COVID-19 Response at Fishpond

An Introduction to Categorical Data Analysis
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Preface ix About the Companion Website xiii 1 Introduction 1 1.1 Categorical Response Data 1 1.2 Probability Distributions for Categorical Data 3 1.3 Statistical Inference for a Proportion 5 1.4 Statistical Inference for Discrete Data 10 1.5 Bayesian Inference for Proportions * 13 1.6 Using R Software for Statistical Inference about Proportions * 17 Exercises 21 2 Analyzing Contingency Tables 25 2.1 Probability Structure for Contingency Tables 26 2.2 Comparing Proportions in 2 x 2 Contingency Tables 29 2.3 The Odds Ratio 31 2.4 Chi-Squared Tests of Independence 36 2.5 Testing Independence for Ordinal Variables 42 2.6 Exact Frequentist and Bayesian Inference * 46 2.7 Association in Three-Way Tables 52 Exercises 56 3 Generalized Linear Models 65 3.1 Components of a Generalized Linear Model 66 3.2 Generalized Linear Models for Binary Data 68 3.3 Generalized Linear Models for Counts and Rates 72 3.4 Statistical Inference and Model Checking 76 3.5 Fitting Generalized Linear Models 82 Exercises 84 4 Logistic Regression 89 4.1 The Logistic Regression Model 89 4.2 Statistical Inference for Logistic Regression 94 4.3 Logistic Regression with Categorical Predictors 98 4.4 Multiple Logistic Regression 102 4.5 Summarizing Effects in Logistic Regression 107 4.6 Summarizing Predictive Power: Classification Tables, ROC Curves, and Multiple Correlation 110 Exercises 113 5 Building and Applying Logistic Regression Models 123 5.1 Strategies in Model Selection 123 5.2 Model Checking 130 5.3 Infinite Estimates in Logistic Regression 136 5.4 Bayesian Inference, Penalized Likelihood, and Conditional Likelihood for Logistic Regression * 140 5.5 Alternative Link Functions: Linear Probability and Probit Models * 145 5.6 Sample Size and Power for Logistic Regression * 150 Exercises 151 6 Multicategory Logit Models 159 6.1 Baseline-Category Logit Models for Nominal Responses 159 6.2 Cumulative Logit Models for Ordinal Responses 167 6.3 Cumulative Link Models: Model Checking and Extensions * 176 6.4 Paired-Category Logit Modeling of Ordinal Responses * 184 Exercises 187 7 Loglinear Models for Contingency Tables and Counts 193 7.1 Loglinear Models for Counts in Contingency Tables 194 7.2 Statistical Inference for Loglinear Models 200 7.3 The Loglinear - Logistic Model Connection 207 7.4 Independence Graphs and Collapsibility 210 7.5 Modeling Ordinal Associations in Contingency Tables 214 7.6 Loglinear Modeling of Count Response Variables * 217 Exercises 221 8 Models for Matched Pairs 227 8.1 Comparing Dependent Proportions for Binary Matched Pairs 228 8.2 Marginal Models and Subject-Specific Models for Matched Pairs 230 8.3 Comparing Proportions for Nominal Matched-Pairs Responses 235 8.4 Comparing Proportions for Ordinal Matched-Pairs Responses 239 8.5 Analyzing Rater Agreement * 243 8.6 Bradley-Terry Model for Paired Preferences * 247 Exercises 249 9 Marginal Modeling of Correlated, Clustered Responses 253 9.1 Marginal Models Versus Subject-Specific Models 254 9.2 Marginal Modeling: The Generalized Estimating Equations (GEE) Approach 255 9.3 Marginal Modeling for Clustered Multinomial Responses 260 9.4 Transitional Modeling, Given the Past 263 9.5 Dealing with Missing Data * 266 Exercises 268 10 Random Effects: Generalized Linear Mixed Models 273 10.1 Random Effects Modeling of Clustered Categorical Data 273 10.2 Examples: Random Effects Models for Binary Data 278 10.3 Extensions to Multinomial Responses and Multiple Random Effect Terms 284 10.4 Multilevel (Hierarchical) Models 288 10.5 Latent Class Models * 291 Exercises 295 11 Classification and Smoothing * 299 11.1 Classification: Linear Discriminant Analysis 300 11.2 Classification: Tree-Based Prediction 302 11.3 Cluster Analysis for Categorical Responses 306 11.4 Smoothing: Generalized Additive Models 310 11.5 Regularization for High-Dimensional Categorical Data (Large p) 313 Exercises 321 12 A Historical Tour of Categorical Data Analysis * 325 Appendix: Software for Categorical Data Analysis 331 A.1 R for Categorical Data Analysis 331 A.2 SAS for Categorical Data Analysis 332 A.3 Stata for Categorical Data Analysis 342 A.4 SPSS for Categorical Data Analysis 346 Brief Solutions to Odd-Numbered Exercises 349 Bibliography 363 Examples Index 365 Subject Index 369  