Transcription of Generalized Linear Models
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Generalized Linear Models
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.
This is a familiar idea from the logit and probit models discussed in Chapter 14, where the object was to model the probability of “success,” represented by μi in our current general notation. As a probability, μi is confined to the unit interval [0,1]. The logit and probit links map this interval to the entire real line, from −∞ to ...
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