The first three sections of this chapter present the theory of maximum likelihood estimation of a vector of means which satisfy a loglinear model under Poisson, multinomial, and product multinomial sampling. Example 1.2.10 (considered in Problem 3.6), Problem 3.3, and Problem 3.4 illustrate loglinear modeling under Poisson sampling for data on valve failures in nuclear plants, breakdowns in electronic equipment, and absences of school children, respectively. Further applications are deferred to Chapter 4 where cross-classified (multinomial) data are studied and to Chapter 5 where binary regression (product multinomial) data are considered. Alternative methods of estimation and non-loglinear models are discussed in Section3.4.
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