Categorical Data Analysis / Edition 1

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Summarizes methods used for the analysis of categorical data, including many recently developed techniques. The emphasis is on loglinear and logit modeling techniques, which share many features with linear model methods for continuous variables. Incorporated into the exposition is interesting historical information (and controversies) on the development of categorical data analysis. Chapters 1-7 cover bivariate categorical data and loglinear and logit model building; chapters 8-11 discuss applications and methods; chapters 12 and 13 address theoretical foundations.
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Editorial Reviews

From the Publisher
“…the essential reference text for statisticians…comprehensive and readable…” (Statistical Methods in Medical Research, Vol. 14, 2005)

"...careful, thorough, up-to-date volume...the new content and emphases in the second edition are sufficient to justify its purchase even by someone who already owns the first edition." (Journal of the American Statistical Association, June 2004)

"I liked this revised edition and recommend it highly to statisticians and graduate students." (Journal of Statistical Computation & Simulation, March 2004)

"...a highly satisfactory text on methods for categorical response variables...more complete and technical [than the First Edition]..." (IIE Transactions on Quality and Reliability Engineering)

"If you own the 1E, you absolutely need to upgrade to the 2E. If you do any analysis of categorical data, this is an essential desktop reference..." (Technometrics, Vol. 45, No. 1, February 2003)

"...this classic book is substantially modified and expanded..." (International Journal of General Systems, Vol. 32, 2003)

" is a total delight reading this book, which should be considered as the current standard textbook for teaching analysis of categorical data." (Pharmaceutical Research, Vol. 20, No. 6, June 2003)

"...written in a highly scientific but vivid style, intelligible for all researchers in that field...simply expressed, grand..." (Zentralblatt Math, 2004)

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Product Details

  • ISBN-13: 9780471853015
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 5/28/1990
  • Series: Wiley Series in Probability and Statistics Series , #218
  • Edition description: Older Edition
  • Edition number: 1
  • Pages: 576
  • Product dimensions: 6.42 (w) x 9.33 (h) x 1.34 (d)

Meet the Author

ALAN AGRESTI is Distinguished Professor Emeritus in the Department of Statistics at the University of Florida. He has presented short courses on categorical data methods in thirty countries. He is the author of five other books, including An Introduction to Categorical Data Analysis, Second Edition and Analysis of Ordinal Categorical Data, Second Edition, both published by Wiley.

