Not to be confused with general linear model or generalized least squares.
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In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression.[1] They proposed an iteratively reweighted least squares method for maximum likelihood estimation (MLE) of the model parameters. MLE remains popular and is the default method on many statistical computing packages. Other approaches, including Bayesian regression and least squares fitting to variance stabilized responses, have been developed.
^Nelder, John; Wedderburn, Robert (1972). "Generalized Linear Models". Journal of the Royal Statistical Society. Series A (General). 135 (3). Blackwell Publishing: 370–384. doi:10.2307/2344614. JSTOR 2344614. S2CID 14154576.
and 27 Related for: Generalized linear model information
In statistics, a generalizedlinearmodel (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizeslinear regression by allowing...
In statistics, a generalizedlinear mixed model (GLMM) is an extension to the generalizedlinearmodel (GLM) in which the linear predictor contains random...
In statistics, a generalized additive model (GAM) is a generalizedlinearmodel in which the linear response variable depends linearly on unknown smooth...
McCullagh, P.; Nelder, J. A. (1989), "An outline of generalizedlinearmodels", GeneralizedLinearModels, Springer US, pp. 21–47, doi:10.1007/978-1-4899-3242-6_2...
hierarchical generalizedlinearmodels extend generalizedlinearmodels by relaxing the assumption that error components are independent. This allows models to...
In statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory...
regression using similar techniques. When viewed in the generalizedlinearmodel framework, the probit model employs a probit link function. It is most often...
statistics, the generalizedlinear array model (GLAM) is used for analyzing data sets with array structures. It based on the generalizedlinearmodel with the...
discuss mainly linear mixed-effects models rather than generalizedlinear mixed models or nonlinear mixed-effects models. Linear mixed models (LMMs) are statistical...
class of vector generalizedlinearmodels (VGLMs) was proposed to enlarge the scope of models catered for by generalizedlinearmodels (GLMs). In particular...
The generalized functional linearmodel (GFLM) is an extension of the generalizedlinearmodel (GLM) that allows one to regress univariate responses of...
Multilevel models (also known as hierarchical linearmodels, linear mixed-effect model, mixed models, nested data models, random coefficient, random-effects...
In statistics, the logistic model (or logit model) is a statistical model that models the log-odds of an event as a linear combination of one or more independent...
Fisher information), the least-squares method may be used to fit a generalizedlinearmodel. The least-squares method was officially discovered and published...
In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalizedlinearmodel with a possible unmeasured correlation...
In statistics, Poisson regression is a generalizedlinearmodel form of regression analysis used to model count data and contingency tables. Poisson regression...
In statistics, a linear probability model (LPM) is a special case of a binary regression model. Here the dependent variable for each observation takes...
In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model. It is used when there...
probabilities less than zero or greater than one. Generalizedlinearmodel § Binary data Fractional model For a detailed example, refer to: Tetsuo Yai, Seiji...
Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables...
In statistics, simple linear regression (SLR) is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample...
Google books Dawes, Robyn M. (1979). "The robust beauty of improper linearmodels in decision making". American Psychologist, volume 34, pages 571-582...
ranking learning. Ordinal regression can be performed using a generalizedlinearmodel (GLM) that fits both a coefficient vector and a set of thresholds...
specialization of generalized least squares, when all the off-diagonal entries of the covariance matrix of the errors, are null. The fit of a model to a data...
nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown...
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