Journal ArticleDOI
Generalized Linear Models
John A. Nelder,R. W. M. Wedderburn +1 more
- Vol. 135, Iss: 3, pp 370-384
Reads0
Chats0
TLDR
In this paper, the authors used iterative weighted linear regression to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation.Abstract:
JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Blackwell Publishing and Royal Statistical Society are collaborating with JSTOR to digitize, preserve and extend access to Journal of the Royal Statistical Society. Series A (General). SUMMARY The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log-likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components). The implications of the approach in designing statistics courses are discussed.read more
Citations
More filters
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
Inference from Iterative Simulation Using Multiple Sequences
Andrew Gelman,Donald B. Rubin +1 more
TL;DR: The focus is on applied inference for Bayesian posterior distributions in real problems, which often tend toward normal- ity after transformations and marginalization, and the results are derived as normal-theory approximations to exact Bayesian inference, conditional on the observed simulations.
Journal ArticleDOI
Generalized Linear Models
TL;DR: This is the rst book on generalized linear models written by authors not mostly associated with the biological sciences, and it is thoroughly enjoyable to read.
Journal ArticleDOI
Generalized linear mixed models: a practical guide for ecology and evolution
Benjamin M. Bolker,Mollie Elizabeth Brooks,Connie J. Clark,Shane W. Geange,John R. Poulsen,M. Henry H. Stevens,Jada-Simone S. White +6 more
TL;DR: The use (and misuse) of GLMMs in ecology and evolution are reviewed, estimation and inference are discussed, and 'best-practice' data analysis procedures for scientists facing this challenge are summarized.
References
More filters
Journal ArticleDOI
The advanced theory of statistics
TL;DR: The Advanced Theory of Statistics by Maurice G. Kendall as discussed by the authors is a very handsomely produced volume which is one which it will be a pleasure to any mathematical statistician to possess.
Journal ArticleDOI
Contingency tables with given marginals
C. T. Ireland,S. Kullback +1 more
TL;DR: It is shown that the estimates are BAN, and that the iterative procedure is convergent, for a four-way contingency table for which the marginal probabilities pi and p j are known and fixed.
Journal ArticleDOI
The Analysis of Multidimensional Contingency Tables
TL;DR: In this paper, a class of models analogous to those used in the analysis of variance is discussed, and a method for computing the expected cell counts for the different models is presented.
Book ChapterDOI
Maximum Likelihood in Three-Way Contingency Tables
TL;DR: In this article, maximum likelihood estimation for many-way and three-way contingency tables is discussed and the solutions given for threeway tables in the cases of greatest interest are given.