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16.1: Generalized Linear Models

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    Generalized Linear Models (GLMs) provide a modeling structure that can relate a linear model to response variables that do not have normal distributions. The distribution of YY is assumed to belong to one of an exponential family of distributions, including the Gaussian, Binomial, and Poisson distributions. GLMs are fit to the data by the method of maximum likelihood.

    Like OLS, GLMs contain a stochastic component and a systematic component. The systematic component is expressed as:


    However, GLMs also contain a link function" that relates the response variable, YiYi, to the systematic linear component, ηη. Table 16.1 shows the major exponential “families”" of GLM models, and indicates the kinds of link functions involved in each. Note that OLS models would fall within the Gaussian family. In the next section we focus on the binomial family, and on logit estimation in particular.

    Figure \(\PageIndex{1}\): Exponential ‘Families’ of GLM Models

    This page titled 16.1: Generalized Linear Models is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Jenkins-Smith et al. (University of Oklahoma Libraries) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.