysis；Gibbs sampling；E-M algorithms；隱藏式類別分析；吉氏取樣；E-M算法
原始連結：連回原系統網址new window
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　　　　　聯考式的一試定終身的測驗方法在現今進步的社會下，逐漸被人們所遺棄。取而 代之的是以多次的在校學科評量成績為主要的學習成就參考依據，但是如何以這些多次的測 量(repaat measurements)結果來看出學生真正的學習成就與能力呢?最簡單的方法便是取平 均數再以之為分類標準，但這似乎不是最好的方法，因為每項試題難易不同，取平均數並無 法兼顧到這個事實，也無法鑑別出受測者的真正能力。本研究便以隱藏式類別分析(Latent Classes Analysis)模式來分析出受測者的真正能力，並以兩種主要的統計方法:E-M算法(E-M algorithms)及吉氏取樣(Gibbs Sampling)做統計計算學的比較研究。
　　　　　Latent class analysis has been shown as an important and practical analytic tool for substantive researchers (see e.g. Wang, et al., 1996, Biometrics; Qu, et al., 1996, Biometrics). Applications of latent class can be seen in a lot of areas, e.g., biomedical, educational, and psychological studies. Though several related models(e.g. Follmann and Lambert, 1989, JASA) were proposed years ago, they have not been used much in practice until recently. One of the reasons is due to the numerical difficulties of xture modeling, especially in the framework of Bayesian statistics. This paper investigates latent class analysis under both classical and Bayesian statistics frameworks and suggests more flexible models with covariates and including possible random effects. Estimation results using EM algorithms and Gibbs sampling are compared. An educational example using LSAY data is analyzed and illustrated in this paper.
期刊論文
1.Wang, P.、Puterman, M. L.、Cockburn, I.、Le, N.(1996)。Mixed Poisson regression models with covariate dependent rates。Biometrics，52，381-400。  new window
2.Pauler, D. K.、Escobar, M. D.、Sweeney, J. A.、Greenhouse, J.(1996)。Mixture models for eye- tracking data: a case study。Statistics in Medicine，15，1365-1376。  new window
3.Stern, H. S.、Arcus, D.、Kagan, J.、Rubin, D. B.、Snidman, B.(1995)。Using mixture models in temperament research。International Journal of Behavioral Development，18，407-423。  new window
4.Wang, P.、Puterman, M. L.(1998)。Mixed Logistic Regression Models。Journal of Agricultural, Biological and Environmental Statistics，3(2)，175-200。  new window
5.Jansen, R. C.(1993)。Maximum likelihood in generalized linear finite mixture model by using the EM algorithm。Biometrics，49，227-231。  new window
6.Dempster, A. P.、Laird, N. M.、Rubin, D. B.(1977)。Maximum likelihood from incomplete data via the EM algorithm (with discussion)。Journal of the Royal Statistical Society, Series B (Methodological)，39(1)，1-38。  new window
7.Mislevy, I. R.(1985)。Estimation of latent group effects。Journal of the American Statistical Association，80，993-997。  new window
8.Macready, G. B.、Dayton, C. M.(1977)。The use of probabilistic models in the assessment of mastery。Journal of Educational Statistics，2，99-120。  new window
9.Pickering, R. M.、Forbes, J. F.(1984)。A classification of Scottish infants using latent class analysis。Statistics in Medicine，3，249-259。  new window
10.Qu, Y.、Tan, M.、Kunter, H. M.(1996)。Random effects models in latent class analysis for evaluating accuracy of diagnostic tests。Biometrics，72，797-810。  new window
11.Goodman, Leo A.(1974)。Exploratory latent structure analysis using both identifiable and unidentifiable models。Biometrika，61(2)，215-231。  new window
會議論文
1.Muthen, B.、Brown, H.、Khoo, S.、Yang, C. C.、Jo, B.(1996)。General growth mixture modeling of latent trajectory classes: perspectives and prospects。The Prevention Science and Methodology Groups meeting in Tempe。Arizona。  new window
2.Yang, C. C.、Muthen, B.(1997)。Mixed Poisson regression models using GEE and Gibbs sampling estimation techniques: an application to a longitudinal study of alcohol use among youth。The 1997 AERA Chicago meeting。Chicago, Illinois。  new window
3.Yang, C. C.、Muthen, B.(1997)。Latent class analyses using Gibbs sampling and EM algorithm。The 1997 IMS Asian and Pacific regional meeting joint with CEPS and CSA。Taipei。  new window
4.Yang, C. C.、Muthen, B.(1997)。Finite mixture of generalized linear models using Gibbs sampling and EM algorithm。The 1997 American Statistical Association (ASA), Anaheim Joint Statistic Meeting (JSM)。California。  new window
研究報告
1.Wang, P.、Puterman, M. L.(1995)。Mixed logistic regression models。University of British Columbia。  new window
學位論文
1.Yang, C. C.(1998)。Finite mixture model selection with psychometrics(博士論文)。UCLA。  new window
圖書
1.Collett, D.(1991)。Modeling binary data。London：Chapman & Hall。  new window
2.Bartholomew, D. J.(1987)。Latent variable models and factor analysis。New York：Oxford University Press。  new window
3.McCullagh, P.、Nelder, J. A.(1989)。Generalized linear models。London：Chapman & Hall。  new window
4.Tanner, M. A.(1996)。Tools for Statistical Inference。New York：Springer-Verlag。  new window
單篇論文
1.Spiegelhalter, D.，Thomas A.，Best, N.，Gilks, W.(1995)。BUGS examples version 0.5，Cambridge：MRC Biostatistics Unit：IPH。  new window
2.Spiegelhalter, D.，Thomas, A.，Best, N.，Gilks, W.(1995)。Bayesian inference using Gibbs sampling，Cambridge：MRC Biostatistics Unit：IPH。  new window
 
 
 
 
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