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Cover image for Loglinear modeling : concepts, interpretation, and application
Title:
Loglinear modeling : concepts, interpretation, and application
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Publication Information:
New York : Wiley, 2013
Physical Description:
xv, 450 pages : illustrations ; 25 cm.
ISBN:
9781118146408
Abstract:
"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"-- Provided by publisher.
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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 models

Throughout 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

Prefacep. xi
Acknowledgmentsp. xv
1 Basics of Hierarchical Log-linear Modelsp. 1
1.1 Scaling: Which Variables Are Considered Categorical?p. 1
1.2 Crossing Two or More Variablesp. 4
1.3 Goodman's Three Elementary Views of Log-linear Modelingp. 8
1.4 Assumptions Made for Log-linear Modelingp. 9
2 Effects in a Tablep. 13
2.1 The Null Modelp. 13
2.2 The Row Effects-Only Modelp. 15
2.3 The Column Effects-Only Modelp. 15
2.4 The Row- and Column-Effects Modelp. 16
2.5 Log-Linear Modelsp. 18
3 Goodness-of-Fitp. 23
3.1 Goodness-of-Fit I: Overall Fit Statisticsp. 23
3.1.1 Selecting between X 2 and G 2p. 25
3.1.2 Degrees of Freedomp. 29
3.2 Goodness-of-Fit II: R 2 Equivalents and Information Criteriap. 29
3.2.1 R 2 Equivalentsp. 30
3.2.2 Information Criteriap. 32
3.3 Goodness-of-Fit III: Null Hypotheses Concerning Parametersp. 35
3.4 Goodness-of-fit IV: Residual Analysisp. 36
3.4.1 Overall Goodness-of-Fit Measures and Residualsp. 36
3.4.2 Other Residual Measuresp. 38
3.4.3 Comparing Residual Measuresp. 42
3.4.4 A Procedure to Identify Extreme Cellsp. 44
3.4.5 Distributions of Residualsp. 48
3.5 The Relationship between Pearson's X 2 and Log-linear Modelingp. 52
4 Hierarchical Log-linear Models and Odds Ratio Analysisp. 55
4.1 The Hierarchy of Log-linear Modelsp. 55
4.2 Comparing Hierarchically Related Modelsp. 57
4.3 Odds Ratios and Log-linear Modelsp. 63
4.4 Odds Ratios in Tables Larger than 2 x 2p. 65
4.5 Testing Null Hypotheses in Odds-Ratio Analysisp. 70
4.6 Characteristics of the Odds Ratiop. 72
4.7 Application of the Odds Ratiop. 75
4.8 The Four Steps to Take When Log-linear Modelingp. 81
4.9 Collapsibilityp. 86
5 Computations I: Basic Log-linear Modelingp. 99
5.1 Log-linear Modeling in Rp. 99
5.2 Log-linear Modeling in SYSTATp. 104
5.3 Log-linear Modeling in lemp. 108
6 The Design Matrix Approachp. 115
6.1 The Generalized Linear Model (GLM)p. 115
6.1.1 Logit Modelsp. 117
6.1.2 Poisson Modelsp. 118
6.1.3 GLM for Continuous Outcome Variablesp. 119
6.2 Design Matrices: Codingp. 119
6.2.1 Dummy Codingp. 120
6.2.2 Effect Codingp. 124
6.2.3 Orthogonality of Vectors in Log-linear Design Matricesp. 127
6.2.4 Design Matrices and Degrees of Freedomp. 129
7 Parameter Interpretation and Significance Testsp. 133
7.1 Parameter Interpretation Based on Design Matricesp. 134
7.2 The Two Sources of Parameter Correlation: Dependency of Vectors and Data Characteristicsp. 143
7.3 Can Main Effects Be Interpreted?p. 147
7.3.1 Parameter Interpretation in Main Effect Modelsp. 147
7.3.2 Parameter Interpretation in Models with Interactionsp. 150
7.4 Interpretation of Higher Order Interactionsp. 154
8 Computations II: Design Matrices and Poisson GLMp. 161
8.1 GLM-Based Log-linear Modeling in Rp. 161
8.2 Design Matrices in SYSTATp. 168
8.3 Log-linear Modeling with Design Matrices in lemp. 174
8.3.1 The Hierarchical Log-linear Modeling Option in lemp. 175
8.3.2 Using lem's Command cov to Specify Hierarchical Log-linear Modelsp. 178
8.3.3 Using lem's Command fac to Specify Hierarchical Log-linear Modelsp. 181
9 Nonhierarchical and Nonstandard Log-linear Modelsp. 185
9.1 Defining Nonhierarchical and Nonstandard Log-linear Modelsp. 186
9.2 Virtues of Nonhierarchical and Nonstandard Log-linear Modelsp. 186
9.3 Scenarios for Nonstandard Log-linear Modelsp. 188
9.3.1 Nonstandard Models for the Examination of Subgroupsp. 188
9.3.2 Nonstandard Nested Modelsp. 193
9.3.3 Models with Structural Zeros I: Blanking out Cellsp. 196
9.3.4 Models with Structural Zeros II: Specific Incomplete Tablesp. 203
9.3.5 Models with Structural Zeros III: The Reduced Table Strategyp. 205
9.3.6 Models with Quantitative Factors I: Quantitative Information in Univariate Marginalsp. 207
9.3.7 Models With Quantitative Factors II: Linear-by-Linear Interaction Modelsp. 217
9.3.8 Models with Log-multiplicative Effectsp. 223
9.3.9 Logit Modelsp. 223
9.3.10 Using Log-linear Models to Test Causal Hypothesesp. 224
9.3.11 Models for Series of Observations I: Axial Symmetryp. 229
9.3.12 Models for Series of Observations II: The Chain Conceptp. 237
9.3.13 Considering Continuous Covariatesp. 241
9.4 Nonstandard Scenarios: Summary and Discussionp. 244
9.5 Schuster's Approach to Parameter Interpretationp. 247
10 Computations III: Nonstandard Modelsp. 255
10.1 Nonhierarchical and Nonstandard Models in Rp. 255
10.1.1 Nonhierarchical Models in Rp. 256
10.1.2 Nonstandard Models in Rp. 258
10.2 Estimating Nonhierarchical and Nonstandard Models with SYSTATp. 260
10.2.1 Nonhierarchical Models in SYSTATp. 261
10.2.2 Nonstandard Models in SYSTATp. 264
10.3 Estimating Nonhierarchical and Nonstandard Models with lemp. 270
10.3.1 Nonhierarchical Models in lem

