Journal ArticleDOI
Approximate inference in generalized linear mixed models
Norman E. Breslow,D. G. Clayton +1 more
TLDR
In this paper, generalized linear mixed models (GLMM) are used to estimate the marginal quasi-likelihood for the mean parameters and the conditional variance for the variances, and the dispersion matrix is specified in terms of a rank deficient inverse covariance matrix.Abstract:
Statistical approaches to overdispersion, correlated errors, shrinkage estimation, and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model (GLMM). Given an unobserved vector of random effects, observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function, known prior weights and a scale factor. The random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components. For problems involving time series, spatial aggregation and smoothing, the dispersion may be specified in terms of a rank deficient inverse covariance matrix. Approximation of the marginal quasi-likelihood using Laplace's method leads eventually to estimating equations based on penalized quasilikelihood or PQL for the mean parameters and pseudo-likelihood for the variances. Im...read more
Citations
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Journal ArticleDOI
The validation of surrogate endpoints in meta-analyses of randomized experiments
TL;DR: In this article, the authors proposed a new method for the validation of surrogate endpoints, which leads to the prediction of the effect of treatment upon the true endpoint, given its observed effect upon the surrogate endpoint.
Journal ArticleDOI
Low‐Rank Scale‐Invariant Tensor Product Smooths for Generalized Additive Mixed Models
TL;DR: The smooths offer several advantages: they have one wiggliness penalty per covariate and are hence invariant to linear rescaling of covariates, making them useful when there is no “natural” way to scale covariates relative to each other.
Journal ArticleDOI
Viable offspring derived from fetal and adult mammalian cells.
TL;DR: Dolly was the first sheep cloned and developed from the nuclei of fully differentiated adult cells, rather than from theuclei of early embryonic cells.
Journal ArticleDOI
Bias correction in generalised linear mixed models with a single component of dispersion
Norman E. Breslow,Xihong Lin +1 more
TL;DR: This paper derived general expressions for the asymptotic biases in three approximate estimators of regression coefficients and variance component, for small values of the variance component in generalised linear mixed models with canonical link function and a single source of extraneous variation.
Journal ArticleDOI
Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data.
TL;DR: It is shown that problems can be overcome in most cases occurring in practice by replacing the approximate normal within-study likelihood by the appropriate exact likelihood, which leads to a generalized linear mixed model that can be fitted in standard statistical software.
References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Book
Generalized Linear Models
Peter McCullagh,John A. Nelder +1 more
TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
Journal ArticleDOI
Longitudinal data analysis using generalized linear models
Kung Yee Liang,Scott L. Zeger +1 more
TL;DR: In this article, an extension of generalized linear models to the analysis of longitudinal data is proposed, which gives consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence.