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
Habitat models of bird species' distribution: an aid to the management of coastal grazing marshes.
T. P. Milsom,T. P. Milsom,S. D. Langton,W. K. Parkin,S. Peel,Julie D. Bishop,J. D. Hart,Niall P. Moore +7 more
TL;DR: In this paper, a generalized linear mixed modeling (GLMM) method was used to investigate the relationship between the presence or absence of ground-nesting birds and the grazing marsh habitat in each of c.430 km2 of the North Kent Marshes ESA.
Journal ArticleDOI
Methods for testing theory and evaluating impact in randomized field trials: intent-to-treat analyses for integrating the perspectives of person, place, and time.
C. Hendricks Brown,Wei Wang,Sheppard G. Kellam,Sheppard G. Kellam,Bengt Muthén,Hanno Petras,Peter Toyinbo,Jeanne M. Poduska,Nicholas Ialongo,Peter A. Wyman,Patricia Chamberlain,Zili Sloboda,David P. MacKinnon,Amy Windham +13 more
TL;DR: Intent-to-treat analyses in group-randomized multilevel field trials are defined and how to make causal inferences more robust to misspecification of covariates in such analyses are described to summarize and present these interactive intervention effects clearly.
Journal ArticleDOI
Estimating multilevel logistic regression models when the number of clusters is low: a comparison of different statistical software procedures.
TL;DR: There were qualitative differences in the performance of different software procedures for estimating multilevel logistic models when the number of clusters was low, and only Bayesian estimation with BUGS allowed for accurate estimation of variance components when there were fewer than 10 clusters.
Journal ArticleDOI
Linking Student Performance in Massachusetts Elementary Schools with the ``Greenness'' of School Surroundings Using Remote Sensing
Chih Da Wu,Eileen McNeely,Jose Guillermo Cedeno-Laurent,Wen Chi Pan,Gary Adamkiewicz,Francesca Dominici,Shih-Chun Candice Lung,Huey Jen Su,John D. Spengler +8 more
TL;DR: Interestingly, the results showed a consistently positive significant association between the greenness of the school in the Spring (when most Massachusetts students take the MCAS tests) and school-wide performance on both English and Math tests, even after adjustment for socio-economic factors and urban residency.
Journal ArticleDOI
On estimation and prediction for spatial generalized linear mixed models.
TL;DR: A Monte Carlo version of the EM gradient algorithm is developed for maximum likelihood estimation of model parameters and shows that the minimum mean-squared error (MMSE) prediction can be done in a linear fashion in spatial GLMMs analogous to linear kriging.
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.