The Analysis of Cross-Classified Data Having Ordered and/or Unordered Categories: Association Models, Correlation Models, and Asymmetry Models for Contingency Tables With or Without Missing Entries

Abstract

1. Introduction and Summary 2. Models for Row Scores and Column Scores in the I X J Table 2.1. Association Models 2.2. Correlation Models 2.3. Comparison between Association Models and Correlation Models 2.3.1. Introductory comments 2.3.2. Association models and a generalized bivariate normal with arbitrary marginals 2.3.3. Correlation models, association models, and generalized bivariate multinomial distributions 2.4. Correlation Models, Association Models, Canonical Correlation, and Correspondence Analysis 2.5. An Overview and Some Additional Models 3. Models for Generalized Symmetry, Independence, and Symmetry + Independence in the K X K Table 3.1. Introductory Comments 3.2. Generalized Symmetry Models 3.3. Generalized Independence Models 3.4. Generalized Symmetry + Independence Models 3.5. Some Comparisons, An Overview, and Some Additional Models 4. Unordered Parameters and/or Ordered Parameters References Appendix: Maximum-Likelihood Estimation