Generalized Linear Models
@inproceedings{McCullagh2020GeneralizedLM, title={Generalized Linear Models}, author={Peter McCullagh and John A. Nelder}, booktitle={Predictive Analytics}, year={2020} }
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…
6,519 Citations
Log Linear Models for Contingency Tables: A Generalization of Classical Least Squares
- Mathematics
- 1974
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
- Mathematics
- 2012
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…
Restricted Estimation of Generalized Linear Models
- Mathematics
- 1991
Maximum likelihood estimation of the generalized linear model under linear restrictions on the parameters is considered. Using a penalty function approach an iterative procedure for obtaining the…
LOGISTIC REGRESSION WITH RANDOM COEFFICIENTS
- Mathematics
- 1993
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
- Mathematics
- 1994
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…
Robust Modeling for Inference From Generalized Linear Model Classes
- Mathematics
- 2007
Generalized linear models (GLMs) are widely used for data analysis; however, their maximum likelihood estimators can be sensitive to outliers. We propose new statistical models that allow robust…
Restricted BLUP for mixed linear models
- Mathematics
- 1991
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…
Generalized Linear Models: Introduction
- Computer Science
- 2014
Generalized linear models provide a unified framework for regression models including multiple regression, logistic regression, analysis of variance, and analysis of covariance. Such models consist…
The Equivalence of Generalized Least Squares and Maximum Likelihood Estimates in the Exponential Family
- Mathematics
- 1976
Abstract The method of iterative weighted least squares can be used to estimate the parameters in a nonlinear regression model. If the dependent variables are observations from a member of the…
Maximum likelihood estimation and large-sample inference for generalized linear and nonlinear regression models
- Mathematics
- 1983
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…
References
SHOWING 1-10 OF 60 REFERENCES
Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method
- Mathematics
- 1974
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…
Composite Link Functions in Generalized Linear Models
- Mathematics
- 1981
SUMMARY In generalized linear models each observation is linked with a predicted value based on a linear function of some systematic effects. We sometimes require to link each observation with a…
Linear statistical inference and its applications
- Mathematics
- 1965
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
- Mathematics
- 1969
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…
Contingency tables with given marginals.
- MathematicsBiometrika
- 1968
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.
A New Analysis of Variance Model for Non-additive Data
- Computer Science
- 1971
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
- Computer Science
- 1977
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
- Mathematics
- 1963
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
- Mathematics
- 1970
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.…
Association Models and Canonical Correlation in the Analysis of Cross-Classifications Having Ordered Categories
- Psychology
- 1981
Abstract The association models considered in Goodman (1979a) for the analysis of cross-classifications having ordered categories are presented in a somewhat different form in the present article to…