Log-Linear Modeling : Concepts, Interpretation, and Application

by von Eye, Alexander; Mun, Eun-Young

• ISBN13: 9781118146408
• ISBN10: 1118146409
• Format: Hardcover
• Copyright: 2012-12-17
• Publisher: Wiley

Summary

Over the past ten years, there have been many important advances in log-linear modeling, including the specification of new models, in particular non-standard models, and their relationships to methods such as Rasch modeling. While most literature on the topic is contained in volumes aimed at advanced statisticians, Applied Log-Linear Modeling presents the topic in an accessible style that is customized for applied researchers who utilize log-linear modeling in the social sciences. The book begins by providing readers with a foundation on the basics of log-linear modeling, introducing decomposing effects in cross-tabulations and goodness-of-fit tests. Popular hierarchical log-linear models are illustrated using empirical data examples, and odds ratio analysis is discussed as an interesting method of analysis of cross-tabulations. Next, readers are introduced to the design matrix approach to log-linear modeling, presenting various forms of coding (effects coding, dummy coding, Helmert contrasts etc.) and the characteristics of design matrices. The book goes on to explore non-hierarchical and nonstandard log-linear models, outlining ten nonstandard log-linear models (including nonstandard nested models, models with quantitative factors, logit models, and log-linear Rasch models) as well as special topics and applications. A brief discussion of sampling schemes is also provided along with a selection of useful methods of chi-square decomposition. Additional topics of coverage include models of marginal homogeneity, rater agreement, methods to test hypotheses about differences in associations across subgroup, the relationship between log-linear modeling to logistic regression, and reduced designs. Throughout the book, Computer Applications chapters feature SYSTAT, Lem, and R illustrations of the previous chapter's material, utilizing empirical data examples to demonstrate the relevance of the topics in modern research.

Author Biography

ALEXANDER von EYE, PhD, is Professor of Psychology at Michigan State University. He has published twenty books and over 350 journal articles on statistical methods, categorical data analysis, and human development. Dr. von Eye serves as Section Editor on Categorical Data Analysis for Wiley's Encyclopedia of Statistics in Behavioral Science.

EUN-YOUNG MUN, PhD, is Associate Professor of Psychology at Rutgers University. Her research focuses on extending generalized latent variable modeling to the study of clustered, repeated measures longitudinal data.

Table of Contents

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