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Summary
Summary
An easily accessible introduction to log-linear modeling for non-statisticians
Highlighting advances that have lent to the topic's distinct, coherent methodology over the past decade, Log-Linear Modeling: Concepts, Interpretation, and Application provides an essential, introductory treatment of the subject, featuring many new and advanced log-linear methods, models, and applications.
The book begins with basic coverage of categorical data, and goes on to describe the basics of hierarchical log-linear models as well as decomposing effects in cross-classifications and goodness-of-fit tests. Additional topics include:
The generalized linear model (GLM) along with popular methods of coding such as effect coding and dummy coding Parameter interpretation and how to ensure that the parameters reflect the hypotheses being studied Symmetry, rater agreement, homogeneity of association, logistic regression, and reduced designs modelsThroughout the book, real-world data illustrate the application of models and understanding of the related results. In addition, each chapter utilizes R, SYSTAT®, and §¤EM software, providing readers with an understanding of these programs in the context of hierarchical log-linear modeling.
Log-Linear Modeling is an excellent book for courses on categorical data analysis at the upper-undergraduate and graduate levels. It also serves as an excellent reference for applied researchers in virtually any area of study, from medicine and statistics to the social sciences, who analyze empirical data in their everyday work.
Author Notes
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 oh extending generalized latent variable modeling to the study of clustered, repeated measures longitudinal data.
Table of Contents
Preface | p. xi |
Acknowledgments | p. xv |
1 Basics of Hierarchical Log-linear Models | p. 1 |
1.1 Scaling: Which Variables Are Considered Categorical? | p. 1 |
1.2 Crossing Two or More Variables | p. 4 |
1.3 Goodman's Three Elementary Views of Log-linear Modeling | p. 8 |
1.4 Assumptions Made for Log-linear Modeling | p. 9 |
2 Effects in a Table | p. 13 |
2.1 The Null Model | p. 13 |
2.2 The Row Effects-Only Model | p. 15 |
2.3 The Column Effects-Only Model | p. 15 |
2.4 The Row- and Column-Effects Model | p. 16 |
2.5 Log-Linear Models | p. 18 |
3 Goodness-of-Fit | p. 23 |
3.1 Goodness-of-Fit I: Overall Fit Statistics | p. 23 |
3.1.1 Selecting between X 2 and G 2 | p. 25 |
3.1.2 Degrees of Freedom | p. 29 |
3.2 Goodness-of-Fit II: R 2 Equivalents and Information Criteria | p. 29 |
3.2.1 R 2 Equivalents | p. 30 |
3.2.2 Information Criteria | p. 32 |
3.3 Goodness-of-Fit III: Null Hypotheses Concerning Parameters | p. 35 |
3.4 Goodness-of-fit IV: Residual Analysis | p. 36 |
3.4.1 Overall Goodness-of-Fit Measures and Residuals | p. 36 |
3.4.2 Other Residual Measures | p. 38 |
3.4.3 Comparing Residual Measures | p. 42 |
3.4.4 A Procedure to Identify Extreme Cells | p. 44 |
3.4.5 Distributions of Residuals | p. 48 |
3.5 The Relationship between Pearson's X 2 and Log-linear Modeling | p. 52 |
4 Hierarchical Log-linear Models and Odds Ratio Analysis | p. 55 |
4.1 The Hierarchy of Log-linear Models | p. 55 |
4.2 Comparing Hierarchically Related Models | p. 57 |
4.3 Odds Ratios and Log-linear Models | p. 63 |
