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.
15.1. The Structure of Generalized Linear Models 383 Here, ny is the observed number of successes in the ntrials, and n(1 −y)is the number of failures; and n ny = n! (ny)![n(1 −y)]! is the binomial coefficient. • The Poisson distributions are a discrete family with probability function indexed by the rate parameter μ>0: p(y)= μy × e−μ y
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