Fienberg S.E. The Analysis of Cross-Classified Categorical Data

Second Edition. — N.-Y.: Springer, 2007. — 216 p. — ISBN: 978-0-387-72824-7.A variety of biological and social science data come in the form of cross-classified tables of counts, commonly referred to as contingency tables. Until recent years the statistical and computational techniques available for the analysis of cross-classified data were quite limited. This book presents some of the recent work on the statistical analysis of cross-classified data using longlinear models, especially in the multidimensional situation.The Analysis of Categorical Data
Forms of Multivariate Analysis
Some Historical Background
A Medical Example
Two-Dimensional Tables
Two Binomials
The Model of Independence
The Loglinear Model
Sampling Models
The Cross-Product Ratio and 2 x 2Tables
Interrelated Two-Dimensional Tables
Problems
Сorrection for Continuity
Other Scales for Analyzing Two-Dimensional Tables
Problems
Three-Dimensional Tables
The General Loglinear Model
Sampling Models
Estimated Expected Values
Iterative Computation of Expected Values
Goodness-of-Fit Statistics
Hierarchical Models
A Further Example
Collapsing Tables
Problems
Selection of a Model
General Issues
Conditional Test Statistics
Partitioning Chi-Square
Using Information about Ordered Categories
Problems
Four- and Higher-Dimensional Contingency Tables
The Loglinear Models and MLEs for Expected Values
Using Partitioning to Select a Model
StepwiseSelection Procedures
Looking at All Possible Effects
Problems
Fixed Margins and Logit Models
AThree-Dimensional Example
Logit Models
Logit Models and Ordered Categories
Linear Logistic Response Models
Logistic Regression vs. Discriminant Analysis
Polytomous and Multivariate Response Variables
Problems
Causal Analysis Involving Logit and Loglinear Models
Path Diagrams
Recursive Systems of Logit Models
Recursive Systems: A More Complex Example
Nonrecursive Systems of Logit Models
Retrospective Epidemiological Studies
Logistic Models for Retrospective Data
Problems
Fixed and Random Zeros
Sampling Zeros and MLEs in Loglinear Models
Incomplete Two-Dimensional Contingency Tables
Incompleteness in Several Dimensions
Some Applications of Incomplete Table Methodology
Problems
Appendix I. Statistical Terminology
Appendix II. Basic Estimation Results for Loglinear Models
Appendix III. Percentage Points of χ² Distribution
Appendix IV. Small-Sample Properties of χ² Statistics