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Analysis of Ordinal Categorical Data / Alan Agresti.

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Statistical science's first coordinated manual of methods for analyzing ordered categorical data, now fully revised and updated, continues to present applications and case studies in fields as diverse as sociology, public health, ecology, marketing, and pharmacy. Analysis of Ordinal Categorical...

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Bibliographic Details
Online Access: Full Text (via ProQuest)
Main Author: Agresti, Alan (Author)
Format: eBook
Language:English
Published: Hoboken : John Wiley & Sons, 2012.
Edition:Second edition.
Subjects:
Multivariate analysis.
Multivariate analysis
Table of Contents:
  • Analysis of Ordinal Categorical Data, Second Edition; Contents; Preface; 1. Introduction; 1.1. Ordinal Categorical Scales; 1.2. Advantages of Using Ordinal Methods; 1.3. Ordinal Modeling Versus Ordinary Regession Analysis; 1.4. Organization of This Book; 2. Ordinal Probabilities, Scores, and Odds Ratios; 2.1. Probabilities and Scores for an Ordered Categorical Scale; 2.2. Ordinal Odds Ratios for Contingency Tables; 2.3. Confidence Intervals for Ordinal Association Measures; 2.4. Conditional Association in Three-Way Tables; 2.5. Category Choice for Ordinal Variables; Chapter Notes; Exercises.
  • 3. Logistic Regression Models Using Cumulative Logits3.1. Types of Logits for An Ordinal Response; 3.2. Cumulative Logit Models; 3.3. Proportional Odds Models: Properties and Interpretations; 3.4. Fitting and Inference for Cumulative Logit Models; 3.5. Checking Cumulative Logit Models; 3.6. Cumulative Logit Models Without Proportional Odds; 3.7. Connections with Nonparametric Rank Methods; Chapter Notes; Exercises; 4. Other Ordinal Logistic Regression Models; 4.1. Adjacent-Categories Logit Models; 4.2. Continuation-Ratio Logit Models.
  • 4.3. Stereotype Model: Multiplicative Paired-Category LogitsChapter Notes; Exercises; 5. Other Ordinal Multinomial Response Models; 5.1. Cumulative Link Models; 5.2. Cumulative Probit Models; 5.3. Cumulative Log-Log Links: Proportional Hazards Modeling; 5.4. Modeling Location and Dispersion Effects; 5.5. Ordinal ROC Curve Estimation; 5.6. Mean Response Models; Chapter Notes; Exercises; 6. Modeling Ordinal Association Structure; 6.1. Ordinary Loglinear Modeling; 6.2. Loglinear Model of Linear-by-Linear Association; 6.3. Row or Column Effects Association Models.
  • 6.4. Association Models for Multiway Tables6.5. Multiplicative Association and Correlation Models; 6.6. Modeling Global Odds Ratios and Other Associations; Chapter Notes; Exercises; 7. Non-Model-Based Analysis of Ordinal Association; 7.1. Concordance and Discordance Measures of Association; 7.2. Correlation Measures for Contingency Tables; 7.3. Non-Model-Based Inference for Ordinal Association Measures; 7.4. Comparing Singly Ordered Multinomials; 7.5. Order-Restricted Inference with Inequality Constraints; 7.6. Small-Sample Ordinal Tests of Independence.
  • 7.7. Other Rank-Based Statistical Methods for Ordered CategoriesAppendix: Standard Errors for Ordinal Measures; Chapter Notes; Exercises; 8. Matched-Pairs Data with Ordered Categories; 8.1. Comparing Marginal Distributions for Matched Pairs; 8.2. Models Comparing Matched Marginal Distributions; 8.3. Models for The Joint Distribution in A Square Table; 8.4. Comparing Marginal Distributions for Matched Sets; 8.5. Analyzing Rater Agreement on an Ordinal Scale; 8.6. Modeling Ordinal Paired Preferences; Chapter Notes; Exercises; 9. Clustered Ordinal Responses: Marginal Models.
  • 2.4 Conditional Association in Three-Way Tables
  • 2.4.1 Summary Measures of Conditional Association
  • 2.4.2 Example: Association Between Political Views and Party, by Education
  • 2.5 Category Choice for Ordinal Variables
  • 2.5.1 Finer Categorizations Provide More Power for Detecting Associations
  • 2.5.2 Finer Categorizations Describe Conditional Associations Better
  • 2.5.3 Guidelines for Category Choice
  • Chapter Notes
  • Exercises
  • Chapter 3 Logistic Regression Models Using Cumulative Logits
  • 3.1 Types of Logits for An Ordinal Response
  • 3.1.1 Cumulative Logits
  • 3.1.2 Adjacent-Categories Logits
  • 3.1.3 Continuation-Ratio Logits
  • 3.1.4 Ordinal Models Use Ordinal Logits Simultaneously
  • 3.2 Cumulative Logit Models
  • 3.2.1 Cumulative Logit Model: Continuous Predictor
  • 3.2.2 Alternative Parameterization with -β'x Predictor
  • 3.2.3 Cumulative Logit Model for Contingency Table: Quantitative Predictor
  • 3.2.4 Cumulative Logit Model for Contingency Table: Qualitative Predictor
  • 3.2.5 Example: Astrology Beliefs and Educational Attainment
  • 3.3 Proportional Odds Models: Properties and Interpretations
  • 3.3.1 Proportional Odds Property
  • 3.3.2 Latent Variable Motivation
  • 3.3.3 Invariance to Choice of Response Categories
  • 3.3.4 Interpretations Comparing Response Probabilities
  • 3.4 Fitting and Inference for Cumulative Logit Models
  • 3.4.1 Maximum Likelihood Model Fitting
  • 3.4.2 Estimating Standard Errors
  • 3.4.3 Inference About Model Parameters and Probabilities
  • 3.4.4 Example: Mental Health by Life Events and SES
  • 3.4.5 Infinite Model Parameter Estimates
  • 3.4.6 Summarizing Predictive Power of Explanatory Variables
  • 3.4.7 Classifying Observations into Ordered Categories
  • 3.5 Checking Cumulative Logit Models.

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