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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Statistical Issues in Studies of the Long-Term Effects of Air Pollution: The Southern California Children’s Health Study
TL;DR: In this paper, statistical techniques for modeling data from cohort studies that examine long-term effects of air pollution on children's health by comparing data from multiple communities with a diverse pollution profile are discussed.
Journal ArticleDOI
A modified em algorithm for estimation in generalized mixed models
TL;DR: Laplace's method is adapted for analytic approximation within the E-step and retains much of the conceptual simplicity of the conventional EM algorithm, although the usual convergence properties are not guaranteed.
Journal ArticleDOI
How to Make Models Add Up — A Primer on GLMMs
TL;DR: In this article, different parts of the generalized linear mixed model (GLMM) are described, building from regression and ANOVA to show how the extra components can be added into the same framework, and how the parameters of the fitted model can be estimated and interpreted.
Journal ArticleDOI
The effectiveness of mammography promotion by volunteers in rural communities.
M. Robyn Andersen,Yutaka Yasui,Hendrika Meischke,Alan Kuniyuki,Ruth Etzioni,Nicole Urban,Nicole Urban +6 more
TL;DR: Volunteers can effectively promote mammography in rural communities and appear to have increased the use of mammography among certain groups of women who were not regular users at baseline, including those in communities without female physicians and among women with no health insurance.
Journal ArticleDOI
Recurrence in affective disorder: analyses with frailty models
TL;DR: The authors concluded that the risk of recurrence seems to increase with the number of episodes of bipolar affective disorder in general and for women with unipolar disorder and for unipolar men.
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.