Generalized Linear Models - SAGE Publications Inc

15 GeneralizedLinear ModelsDue originally to Nelder and Wedderburn (1972), Generalized Linear Models are a remarkablesynthesis and extension of familiar regression Models such as the Linear Models described inPart II of this text and the logit and probit Models described in the preceding chapter. The currentchapter begins with a consideration of the general structure and range of application of generalizedlinear Models ; proceeds to examine in greater detail Generalized Linear Models for count data,including contingency tables; briefly sketches the statistical theory underlying Generalized linearmodels; and concludes with the extension of regression diagnostics to Generalized Linear unstarred sections of this chapter are perhaps more difficult than the unstarred material inpreceding cha

of the explanatory variables in the model. In the initial formulation of GLMs, the distribution of Yi was a member of an exponential family, such as the Gaussian, binomial, Poisson, gamma, or inverse-Gaussian families of distributions. 2. A linear predictor—that is a linear function of regressors, ηi = α +β1Xi1 +β2Xi2 +···+βkXik 3.

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