Table of contents for The analysis of cross-classified categorical data / Stephen E. Fienberg.


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Preface to the Second Edition                                 vii
Preface to the First Edition                                  ix
1   Introduction
1.1 The Analysis of Categorical Data                           1
1.2 Forms of Multivariate Analysis                             2
1.3 Some Historical Background                                 4
1.4  A Medical Example                                         6
2   Two-Dimensional Tables                                     8
2.1 Two Binomials                                              8
2.2 The Model of Independence                                 10
2.3 The Loglinear Model                                       13
2.4 Sampling Models                                           15
2.5 The Cross-Product Ratio and 2 x 2 Tables                  16
2.6 Interrelated Two-Dimensional Tables                       20
2.7 Correction for Continuity                                 21
2.8 Other Scales for Analyzing Two-Dimensional Tables         22
Problems                                                      23
3   Three-Dimensional Tables                                  27
3.1  The General Loglinear Model                              27
3.2 Sampling Models                                           29
33  Estimated Expected Values                                 32
314 Iterative Computation of Expected Values                  37
3.5 Goodness-of-Fit Statistics                                40
3.6  Hierarchical Models                                      43
3.7 A Further Example                                         44
3.8 Collapsing Tables                                         48
Problems                                                      51
4   Selection of a Model                                      56
4.1 General Issues                                            56
4.2 Conditional Test Statistics                               56
4.3 Partitioning Chi-Square                                   57
4.4  Using Information about Ordered Categories               61
Problems                                                      68
5   Four- and Higher-Dimensional Contingency Tables           71
5.1 The Loglinear Models and MLEs for Expected Values         71
5.2  Using Partitioning to Select a Mode                       74
5.3 Stepwise Selection Procedures                             77
5.4  Looking at All Possible Effects                          80
Problems                                                      88
6   Fixed Margins and Logit Models                            95
6.1 A Three-Dimensional Example                                95
6.2  Logit Models                                              97
6.3  Logit Models and Ordered Categories                       99
6.4  Linear Logistic Response Models                          102
6.5  Logistic Regression vs. Discriminant Analysis            105
6.6  Polytomous and Multivariate Response Variables           110
Problems                                                      116
7   Causal Analysis Involving Logit and Loglinear Models      120
7.1 Path Diagrams                                             120
7.2  Recursive Systems of Logit Models                        123
7.3  Recursive Systems: A More Complex Example                129
7.4  Nonrecursive Systems of Logit Models                     133
7.5 Retrospective Epidemiological Studies                     135
7.6  Logistic Models for Retrospective Data                   137
Problems                                                      138
8   Fixed and Random Zeros                                    140
8.1 Sampling Zeros and MLEs in Loglinear Models               140
8.2 Incomplete Two-Dimensional Contingency Tables             142
8.3 Incompleteness in Several Dimensions                      146
8.4 Some Applications of Incomplete Table Methodology         150
Problems                                                      159
Appendix I   Statistical Terminology                          165
Appendix II  Basic Estimation Results for Loglinear Models    167
Appendix III Percentage Points of 2 Distribution              171
Appendix IV  Small-Sample Properties of X2 Statistics         172



Library of Congress subject headings for this publication: Multivariate analysis, Contingency tables, Log-linear models