Log-Linear Modeling

Preface xiii Acknowledgments xvii 1 Basics of Hierarchical Log-linear Models 1 1.1 Scaling: Which Variables Are Considered Categorical? 2 1.2 Crossing Two or More Variables 4 1.3 Goodman's Three Elementary Views 8 1.4 Assumptions Made for Log-linear modeling 9 2 Effects in a Table 13 2.1 The Null Model 13 2.2 The Row Effects-Only Model 15 2.3 The Column Effects-Only Model 15 2.4 The Row-and Column-Effects-Model 16 2.5 Log-Linear Models 18 3 Goodness-of-Fit 23 3.1 Goodness of Fit I: Overall Fit Statistics 23 3.2 Goodness-of-Fit II: R2 Equivalents and Information Criteria 30 3.3 Goodness-of-Fit III: Null Hypotheses Concerning Parameters 35 3.4 Goodness-of-fit IV: Residual Analysis 36 3.5 The Relationship Between Pearson's X2 and Log-linear Modeling 52 4 Hierarchical Log-linear Models and Odds Ratio Analysis 55 4.1 The Hierarchy of Log-linear Models 55 4.2 Comparing Hierarchically Related Models 57 4.3 Odds Ratios and Log-linear-Models 63 4.4 Odds Ratios in Tables Larger than 2 x 2 65 4.5 Testing Null Hypotheses in Odds Ratio Analysis 70 4.6 Characteristics of the Odds Ratio 72 4.7 Application of the Odds Ratio 75 4.8 The Four Steps to Take When Log-linear-Modeling 81 4.9 Collapsibility 86 5 Computations I: Basic Log-linear Modeling 97 5.1 Log-linear Modeling in R 97 5.2 Log- linear Modeling in SYSTAT 102 5.3 Log-linear Modeling in lEM 106 6 The Design Matrix Approach 111 6.1 The Generalized Linear Model (GLM) 111 6.2 Design Matrices: Coding 115 7 Parameter Interpretation and Significance Tests 129 7.1 Parameter Interpretation Based on Design Matrices 130 7.2 The Two Sources of Parameter Correlation: Dependency of Vectors and Data Characteristics 139 7.3 Can Main Effects Be Interpreted? 143 7.4 Interpretation of Higher Order Interactions 150 8 Computations II: Design Matrices and Poisson GLM 157 8.1 GLM-based Log-linear-Modeling in R 157 8.2 Design Matrices in SYSTAT 164 8.3 Log-linear-Modeling with Design Matrices in lEM 170 9 Nonhierarchical and Nonstandard Log-linear Models 181 9.1 Defining Nonhierarchical and Nonstandard Log-linear-Models 182 9.2 Virtues of Nonhierarchical and Nonstandard Log-linear-Models 182 9.3 Scenarios for Nonstandard Log-linear-Models 184 9.4 Nonstandard Scenarios: Summary and Discussion 240 9.5 Schuster's Approach to Parameter Interpretation 242 10 Computations III: Nonstandard Models 251 10.1 Non-Hierarchical and Nonstandard Models in R 251 10.2 Estimating Non-Hierarchical and Nonstandard Models with SYSTAT 256 10.3 Estimating Non-Hierarchical and Nonstandard Models with lEM 265 11 Sampling Schemes and Chisquare Decomposition 273 11.1 Sampling Schemes 273 11.2 Chi-Square Decomposition 276 12 Symmetry Models 289 12.1 Axial Symmetry 289 12.2 Point-symmetry 294 12.3 Point-axial Symmetry 295 12.4 Symmetry in Higher-Dimensional Cross-Classifications 296 12.5 Quasi-Symmetry 298 12.6 Extensions and Other Symmetry Models 301 12.7 Marginal Homogeneity: Symmetry in the Marginals 305 13 Log-linear Models of Rater Agreement 309 13.1 Measures of Rater Agreement in Contingency Tables 309 13.2 The Equal Weight Agreement Model 313 13.3 The Differential Weight Agreement Model 315 13.4 Agreement in Ordinal Variables 316 13.5 Extensions of Rater Agreement Models 319 14 Homogeneity of Associations 327 14.1 The Mantel-Haenszel and Breslow-Day Tests 327 14.2 Log-linear-Models to Test Homogeneity of Associations 330 14.3 Extensions and Generalizations 335 15 Logistic Regression and Logit Models 339 15.1 Logistic Regression 339 15.2 Log-linear Representation of Logistic Regression Models 344 15.3 Overdispersion in Logistic Regression 347 15.4 Logistic Regression Versus Log-linear Modeling Modules 349 15.5 Logit Models and Discriminant Analysis 351 15.6 Path Models 357 16 Reduced Designs 363 16.1 Fundamental Principles for Factorial Design 364 16.2 The Resolution Level of a Design 365 16.3 Sample Fractional Factorial Designs 368 17 Computations IV: Additional Models 379 17.1 Additional Log-linear-Models in R 379 17.2 Additional Log-linear-Models in SYSTAT 388 17.3 Additional Log-linear-Models in lEM 404 References 417