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Loglinear Analysis of Contingency Tables
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Loglinear Analysis of Contingency Tables
by Paul D. Allison
Logistic Regression Using SAS®: Theory and Application
Copyright
Acknowledgments
Introduction
What This Book Is About
What This Book Is Not About
What You Need to Know
Computing
References
Binary Logit Analysis: Basics
Introduction
Dichotomous Dependent Variables: Example
Problems with Ordinary Linear Regression
Odds and Odds Ratios
The Logit Model
Estimation of the Logit Model: General Principles
Maximum Likelihood Estimation with PROC LOGISTIC
Maximum Likelihood Estimation with PROC GENMOD
Interpreting Coefficients
Binary Logit Analysis: Details and Options
Introduction
Confidence Intervals
Details of Maximum Likelihood Estimation
Convergence Problems
Multicollinearity
Goodness-of-Fit Statistics
Statistics Measuring Predictive Power
Predicted Values, Residuals, and Influence Statistics
Latent Variables and Standardized Coefficients
Probit and Complementary Log-Log Models
Unobserved Heterogeneity
Sampling on the Dependent Variable
Logit Analysis of Contingency Tables
Introduction
A Logit Model for a 2 × 2 Table
A Three-Way Table
A Four-Way Table
A Four-Way Table with Ordinal Explanatory Variables
Overdispersion
Multinomial Logit Analysis
Introduction
Example
A Model for Three Categories
Estimation with CATMOD
Estimation with a Binary Logit Procedure
General Form of the Model
Contingency Table Analysis
CATMOD Coding of Categorical Variables
Problems of Interpretation
Logit Analysis for Ordered Categories
Introduction
Cumulative Logit Model: Example
Cumulative Logit Model: Explanation
Cumulative Logit Model: Practical Considerations
Cumulative Logit Model: Contingency Tables
Adjacent Categories Model
Continuation Ratio Model
Discrete Choice Analysis
Introduction
Chocolate Example
Model and Estimation
Travel Example
Other Applications
Ranked Data
Logit Analysis of Longitudinal and Other Clustered Data
Introduction
Longitudinal Example
GEE Estimation
Fixed-Effects with Conditional Logit Analysis
Postdoctoral Training Example
Matching
Mixed Logit Models
Comparison of Methods
A Hybrid Method
Poisson Regression
Introduction
The Poisson Regression Model
Scientific Productivity Example
Overdispersion
Negative Binomial Regression
Adjustment for Varying Time Spans
Loglinear Analysis of Contingency Tables
Introduction
A Loglinear Model for a 2 × 2 Table
Loglinear Models for a Four-Way Table
Fitting the Adjacent Categories Model as a Loglinear Model
Loglinear Models for Square, Ordered Tables
Marginal Tables
The Problem of Zeros
GENMOD versus CATMOD
Appendix
The ROBUST Macro
The PENALTY Data Set: Outcomes for Murder Defendants
The WALLET Data Set: Altruistic Behavior by College Students
The TRAVEL Data Set: Transportation Choices to Australian Cities
The JUDGERNK Data Set: Rankings of Seriousness of Murder Cases
The PTSD Data Set: Psychological Distress among Fire Victims
The POSTDOC Data Set: Postdoctoral Training among Biochemists
The CASECONT Data Set: Women in Homeless Shelters
The PROGNOSI Data Set: Physicians’ Utterances about Prognosis
Books Available from SAS® Press
JMP® Books
Wiley Series in Probability and Statistics
Wiley Series in Probability and Statistics
References
Index
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Prev
Previous Chapter
Adjustment for Varying Time Spans
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Introduction
Chapter 10. Loglinear Analysis of Contingency Tables
10.1
Introduction
233
10.2
A Loglinear Model for a 2 × 2 Table
234
10.3
Loglinear Models for a Four-Way Table
240
10.4
Fitting the Adjacent Categories Model as a Loglinear Model
246
10.5
Loglinear Models for Square, Ordered Tables
252
10.6
Marginal Tables
259
10.7
The Problem of Zeros
261
10.8
GENMOD versus CATMOD
266
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