Log Linear Models And Logistic Regression
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Log-Linear Models and Logistic Regression
Author: Ronald Christensen
language: en
Publisher: Springer Science & Business Media
Release Date: 2006-04-06
As the new title indicates, this second edition of Log-Linear Models has been modi?ed to place greater emphasis on logistic regression. In addition to new material, the book has been radically rearranged. The fundamental material is contained in Chapters 1-4. Intermediate topics are presented in Chapters 5 through 8. Generalized linear models are presented in Ch- ter 9. The matrix approach to log-linear models and logistic regression is presented in Chapters 10-12, with Chapters 10 and 11 at the applied Ph.D. level and Chapter 12 doing theory at the Ph.D. level. The largest single addition to the book is Chapter 13 on Bayesian bi- mial regression. This chapter includes not only logistic regression but also probit and complementary log-log regression. With the simplicity of the Bayesian approach and the ability to do (almost) exact small sample s- tistical inference, I personally ?nd it hard to justify doing traditional large sample inferences. (Another possibility is to do exact conditional inference, but that is another story.) Naturally,Ihavecleaneduptheminor?awsinthetextthatIhavefound. All examples, theorems, proofs, lemmas, etc. are numbered consecutively within each section with no distinctions between them, thus Example 2.3.1 willcomebeforeProposition2.3.2.Exercisesthatdonotappearinasection at the end have a separate numbering scheme. Within the section in which it appears, an equation is numbered with a single value, e.g., equation (1).
Log-Linear Models
Author: Ronald Christensen
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-12-14
This book examines log-linear models for contingency tables. Logistic re gression and logistic discrimination are treated as special cases and gener alized linear models (in the GLIM sense) are also discussed. The book is designed to fill a niche between basic introductory books such as Fienberg (1980) and Everitt (1977) and advanced books such as Bishop, Fienberg, and Holland (1975), Haberman (1974), and Santner and Duffy (1989). lt is primarily directed at advanced Masters degree students in Statistics but it can be used at both higher and lower levels. The primary theme of the book is using previous knowledge of analysis of variance and regression to motivate and explicate the use of log-linear models. Of course, both the analogies and the distinctions between the different methods must be kept in mind. The book is written at several levels. A basic introductory course would take material from Chapters I, II (deemphasizing Section II. 4), III, Sec tions IV. 1 through IV. 5 (eliminating the material on graphical models), Section IV. lü, Chapter VII, and Chapter IX. The advanced modeling ma terial at the end of Sections VII. 1, VII. 2, and possibly the material in Section IX. 2 should be deleted in a basic introductory course. For Mas ters degree students in Statistics, all the material in Chapters I through V, VII, IX, and X should be accessible. For an applied Ph. D.
Log-Linear Models and Logistic Regression
Author: Ronald Christensen
language: en
Publisher: Springer Nature
Release Date: 2025-05-19
This book examines statistical models for frequency data. The primary focus is on log-linear models for contingency tables but also includes extensive discussion of logistic regression. Topics such as logistic discrimination, generalized linear models, and correspondence analysis are also explored. The treatment is designed for readers with prior knowledge of analysis of variance and regression. It builds upon the relationships between these basic models for continuous data and the analogous log-linear and logistic regression models for discrete data. While emphasizing similarities between methods for discrete and continuous data, this book also carefully examines the differences in model interpretations and evaluation that occur due to the discrete nature of the data. Numerous data sets from fields as diverse as engineering, education, sociology, and medicine are used to illustrate procedures and provide exercises. A major addition to the third edition is the availability of a companion online manual providing R code for the procedures illustrated in the book. The book begins with an extensive discussion of odds and odds ratios as well as concrete illustrations of basic independence models for contingency tables. After developing a sound applied and theoretical basis for frequency models analogous to ANOVA and regression, the book presents, for contingency tables, detailed discussions of the use of graphical models, of model selection procedures, and of models with quantitative factors. It then explores generalized linear models, after which all the fundamental results are reexamined using powerful matrix methods. The book then gives an extensive treatment of Bayesian procedures for analyzing logistic regression and other regression models for binomial data. Bayesian methods are conceptually simple and unlike traditional methods allow accurate conclusions to be drawn without requiring large sample sizes. The book concludes with two new chapters: one on exact conditional tests for small sample sizes and another on the graphical procedure known as correspondence analysis.