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Generalized linear model
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<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, a generalized linear model (GLM) is a flexible generalization of ordinary <a href="/facts/Linear_regression/5n998IhK">linear regression</a>. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a <i>link function</i> and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. </p><p>Generalized linear models were formulated by <a href="/facts/John_Nelder/28u4s8J9">John Nelder</a> and <a href="/facts/Robert_Wedderburn_(statistician)/hIhtNb5g">Robert Wedderburn</a> as a way of unifying various other statistical models, including <a href="/facts/Linear_regression/5n998IhK">linear regression</a>, <a href="/facts/Logistic_regression/mGj6mc8y">logistic regression</a> and <a href="/facts/Poisson_regression/XWn6AW7A">Poisson regression</a>. They proposed an <a href="/facts/Iteratively_reweighted_least_squares/cqU60Scd">iteratively reweighted least squares</a> <a href="/facts/Iterative_method/uKMAJhEh">method</a> for <a href="/facts/Maximum_likelihood_estimation/0Yq2dpQD">maximum likelihood estimation</a> (MLE) of the model parameters. MLE remains popular and is the default method on many statistical computing packages. Other approaches, including <a href="/facts/Bayesian_regression/7Dj2c1PQ">Bayesian regression</a> and <a href="/facts/Least_squares_fitting/50jIwbxC">least squares fitting</a> to <a href="/facts/Variance-stabilizing_transformation/HvxV5l98">variance stabilized</a> responses, have been developed. </p>