![]() The linear predictor is a linear function in the parameters. ![]() The systematic component is a linear predictor similar to that in linear models. To put this generalization in place requires a slightly more sophisticated model setup than that required for linear models for normal data: Furthermore, generalized linear model take the distribution of the data into account, rather than assuming that a transformation of the data leads to normally distributed data to which standard linear modeling techniques can be applied. Generalized linear models also apply a transformation, known as the link function, but it is applied to a deterministic component, the mean of the data. Such transformations have to be performed with care because they also have implications for the error structure of the model, Also, back-transforming estimates or predicted values can introduce bias. ![]() Before this theory was developed, modeling of nonnormal data typically relied on transformations of the data, and the transformations were chosen to improve symmetry, homogeneity of variance, or normality. This class of models extends the theory and methods of linear models to data with nonnormal responses. The theory of generalized linear models originated with Nelder and Wedderburn (1972) and Wedderburn (1974), and was subsequently made popular in the monograph by McCullagh and Nelder (1989). A class of models that has gained increasing importance in the past several decades is the class of generalized linear models.
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