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Table of Contents

1 Introduction: Distributions and Inference for Categorical Data 1
1.1 Categorical Response Data 1
1.2 Distributions for Categorical Data 5
1.3 Statistical Inference for Categorical Data 9
1.4 Statistical Inference for Binomial Parameters 14
1.5 Statistical Inference for Multinomial Parameters 21
2 Describing Contingency Tables 36
2.1 Probability Structure for 'Contingency Tables 36
2.2 Comparing Two Proportions 43
2.3 Partial Association in Stratified 2 X 2 Tables 47
2.4 Extensions for I X J Tables 54
3 Inference for Contingency Tables 70
3.1 Confidence Intervals for Association Parameters 70
3.2 Testing Independence in Two-Way Contingency Tables 78
3.3 Following-Up Chi-Squared Tests 80
3.4 Two-Way Tables with Ordered Classifications 86
3.5 Small-Sample Tests of Independence 91
3.6 Small-Sample Confidence Intervals for 2 X 2 Tables 98
3.7 Extensions for Multiway Tables and Nontabulated Responses 101
4 Introduction to Generalized Linear Models 115
4.1 Generalized Linear Model 116
4.2 Generalized Linear Models for Binary Data 120
4.3 Generalized Linear Models for Counts 125
4.4 Moments and Likelihood for Generalized Linear Models 132
4.5 Inference for Generalized Linear Models 139
4.6 Fitting Generalized Linear Models 143
4.7 Quasi-likelihood and Generalized Linear Models 149
4.8 Generalized Additive Models 153
5 Logistic Regression 165
5.1 Interpreting Parameters in Logistic Regression 166
5.2 Inference for Logistic Regression 172
5.3 Logit Models with Categorical Predictors 177
5.4 Multiple Logistic Regression 182
5.5 Fitting Logistic Regression Models 192
6 Building and Applying Logistic Regression Models 211
6.1 Strategies in Model Selection 211
6.2 Logistic Regression Diagnostics 219
6.3 Inference About Conditional Associations in 2 X 2 X K Tables 230
6.4 Using Models to Improve Inferential Power 236
6.5 Sample Size and Power Considerations 240
6.6 Probit and Complementary Log-Log Models 245
6.7 Conditional Logistic Regression and Exact Distributions 250
7 Logit Models for Multinomial Responses 267
7.1 Nominal Responses: Baseline-Category Logit Models 267
7.2 Ordinal Responses: Cumulative Logit Models 274
7.3 Ordinal Responses: Cumulative Link Models 282
7.4 Alternative Models for Ordinal Responses 286
7.5 Testing Conditional Independence in I X J X K Tables 293
7.6 Discrete-Choice Multinomial Logit Models 298
8 Loglinear Models for Contingency Tables 314
8.1 Loglinear Models for Two-Way Tables 314
8.2 Loglinear Models for Independence and Interaction in Three-Way Tables 318
8.3 Inference for Loglinear Models 324
8.4 Loglinear Models for Higher Dimensions 326
8.5 The Loglinear-Logit Model Connection 330
8.6 Loglinear Model Fitting: Likelihood Equations and Asymptotic Distributions 333
8.7 Loglinear Model Fitting: Iterative Methods and their Application 342
9 Building and Extending Loglinear/Logit Models 357
9.1 Association Graphs and Collapsibility 357
9.2 Model Selection and Comparison 360
9.3 Diagnostics for Checking Models 366
9.4 Modeling Ordinal Associations 367
9.5 Association Models 373
9.6 Association Models, Correlation Models, and Correspondence Analysis 379
9.7 Poisson Regression for Rates 385
9.8 Empty Cells and Sparseness in Modeling Contingency Tables 391
10 Models for Matched Pairs 409
10.1 Comparing Dependent Proportions 410
10.2 Conditional Logistic Regression for Binary Matched Pairs 414
10.3 Marginal Models for Square Contingency Tables 420
10.4 Symmetry, Quasi-symmetry, and Quasi-independence 423
10.5 Measuring Agreement Between Observers 431
10.6 Bradley-Terry Model for Paired Preferences 436
10.7 Marginal Models and Quasi-symmetry Models for Matched Sets 439
11 Analyzing Repeated Categorical Response Data 455
11.1 Comparing Marginal Distributions: Multiple Responses 456
11.2 Marginal Modeling: Maximum Likelihood Approach 459
11.3 Marginal Modeling: Generalized Estimating Equations Approach 466
11.4 Quasi-likelihood and Its GEE Multivariate Extension: Details 470
11.5 Markov Chains: Transitional Modeling 476
12 Random Effects: Generalized Linear Mixed Models for Categorical Responses 491
12.1 Random Effects Modeling of Clustered Categorical Data 492
12.2 Binary Responses: Logistic-Normal Model 496
12.3 Examples of Random Effects Models for Binary Data 502
12.4 Random Effects Models for Multinomial Data 513
12.5 Multivariate Random Effects Models for Binary Data 516
12.6 GLMM Fitting, Inference, and Prediction 520
13 Other Mixture Models for Categorical Data 538
13.1 Latent Class Models 538
13.2 Nonparametric Random Effects Models 545
13.3 Beta-Binomial Models 553
13.4 Negative Binomial Regression 559
13.5 Poisson Regression with Random Effects 563
14 Asymptotic Theory for Parametric Models 576
14.1 Delta Method 577
14.2 Asymptotic Distributions of Estimators of Model Parameters and Cell Probabilities 582
14.3 Asymptotic Distributions of Residuals and Goodness-of-Fit Statistics 587
14.4 Asymptotic Distributions for Logit/Loglinear Models 592
15 Alternative Estimation Theory for Parametric Models 600
15.1 Weighted Least Squares for Categorical Data 600
15.2 Bayesian Inference for Categorical Data 604
15.3 Other Methods of Estimation 611
16 Historical Tour of Categorical Data Analysis 619
16.1 Pearson-Yule Association Controversy 619
16.2 R. A. Fisher's Contributions 622
16.3 Logistic Regression 624
16.4 Multiway Contingency Tables and Loglinear Models 625
16.5 Recent (and Future?) Developments 629
App. A Using Computer Software to Analyze Categorical Data 632
App. B Chi-Squared Distribution Values 654
References 655
Examples Index 689
Author Index 693
Subject Index 701
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