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 chapters. Generalized Linear Models have become so central to effective statistical dataanalysis, however, that it is worth the additional effort required to acquire a basic understandingof the The Structure of Generalized Linear ModelsAgeneralized Linear model(or GLM1) consists of three components:1.

NOTE: μi is the expected value of the response; ηi is the linear predictor; and (·) is the cumulative distribution function of the standard-normal distribution. Because the link function is invertible, we can also write μi = g−1(ηi) = g−1(α +β1Xi1 +β2Xi2 +···+βkXik) and, thus ...

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