Generalized linear model

The generalized linear model (GLM) is a statistical, linear model that generalizes the General linear model in the following ways:

Related Topics:
Linear model - General linear model

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• Error distributions from the Exponential family, besides the normal distribution are permitted.
• The variance may depend on a known function of the mean. (For example, for the binomial distribution, $mu=np\; ,$ and $sigma^\{2\}=npq\; ,$, and thus $sigma^\{2\}=qmu\; ,$.)
• A non-linear relationship between $E(Y)\; ,$ and is allowed, with the aid of a link function.

The GLM may be written as

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: g(Y) = Xeta + epsilon, ,

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where g is a monotone, twice-differentiable function, called the link function and Y comes from a multivariate normal distribution with mean E(Y) and variance epsilon. It is often assumed that the distribution of y is a member of an exponential family. Each specific choice of the link function and the distribution for the dependent variable yields a different generalized linear model. As in the notation of other regression models such as the General linear model, X is the design matrix, and B is a matrix containing parameters that must be estimated. The residual, U is usually assumed to follow a multivariate normal distribution.

Related Topics:
Multivariate normal distribution - Exponential family - General linear model - Design matrix

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Generalized linear models include, as special cases, ordinary linear regression, logistic regression, Poisson regression, and several other interesting models.

Related Topics:
Linear regression - Logistic regression - Poisson regression

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Generalized linear model: References ►