p. 270

10.3.2 Nonstandard Models in lemp. 273
11 Sampling Schemes and Chi-square Decompositionp. 277
11.1 Sampling Schemesp. 277
11.2 Chi-Square Decompositionp. 280
11.2.1 Partitioning Cross-classifications of Polytomous Variablesp. 282
11.2.2 Constraining Parametersp. 287
11.2.3 Local Effects Modelsp. 289
11.2.4 Caveatsp. 291
12 Symmetry Modelsp. 293
12.1 Axial Symmetryp. 293
12.2 Point Symmetryp. 298
12.3 Point-axial Symmetryp. 299
12.4 Symmetry in higher dimensional Cross-Classificationsp. 300
12.5 Quasi-Symmetryp. 301
12.6 Extensions and Other Symmetry Modelsp. 305
12.6.1 Symmetry in Two-Group Turnover Tablesp. 305
12.6.2 More Extensions of the Model of Axial Symmetryp. 307
12.7 Marginal Homogeneity: Symmetry in the Marginalsp. 309
13 Log-linear Models of Rater Agreementp. 313
13.1 Measures of Rater Agreement in Contingency Tablesp. 313
13.2 The Equal Weight Agreement Modelp. 317
13.3 The Differential Weight Agreement Modelp. 319
13.4 Agreement in Ordinal Variablesp. 320
13.5 Extensions of Rater Agreement Modelsp. 323
13.5.1 Agreement of Three Ratersp. 323
13.5.2 Rater-Specific Trendsp. 328
14 Comparing Associations in Subtables: Homogeneity of Associationsp. 331
14.1 The Mantel-Haenszel and Breslow-Day Testsp. 331
14.2 Log-linear Models to Test Homogeneity of Associationsp. 334
14.3 Extensions and Generalizationsp. 339
15 Logistic Regression and Logit Modelsp. 345
15.1 Logistic Regressionp. 345
15.2 Log-linear Representation of Logistic Regression Modelsp. 350
15.3 Overdispersion in Logistic Regressionp. 353
15.4 Logistic Regression versus Log-linear Modelingp. 355
15.5 Logit Models and Discriminant Analysisp. 357
15.6 Path Modelsp. 363
16 Reduced Designsp. 371
16.1 Fundamental Principles for Factorial Designp. 372
16.2 The Resolution Level of a Designp. 373
16.3 Sample Fractional Factorial Designsp. 376
17 Computations IV: Additional Modelsp. 387
17.1 Additional Log-linear Models in Rp. 387
17.1.1 Axial Symmetry Models in Rp. 387
17.1.2 Modeling Rater Agreement in Rp. 389
17.1.3 Modeling Homogeneous Associations in Rp. 391
17.1.4 Logistic Regression in Rp. 392
17.1.5 Some Helpful R Packagesp. 396
17.2 Additional Log-linear Models in SYSTATp. 396
17.2.1 Axial Symmetry Models in SYSTATp. 396
17.2.2 Modeling Rater Agreement in SYSTAT: Problems with Continuous Covariatesp. 402
17.2.3 Modeling the Homogeneous Association Hypothesis in SYSTATp. 404
17.2.4 Logistic Regression in SYSTATp. 407
17.3 Additional Log-linear Models in lemp. 412
17.3.1 Axial Symmetry Models in lemp. 413
17.3.2 Modeling Rater Agreement in lemp. 415
17.3.3 Modeling the Homogeneous Association Hypothesis in lemp. 417
17.3.4 Logistic Regression in lemp. 419
17.3.5 Path Modeling in lemp. 421
Referencesp. 425
Topic Indexp. 441
Author Indexp. 447
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