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請使用永久網址來引用或連結此文件:
http://ir.ncue.edu.tw/ir/handle/987654321/14456
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| 題名: | Computation of Reference Bayesian Inference for Variance Components in Longitudinal Studies |
| 作者: | Tsai, Miao-Yu;Hsiao, Chuhsing K. |
| 貢獻者: | 統計資訊研究所 |
| 關鍵詞: | Bayesian;GLMM;Jeffreys’prior;PQL;Reference prior;Uniform shrinkage prior;Variance component |
| 日期: | 2008-10
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| 上傳時間: | 2012-10-25T09:03:32Z
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| 出版者: | SpringLink |
| 摘要: | Generalized linear mixed models (GLMMs) have been applied widely
in the analysis of longitudinal data. This model confers two important advantages,
namely, the flexibility to include random effects and the ability to make inference about
complex covariances. In practice, however, the inference of variance components can
be a difficult task due to the complexity of the model itself and the dimensionality of
the covariance matrix of random effects. Here we first discuss for GLMMs the relation
between Bayesian posterior estimates and penalized quasi-likelihood (PQL) estimates,
based on the generalization of Harville’s result for general linear models. Next, we
perform fully Bayesian analyses for the random covariance matrix using three different
reference priors, two with Jeffreys’ priors derived from approximate likelihoods and
one with the approximate uniform shrinkage prior. Computations are carried out via the
combination of asymptotic approximations and Markov chain Monte Carlo methods.
Under the criterion of the squared Euclidean norm, we compare the performances
of Bayesian estimates of variance components with that of PQL estimates when the
responses are non-normal, and with that of the restrictedmaximum likelihood (REML)
estimates when data are assumed normal. Three applications and simulations of binary,
normal, and count responses with multiple random effects and of small sample sizes
are illustrated. The analyses examine the differences in estimation performance when
the covariance structure is complex, and demonstrate the equivalence between PQL
and the posterior modes when the former can be derived. The results also show that the Bayesian approach, particularly under the approximate Jeffreys’ priors, outperforms
other procedures. |
| 關聯: | Computational Statistics, 23(4): 587-604 |
| 顯示於類別: | [統計資訊研究所] 期刊論文
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