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Generalized Linear Model Theory

Appendix BGeneralized Linear ModelTheoryWe describe the Generalized Linear Model as formulated by Nelder and Wed-derburn (1972), and discuss estimation of the parameters and tests of The ModelLety1, .. , yndenotenindependent observations on a response. We treatyias a realization of a random variableYi. In the general Linear Model weassume thatYihas a normal distribution with mean iand variance 2Yi N( i, 2),and we further assume that the expected value iis a Linear function ofppredictors that take valuesx i= (xi1, .. , xip) for thei-th case , so that i=x i ,where is a vector of unknown will generalize this in two steps, dealing with the stochastic andsystematic components of the Rodr guez.

B.1. THE MODEL 3 Try to generalize this result to the case where Y i has a normal distribution with mean µ i and variance σ2/n i for known constants n i, as would be the case if the Y i represented sample means. Example: In Problem Set 1 …

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