Loglinear modeling : concepts, interpretation, and application
 Author/Creator
 Eye, Alexander von.
 Language
 English.
 Publication
 Hoboken, New Jersey : Wiley, [2013]
 Copyright notice
 ©2013
 Physical description
 xv, 450 pages : illustrations ; 24 cm.
Access
Available online

Stacks

Unknown
QA278 .E95 2013

Unknown
QA278 .E95 2013
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Contributors
 Contributor
 Mun, Eun Young.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Preface xiii Acknowledgments xvii 1 Basics of Hierarchical Loglinear 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 Loglinear modeling 9 2 Effects in a Table 13 2.1 The Null Model 13 2.2 The Row EffectsOnly Model 15 2.3 The Column EffectsOnly Model 15 2.4 The Rowand ColumnEffectsModel 16 2.5 LogLinear Models 18 3 GoodnessofFit 23 3.1 Goodness of Fit I: Overall Fit Statistics 23 3.2 GoodnessofFit II: R2 Equivalents and Information Criteria 30 3.3 GoodnessofFit III: Null Hypotheses Concerning Parameters 35 3.4 Goodnessoffit IV: Residual Analysis 36 3.5 The Relationship Between Pearson's X2 and Loglinear Modeling 52 4 Hierarchical Loglinear Models and Odds Ratio Analysis 55 4.1 The Hierarchy of Loglinear Models 55 4.2 Comparing Hierarchically Related Models 57 4.3 Odds Ratios and LoglinearModels 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 LoglinearModeling 81 4.9 Collapsibility 86 5 Computations I: Basic Loglinear Modeling 97 5.1 Loglinear Modeling in R 97 5.2 Log linear Modeling in SYSTAT 102 5.3 Loglinear 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 GLMbased LoglinearModeling in R 157 8.2 Design Matrices in SYSTAT 164 8.3 LoglinearModeling with Design Matrices in lEM 170 9 Nonhierarchical and Nonstandard Loglinear Models 181 9.1 Defining Nonhierarchical and Nonstandard LoglinearModels 182 9.2 Virtues of Nonhierarchical and Nonstandard LoglinearModels 182 9.3 Scenarios for Nonstandard LoglinearModels 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 NonHierarchical and Nonstandard Models in R 251 10.2 Estimating NonHierarchical and Nonstandard Models with SYSTAT 256 10.3 Estimating NonHierarchical and Nonstandard Models with lEM 265 11 Sampling Schemes and Chisquare Decomposition 273 11.1 Sampling Schemes 273 11.2 ChiSquare Decomposition 276 12 Symmetry Models 289 12.1 Axial Symmetry 289 12.2 Pointsymmetry 294 12.3 Pointaxial Symmetry 295 12.4 Symmetry in HigherDimensional CrossClassifications 296 12.5 QuasiSymmetry 298 12.6 Extensions and Other Symmetry Models 301 12.7 Marginal Homogeneity: Symmetry in the Marginals 305 13 Loglinear 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 MantelHaenszel and BreslowDay Tests 327 14.2 LoglinearModels 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 Loglinear Representation of Logistic Regression Models 344 15.3 Overdispersion in Logistic Regression 347 15.4 Logistic Regression Versus Loglinear 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 LoglinearModels in R 379 17.2 Additional LoglinearModels in SYSTAT 388 17.3 Additional LoglinearModels in lEM 404 References 417.
 (source: Nielsen Book Data)
 Publisher's Summary
 Over the past ten years, there have been many important advances in loglinear modeling, including the specification of new models, in particular nonstandard 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 LogLinear Modelingpresents the topic in an accessible style that iscustomized for applied researchers who utilize loglinear modeling in the social sciences. The book begins by providing readers with a foundation on the basics of loglinear modeling, introducing decomposing effects in crosstabulations and goodnessoffit tests. Popular hierarchical loglinear models are illustrated using empirical data examples, and odds ratio analysis is discussed as an interesting method of analysis of crosstabulations. Next, readers are introduced to the design matrix approach to loglinear 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 nonhierarchical and nonstandard loglinear models, outlining ten nonstandard loglinear models (including nonstandard nested models, models with quantitative factors, logit models, and loglinear 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 chisquare 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 loglinear 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, utilizingempirical data examples to demonstrate the relevance of the topics in modern research.
(source: Nielsen Book Data)
Subjects
 Subject
 Loglinear models.
Bibliographic information
 Publication date
 2013
 Copyright date
 2013
 Responsibility
 Alexander von Eye, Michigan State University, Department of Psychology, East Lansing, MI, EunYoung Mun, Rutgers, The State University of New Jersey, Center for Alcohol Studies, Piscataway, NJ.
 Title Variation
 Loglinear modeling
 ISBN
 9781118146408 (hardback)
 1118146409 (hardback)