4.4 Odds Ratios in Tables Larger than 2 x 2 | p. 65 |
4.5 Testing Null Hypotheses in Odds-Ratio Analysis | p. 70 |
4.6 Characteristics of the Odds Ratio | p. 72 |
4.7 Application of the Odds Ratio | p. 75 |
4.8 The Four Steps to Take When Log-linear Modeling | p. 81 |
4.9 Collapsibility | p. 86 |
5 Computations I: Basic Log-linear Modeling | p. 99 |
5.1 Log-linear Modeling in R | p. 99 |
5.2 Log-linear Modeling in SYSTAT | p. 104 |
5.3 Log-linear Modeling in lem | p. 108 |
6 The Design Matrix Approach | p. 115 |
6.1 The Generalized Linear Model (GLM) | p. 115 |
6.1.1 Logit Models | p. 117 |
6.1.2 Poisson Models | p. 118 |
6.1.3 GLM for Continuous Outcome Variables | p. 119 |
6.2 Design Matrices: Coding | p. 119 |
6.2.1 Dummy Coding | p. 120 |
6.2.2 Effect Coding | p. 124 |
6.2.3 Orthogonality of Vectors in Log-linear Design Matrices | p. 127 |
6.2.4 Design Matrices and Degrees of Freedom | p. 129 |
7 Parameter Interpretation and Significance Tests | p. 133 |
7.1 Parameter Interpretation Based on Design Matrices | p. 134 |
7.2 The Two Sources of Parameter Correlation: Dependency of Vectors and Data Characteristics | p. 143 |
7.3 Can Main Effects Be Interpreted? | p. 147 |
7.3.1 Parameter Interpretation in Main Effect Models | p. 147 |
7.3.2 Parameter Interpretation in Models with Interactions | p. 150 |
7.4 Interpretation of Higher Order Interactions | p. 154 |
8 Computations II: Design Matrices and Poisson GLM | p. 161 |
8.1 GLM-Based Log-linear Modeling in R | p. 161 |
8.2 Design Matrices in SYSTAT | p. 168 |
8.3 Log-linear Modeling with Design Matrices in lem | p. 174 |
8.3.1 The Hierarchical Log-linear Modeling Option in lem | p. 175 |
8.3.2 Using lem's Command cov to Specify Hierarchical Log-linear Models | p. 178 |
8.3.3 Using lem's Command fac to Specify Hierarchical Log-linear Models | p. 181 |
9 Nonhierarchical and Nonstandard Log-linear Models | p. 185 |
9.1 Defining Nonhierarchical and Nonstandard Log-linear Models | p. 186 |
9.2 Virtues of Nonhierarchical and Nonstandard Log-linear Models | p. 186 |
9.3 Scenarios for Nonstandard Log-linear Models | p. 188 |
9.3.1 Nonstandard Models for the Examination of Subgroups | p. 188 |
9.3.2 Nonstandard Nested Models | p. 193 |
9.3.3 Models with Structural Zeros I: Blanking out Cells | p. 196 |
9.3.4 Models with Structural Zeros II: Specific Incomplete Tables | p. 203 |
9.3.5 Models with Structural Zeros III: The Reduced Table Strategy | p. 205 |
9.3.6 Models with Quantitative Factors I: Quantitative Information in Univariate Marginals | p. 207 |
9.3.7 Models With Quantitative Factors II: Linear-by-Linear Interaction Models | p. 217 |
9.3.8 Models with Log-multiplicative Effects | p. 223 |
9.3.9 Logit Models | p. 223 |
9.3.10 Using Log-linear Models to Test Causal Hypotheses | p. 224 |
9.3.11 Models for Series of Observations I: Axial Symmetry | p. 229 |
9.3.12 Models for Series of Observations II: The Chain Concept | p. 237 |
9.3.13 Considering Continuous Covariates | p. 241 |
9.4 Nonstandard Scenarios: Summary and Discussion | p. 244 |
9.5 Schuster's Approach to Parameter Interpretation | p. 247 |
10 Computations III: Nonstandard Models | p. 255 |
10.1 Nonhierarchical and Nonstandard Models in R | p. 255 |
10.1.1 Nonhierarchical Models in R | p. 256 |
10.1.2 Nonstandard Models in R | p. 258 |
