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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 restricted maximum 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. 相似文献
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《Journal of computational and graphical statistics》2013,22(1):140-153
Boosting is a successful method for dealing with problems of high-dimensional classification of independent data. However, existing variants do not address the correlations in the context of longitudinal or cluster study-designs with measurements collected across two or more time points or in clusters. This article presents two new variants of boosting with a focus on high-dimensional classification problems with matched-pair binary responses or, more generally, any correlated binary responses. The first method is based on the generic functional gradient descent algorithm and the second method is based on a direct likelihood optimization approach. The performance and the computational requirements of the algorithms were evaluated using simulations. Whereas the performance of the two methods is similar, the computational efficiency of the generic-functional-gradient-descent-based algorithm far exceeds that of the direct-likelihood-optimization-based algorithm. The former method is illustrated using data on gene expression changes in de novo and relapsed childhood acute lymphoblastic leukemia. Computer code implementing the algorithms and the relevant dataset are available online as supplemental materials. 相似文献
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