Categorical Data Analysis / Edition 1

Categorical Data Analysis / Edition 1

by Alan Agresti

ISBN-10: 0471853011

ISBN-13: 9780471853015

Pub. Date: 05/28/1990

Publisher: Wiley

The past quarter-century has seen an explosion in the development of methods for analyzing categorical data. These methods have influenced—and been influenced by—the increasing availability of multivariate data sets with categorical responses in the social, behavioral, and biomedical sciences, as well as in public health, ecology, education, marketing,

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The past quarter-century has seen an explosion in the development of methods for analyzing categorical data. These methods have influenced—and been influenced by—the increasing availability of multivariate data sets with categorical responses in the social, behavioral, and biomedical sciences, as well as in public health, ecology, education, marketing, food science, and industrial quality control. Categorical Data Analysis describes the most important new methods, offering a unified presentation of modeling using generalized linear models and emphasizing loglinear and logit modeling techniques. Contributions of noted statisticians (Pearson, Yule, Fisher, Neyman, Cochran), whose pioneering efforts set the pace for the evolution of modern methods, are examined as well. Special features of the book include:

  • Coverage of methods for repeated measurement data, which have become increasingly important in biomedical applications
  • Prescriptions for how ordinal variables should be treated differently than nominal variables
  • Derivations of basic asymptotic and fixed-sample-size inferential methods
  • Discussion of exact small sample procedures
  • More than 40 examples of analyses of "real" data sets, including: aspirin use and heart disease; job satisfaction and income; seat belt use and injuries in auto accidents; and predicting outcomes of baseball games
  • More than 400 exercises to facilitate interpretation and application of methods
Categorical Data Analysis also contains an appendix that describes the use of computer software currently available for performing the analyses presented in the book. A comprehensive bibliography and notes at the end of each chapter round out the work, making it a complete, invaluable reference for statisticians, biostatisticians, and professional researchers.

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Product Details

Publication date:
Wiley Series in Probability and Statistics Series, #218
Edition description:
Older Edition
Product dimensions:
6.42(w) x 9.33(h) x 1.34(d)

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Table of Contents

1Introduction: Distributions and Inference for Categorical Data1
1.1Categorical Response Data1
1.2Distributions for Categorical Data5
1.3Statistical Inference for Categorical Data9
1.4Statistical Inference for Binomial Parameters14
1.5Statistical Inference for Multinomial Parameters21
2Describing Contingency Tables36
2.1Probability Structure for 'Contingency Tables36
2.2Comparing Two Proportions43
2.3Partial Association in Stratified 2 X 2 Tables47
2.4Extensions for I X J Tables54
3Inference for Contingency Tables70
3.1Confidence Intervals for Association Parameters70
3.2Testing Independence in Two-Way Contingency Tables78
3.3Following-Up Chi-Squared Tests80
3.4Two-Way Tables with Ordered Classifications86
3.5Small-Sample Tests of Independence91
3.6Small-Sample Confidence Intervals for 2 X 2 Tables98
3.7Extensions for Multiway Tables and Nontabulated Responses101
4Introduction to Generalized Linear Models115
4.1Generalized Linear Model116
4.2Generalized Linear Models for Binary Data120
4.3Generalized Linear Models for Counts125
4.4Moments and Likelihood for Generalized Linear Models132
4.5Inference for Generalized Linear Models139
4.6Fitting Generalized Linear Models143
4.7Quasi-likelihood and Generalized Linear Models149
4.8Generalized Additive Models153
5Logistic Regression165
5.1Interpreting Parameters in Logistic Regression166
5.2Inference for Logistic Regression172
5.3Logit Models with Categorical Predictors177
5.4Multiple Logistic Regression182
5.5Fitting Logistic Regression Models192
6Building and Applying Logistic Regression Models211
6.1Strategies in Model Selection211
6.2Logistic Regression Diagnostics219
6.3Inference About Conditional Associations in 2 X 2 X K Tables230
6.4Using Models to Improve Inferential Power236
6.5Sample Size and Power Considerations240
6.6Probit and Complementary Log-Log Models245
6.7Conditional Logistic Regression and Exact Distributions250
7Logit Models for Multinomial Responses267
7.1Nominal Responses: Baseline-Category Logit Models267
7.2Ordinal Responses: Cumulative Logit Models274
7.3Ordinal Responses: Cumulative Link Models282
7.4Alternative Models for Ordinal Responses286
7.5Testing Conditional Independence in I X J X K Tables293
7.6Discrete-Choice Multinomial Logit Models298
8Loglinear Models for Contingency Tables314
8.1Loglinear Models for Two-Way Tables314
8.2Loglinear Models for Independence and Interaction in Three-Way Tables318
8.3Inference for Loglinear Models324
8.4Loglinear Models for Higher Dimensions326
8.5The Loglinear-Logit Model Connection330
8.6Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions333
8.7Loglinear Model Fitting: Iterative Methods and their Application342
9Building and Extending Loglinear/Logit Models357
9.1Association Graphs and Collapsibility357
9.2Model Selection and Comparison360
9.3Diagnostics for Checking Models366
9.4Modeling Ordinal Associations367
9.5Association Models373
9.6Association Models, Correlation Models, and Correspondence Analysis379
9.7Poisson Regression for Rates385
9.8Empty Cells and Sparseness in Modeling Contingency Tables391
10Models for Matched Pairs409
10.1Comparing Dependent Proportions410
10.2Conditional Logistic Regression for Binary Matched Pairs414
10.3Marginal Models for Square Contingency Tables420
10.4Symmetry, Quasi-symmetry, and Quasi-independence423
10.5Measuring Agreement Between Observers431
10.6Bradley-Terry Model for Paired Preferences436
10.7Marginal Models and Quasi-symmetry Models for Matched Sets439
11Analyzing Repeated Categorical Response Data455
11.1Comparing Marginal Distributions: Multiple Responses456
11.2Marginal Modeling: Maximum Likelihood Approach459
11.3Marginal Modeling: Generalized Estimating Equations Approach466
11.4Quasi-likelihood and Its GEE Multivariate Extension: Details470
11.5Markov Chains: Transitional Modeling476
12Random Effects: Generalized Linear Mixed Models for Categorical Responses491
12.1Random Effects Modeling of Clustered Categorical Data492
12.2Binary Responses: Logistic-Normal Model496
12.3Examples of Random Effects Models for Binary Data502
12.4Random Effects Models for Multinomial Data513
12.5Multivariate Random Effects Models for Binary Data516
12.6GLMM Fitting, Inference, and Prediction520
13Other Mixture Models for Categorical Data538
13.1Latent Class Models538
13.2Nonparametric Random Effects Models545
13.3Beta-Binomial Models553
13.4Negative Binomial Regression559
13.5Poisson Regression with Random Effects563
14Asymptotic Theory for Parametric Models576
14.1Delta Method577
14.2Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities582
14.3Asymptotic Distributions of Residuals and Goodness-of-Fit Statistics587
14.4Asymptotic Distributions for Logit/Loglinear Models592
15Alternative Estimation Theory for Parametric Models600
15.1Weighted Least Squares for Categorical Data600
15.2Bayesian Inference for Categorical Data604
15.3Other Methods of Estimation611
16Historical Tour of Categorical Data Analysis619
16.1Pearson-Yule Association Controversy619
16.2R. A. Fisher's Contributions622
16.3Logistic Regression624
16.4Multiway Contingency Tables and Loglinear Models625
16.5Recent (and Future?) Developments629
App. AUsing Computer Software to Analyze Categorical Data632
App. BChi-Squared Distribution Values654
Examples Index689
Author Index693
Subject Index701

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