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Karl Taps.
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Each chapter in the book is well written and has real examples to illustrate concepts. At the end of each chapter is a section summarizing related references to the literature by sections in the chapter. This is then followed by a large set of exercises that can be used for homework or test problems. Many of the exercises incorporate data from interesting real world problems. Many of the problems can be solved with the software GLIM. Other software including Minitab, SPlus, StatXact and LogXact are used from time to time. Manuals for the software and some S algorithms are provided on a Wiley web site set up for the text and described in the Preface.
Chapter 1 starts out with the basic parametric theory of statistics including maximum likelihood, asymptotic distribution theory, hypothesis testing and goodness of fit measures. It also includes a section on transformations of data and parameters.
Chapter 2 describes categorical data and the general multinomial model. The Poisson model is also discussed and goodness of fit procedures are described. Confidence intervals and hypothesis testing are also included. A connection between the multinomial and Poisson models is given.
Chapter 3 deals with the special case of binary data. Contingency tables and binomial models are discussed. Methods for comparing two or more binomial populations are covered as are the testing of independence in a 2x2 contingency table and the comparison of several 2x2 tables. Generalized linear models are introduced here as a tool for dealing with these problems. Lloyd is careful not to gloss over important issues and he includes discussion of hidden factors. Simpson's paradox is covered in Section 3.6. Asymptotic chi-square distributions are often needed for these unconditional tests.
Chapter 4 covers binomial regression models, issues of overdispersion and the use of the normal general linear model as an approximation. Weighted least squares using the inverse of the variance for weights is presented. Chapter 5 adds nonparametric smoothing to the tools for binary data.
Chapter 6 covers Poisson regression models. There is also some discussion fo the treatment of ordinal data as well as categorical data in Chapter 6. Models for incomplete data are also treated in Chapter 6. Log linear models and multinomial logit models are also considered in Chapter 6.
Chapter 7 deals with the simpler conditional tests. These tests are sometimes preferred because of their simplicity and because they have properties of exactness due to the conditioning on the observed data that reduces the class of possible probability models. These procedures have the advantage of being distribution free as well as exact but also have the slight disadvantage of being computer-intensive. Lloyd is careful to point out the advantages of tests based on conditional inference and the available software that makes these techniques very practical. However, he should also be commended for pointing out that the conditioning argument is not universally accepted. A point that is often neglected when dealing with permutation tests like Fisher's exact test. The chapter also includes an interesting section on saddlepoint approximations that can be used to get a good analytic approximation to the exact procedure.
Good features of the book include, the careful and clearly stated theoretical ideas and the wide range of applications used to show practicality of the methods. Important questions related to outliers and missing data are properly covered.
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