Generalized linear models (GLMs, not to be confused with General Linear Mod-els) is a generalization of linear regression to response types other than Gaus-sian, as long as the distribution of that response is a member of the exponential family.

Members of a family should have many basic characteristics in common, hopefully enough that we can develop general methods that will work for any member of the family, but should be different enough from one another to provide a variety of possibilities within the same family.

In this topic, we will show that both of these methods are special cases of a broader family of models, called Generalized Linear Models (GLMs). We will also show how other models in the GLM family can be derived and applied to other classification and regression problems.

MSH3 Generalized linear model Ch.2 Exponential Family x2.2 Exponential Family Nelder and Wedderburn (1972, JRSSA 135, 221-32) stated that many common statistical models including regression for continuous data, lo-gistic model for binary data, and log-linear models for count data were members of a general model, the exponential family (EF ...

Exponential family comprises a set of flexible distribution ranging both continuous and discrete random variables. The members of this family have many important properties which merits discussing them in some general format. Many of the probability distributions that we have studied so far are specific members of this family: Gaussian: Rp ...

The classical linear regression model is the most widely employed statistical method in family research. The Journal of Marriage and Family has published hundreds of applications of linear models (LMs) over the past several decades. LMs also form the main content in undergradu-ate statistical methods courses across the social sciences. LMs are ...

Many common distributions are members of the exponential family, for instance normal, exponential, Poisson, Bernoulli, etc., and are thus suitable choices for the assumed outcome variable.

Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression.

Key features of a generalized linear model include 1) having a response, or de-pendent variable, selected from the single parameter exponential family of probability distributions, 2) having a link function that linearizes the relationship between the fitted value and explanatory predictors, and 3) having the ability to be estimated using an Ite...

2 Generalized linear models (GLIMs) Generalized linear models (GLIMs) are a statistical framework for unifying classi cation and regression. In this framework, we assume: Y ˘ exponentialFamily = ( = f(˘= Tx)); where Y are the responses, x are the xed inputs, are parameters we need to learn, and f (called the response function) and give us added