Generalized Linear Models

  title={Generalized Linear Models},
  author={Peter McCullagh and John A. Nelder},
  booktitle={Predictive Analytics},
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… 

Tables from this paper

Log Linear Models for Contingency Tables: A Generalization of Classical Least Squares
SUMMARY Log linear models for contingency tables of counts are formulated as a special case of generalized linear models with an additive systematic component Y, Poisson errors for the data and an
Generalized Linear Models
Generalized linear models (GLM) extend the concept of the well understood linear regression model. The linear model assumes that the conditional expectation of the dependent variable Y is equal to a
An approximation to the likelihood for the generalized linear models with random coefficients is derived and is the basis for an approximate Fisher scoring algorithm. The method is illustrated on the
Estimation in the generalized linear empirical bayes model using the extended quasi-likelihood
A generalized linear empirical Bayes model is developed for empirical Bayes analysis of several means in natural exponential families. A unified approach is presented for all natural exponential
Restricted BLUP for mixed linear models
A new estimation procedure for mixed regression models is introduced. It is a development of Henderson's best linear unbiased prediction procedure which uses the joint distribution of the observed
Maximum likelihood estimation and large-sample inference for generalized linear and nonlinear regression models
SUMMARY The class of generalized linear models is extended to allow for correlated observations, nonlinear models and error distributions not of the exponential family form. The extended class of
Multivariate Mean Parameter Estimation by Using a Partly Exponential Model
SUMMARY A class of partly exponential models is proposed for the regression analysis of multivariate response data. The class is parameterized in terms of the response mean and a general shape
Simultaneous estimation of gamma means using a hierarchical generalized linear model
The problem of simultaneously estimating p Gamma means is investigated when the means are believed a priori to satisfy an r-dimensional generalized linear model. Using a Bayesian hierarchical model
A simple approach for the analysis of generalizea linear mixed models
A broad class of generalized linear mixed models, e.g. variance components models for binary data, percentages or count data, will be introduced by incorporating additional random effects into the
The Null Expected Deviance for an Extended Class of Generalized Linear Models
Jorgensen (19 83) developed a class of extended generalized linear models including error distributions not of the exponential family form. We give the null expected likelihood ratio statistic up to


Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method
SUMMARY To define a likelihood we have to specify the form of distribution of the observations, but to define a quasi-likelihood function we need only specify a relation between the mean and variance
Linear statistical inference and its applications
Algebra of Vectors and Matrices. Probability Theory, Tools and Techniques. Continuous Probability Models. The Theory of Least Squares and Analysis of Variance. Criteria and Methods of Estimation.
Full Contingency Tables, Logits, and Split Contingency Tables
Three methods of fitting log-linear models to multivariate contingency-table data with one dichotomous variable are discussed. Logit analysis is commonly used when a full contingency table of s
A New Analysis of Variance Model for Non-additive Data
All advantage of the additive model will be lost, unless one can again partition the non-random portion of n7.i into functions of only one variable each.
Linear regression analysis
This new edition takes into serious consideration the furthering development of regression computer programs that are efficient, accurate, and considered an important part of statistical research.
Maximum Likelihood in Three-Way Contingency Tables
Interactions in three-way and many-way contingency tables arc defined as certain linear combinations of the logarithms of the expected frequencies. Maximum-likelihood estimation is discussed for
The Analysis of Multidimensional Contingency Tables
Ecological data often come in the form of multidimensional tables of counts, referred to as contingency tables. During the last decade several new methods of analyzing such tables have been proposed.
Discrete Multivariate Analysis: Theory and Practice
Discrete Multivariate Analysis is a comprehensive text and general reference on the analysis of discrete multivariate data, particularly in the form of multidimensional tables, and contains a wealth of material on important topics.
An overview of multivariate data analysis
A Reformulation of Linear Models
SUMMARY Dissatisfaction is expressed with aspects of the current exposition of linear models, including the neglect of marginality, unnecessary differences between models for finite and infinite