10.2 Estimating Nonhierarchical and Nonstandard Models with SYSTAT | p. 260 |
10.2.1 Nonhierarchical Models in SYSTAT | p. 261 |
10.2.2 Nonstandard Models in SYSTAT | p. 264 |
10.3 Estimating Nonhierarchical and Nonstandard Models with lem | p. 270 |
10.3.1 Nonhierarchical Models in lem p. 270 | |
10.3.2 Nonstandard Models in lem | p. 273 |
11 Sampling Schemes and Chi-square Decomposition | p. 277 |
11.1 Sampling Schemes | p. 277 |
11.2 Chi-Square Decomposition | p. 280 |
11.2.1 Partitioning Cross-classifications of Polytomous Variables | p. 282 |
11.2.2 Constraining Parameters | p. 287 |
11.2.3 Local Effects Models | p. 289 |
11.2.4 Caveats | p. 291 |
12 Symmetry Models | p. 293 |
12.1 Axial Symmetry | p. 293 |
12.2 Point Symmetry | p. 298 |
12.3 Point-axial Symmetry | p. 299 |
12.4 Symmetry in higher dimensional Cross-Classifications | p. 300 |
12.5 Quasi-Symmetry | p. 301 |
12.6 Extensions and Other Symmetry Models | p. 305 |
12.6.1 Symmetry in Two-Group Turnover Tables | p. 305 |
12.6.2 More Extensions of the Model of Axial Symmetry | p. 307 |
12.7 Marginal Homogeneity: Symmetry in the Marginals | p. 309 |
13 Log-linear Models of Rater Agreement | p. 313 |
13.1 Measures of Rater Agreement in Contingency Tables | p. 313 |
13.2 The Equal Weight Agreement Model | p. 317 |
13.3 The Differential Weight Agreement Model | p. 319 |
13.4 Agreement in Ordinal Variables | p. 320 |
13.5 Extensions of Rater Agreement Models | p. 323 |
13.5.1 Agreement of Three Raters | p. 323 |
13.5.2 Rater-Specific Trends | p. 328 |
14 Comparing Associations in Subtables: Homogeneity of Associations | p. 331 |
14.1 The Mantel-Haenszel and Breslow-Day Tests | p. 331 |
14.2 Log-linear Models to Test Homogeneity of Associations | p. 334 |
14.3 Extensions and Generalizations | p. 339 |
15 Logistic Regression and Logit Models | p. 345 |
15.1 Logistic Regression | p. 345 |
15.2 Log-linear Representation of Logistic Regression Models | p. 350 |
15.3 Overdispersion in Logistic Regression | p. 353 |
15.4 Logistic Regression versus Log-linear Modeling | p. 355 |
15.5 Logit Models and Discriminant Analysis | p. 357 |
15.6 Path Models | p. 363 |
16 Reduced Designs | p. 371 |
16.1 Fundamental Principles for Factorial Design | p. 372 |
16.2 The Resolution Level of a Design | p. 373 |
16.3 Sample Fractional Factorial Designs | p. 376 |
17 Computations IV: Additional Models | p. 387 |
17.1 Additional Log-linear Models in R | p. 387 |
17.1.1 Axial Symmetry Models in R | p. 387 |
17.1.2 Modeling Rater Agreement in R | p. 389 |
17.1.3 Modeling Homogeneous Associations in R | p. 391 |
17.1.4 Logistic Regression in R | p. 392 |
17.1.5 Some Helpful R Packages | p. 396 |
17.2 Additional Log-linear Models in SYSTAT | p. 396 |
17.2.1 Axial Symmetry Models in SYSTAT | p. 396 |
17.2.2 Modeling Rater Agreement in SYSTAT: Problems with Continuous Covariates | p. 402 |
17.2.3 Modeling the Homogeneous Association Hypothesis in SYSTAT | p. 404 |
17.2.4 Logistic Regression in SYSTAT | p. 407 |
17.3 Additional Log-linear Models in lem | p. 412 |
17.3.1 Axial Symmetry Models in lem | p. 413 |
17.3.2 Modeling Rater Agreement in lem | p. 415 |
17.3.3 Modeling the Homogeneous Association Hypothesis in lem | p. 417 |
17.3.4 Logistic Regression in lem | p. 419 |
17.3.5 Path Modeling in lem | p. 421 |
References | p. 425 |
Topic Index | p. 441 |
Author Index | p. 447 |