1997 LogLinearModelsAndLogisticReg

• (Christensen, 1997) ⇒ Ronald Christensen. (1997). “Log-Linear Models and Logistic Regression, 2nd edition." Springer. ISBN:0387982477

Subject Headings: Log-Linear Models, Logistic Regression, Saturated Model, Cook's Distance, Odds Ratio.

Notes

• Book webpage: http://www.math.unm.edu/~fletcher/llm.html
• Google Books webpage: http://books.google.com/books?id=7acdFD_eX24C

Cited By

• http://scholar.google.com/scholar?cluster=15398729168135750441

Quotes

Book Overview

The primary focus here is on log-linear models for contingency tables, but in this second edition, greater emphasis has been placed on logistic regression. The book explores topics such as logistic discrimination and generalised linear models, and builds upon the relationships between these basic models for continuous data and the analogous log-linear and logistic regression models for discrete data. It also carefully examines the differences in model interpretations and evaluations that occur due to the discrete nature of the data. Sample commands are given for analyses in SAS, BMFP, and GLIM, while numerous data sets from fields as diverse as engineering, education, sociology, and medicine are used to illustrate procedures and provide exercises. Throughout the book, the treatment is designed for students with prior knowledge of analysis of variance and regression.

Table of Contents

• Introduction
  • Conditional Probability and Independence
  • Random Variables and Expectations
  • The Binomial Distribution
  • The Multinomial Distribution
  • The Poisson Distribution
  • Exercises
• Two-Dimensional Tables
  • Two Independent Binomials
    • The Odds Ratio
  • Testing Independence in a 2 xs 2 Table
    • The Odds Ratio
  • I x J Tables
    • Response Factors
    • Odds Ratios
  • Maximum Likelihood Theory for Two-Dimensional Tables
  • Log-Linear Models for Two-Dimensional Tables
    • Odds Ratios
  • Simple Logistic Regression
    • Computer Commands
  • Exercises
• Three-Dimensional Tables
  • Simpson's Paradox and the Need for Higher Dimensional Tables
  • Independence and Odds Ratio Models for 3-dimensional Tables
    • The Model of Complete Independence
    • Models with One Factor Independent of the Other Two
    • Models of Conditional Independence
    • A Final Model for Three-Way Tables
    • Odds Ratios and Independence Models
  • Iterative Computation of Estimates
  • Log-Linear Models for 3-Dimensional Tables
    • Estimation
    • Testing Models
  • Product Multinomial and Other Sampling Plans
    • Other Sampling Models
  • Model Selection Criteria
    • R^2
    • Adjusted R^2
    • Akaike's Information Criterion
  • Higher-Dimensional Tables
    • Computer Commands
  • Exercises
• Logistic Regression, Logit Models, and Logistic Discrimination
  • Multiple Logistic Regression
    • Informal Model Selection
  • Measuring Model Fit
    • Checking Lack of Fit
  • Logistic Regression Diagnostics
  • Model Selection Methods
    • Computations for Nonbinary Data
    • Computer Commands
  • ANOVA Type Logit Models
    • Computer Commands
  • Logit Models for a Multinomial Response Factor
  • Logistic Discrimination and Allocation
  • Recursive Causal Models
  • Exercises
• Independence Relationships and Graphical Models
  • Model Interpretations
  • Graphical and Decomposable Models
  • Collapsing Tables
  • Recursive Causal Models
• Model Selection Methods and Model Evaluation
  • Stepwise Procedures for Model Selection
  • Initial Models for Selection Methods
    • All s-Factor Effects
    • Examining Each Term Individually
    • Tests of Marginal and Partial Association
    • Testing Each Term Last
  • Example of Stepwise Methods
    • Forward Selection
    • Backward Elimination
    • Comparison of Stepwise Methods
    • Computer Commands
  • Aitkin's Method of Backward Selection
  • Model Selection Among Decomposable and Graphical Models
  • Use of Model Selection Criteria
  • Residuals and Influential Observations
    • Computations
    • Computing Commands
  • Drawing Conclusions
  • Exercises
• Models for Factors with Quantitative Levels
  • Models for Two-Factor Tables
    • Log-Linear Models with Two Quantitative Factors
    • Models with One Quantitative Factor
  • Higher Dimensional Tables
    • Computing Commands
  • Unknown Factor Scores
  • Logit Models
  • Exercises
• Fixed and Random Zeros
  • Fixed Zeros
  • Partitioning Polytomous Variables
  • Random Zeros
  • Exercises
• Generalized Linear Models
  • Distributions for Generalized Linear Models
  • Estimation of Linear Parameters
  • Estimation of Dispersion and Model Fitting
  • Summary and Discussion
  • Exercises
• The Matrix Approach to Log-Linear Models
  • Maximum Likelihood Theory for Multinomial Sampling
  • Asymptotic Results
  • Product-Multinomial Sampling
  • Inference for Model Parameters
  • Methods for Finding Maximum Likelihood Estimates
  • Regression Analysis of Categorical Data
  • Residual Analysis and Outliers
  • Exercises
• The Matrix Approach to Logit Models
  • Estimation and Testing for Logistic Models
  • Asymptotic Results
  • Model Selection Criteria for Logistic Regression
  • Likelihood Equations and Newton-Raphson
  • Weighted Least Squares for Logit Models
  • Multinomial Response Models
  • Discrimination, Allocation and Retrospective Data
  • Exercises
• Maximum Likelihood Theory for Log-Linear Models
  • Notation
  • Fixed Sample Size Properties
  • Asymptotic Properties
  • Applications
  • Proofs of Lemma 15.3.2 and Theorem 15.3.8
• Bayesian Binomial Regression
  • Introduction
  • Bayesian Inference
    • Specifying the Prior and Approximating the Posterior
    • Predictive Probabilities
    • Inference for Regression Coefficients
    • Inference for LD(50)
  • Diagnostics
    • Case Deletion Influence Measures
    • Model Checking
    • Link Selection
    • Sensitivity Analysis
  • Posterior Computations and Sample Size Calculation

  References

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  	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
  1997 LogLinearModelsAndLogisticReg	Ronald Christensen			Log-Linear Models and Logistic Regression, 2nd edition			http://www.math.unm.edu/~fletcher/llm.html			1997