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The Statistical Analysis of Categorical Data

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概要 The aim of this book is to give an up to date account of the most commonly uses statisti cal models for categorical data. The emphasis is on the connection between theory and applications to real data... sets. The book only covers models for categorical data. Various models for mixed continuous and categorical data are thus excluded. The book is written as a textbook, although many methods and results are quite recent. This should imply, that the book can be used for a graduate course in categorical data analysis. With this aim in mind chapters 3 to 12 are concluded with a set of exer cises. In many cases, the data sets are those data sets, which were not included in the examples of the book, although they at one point in time were regarded as potential can didates for an example. A certain amount of general knowledge of statistical theory is necessary to fully benefit from the book. A summary of the basic statistical concepts deemed necessary pre requisites is given in chapter 2. The mathematical level is only moderately high, but the account in chapter 3 of basic properties of exponential families and the parametric multinomial distribution is made as mathematical precise as possible without going into mathematical details and leaving out most proofs.続きを見る
目次 1. Categorical Data
2. Preliminaries
2.1 Statistical models
2.2 Estimation
2.3 Testing statistical hypotheses
2.4 Checking the model
3. Statistical Inference
3.1 Log-linear models
3.2 The one-dimensional case
3.3 The multi-dimensional case
3.4 Testing composite hypotheses
3.5 The parametric multinomial distribution
3.6 Generalized linear models
3.7 Solution of likelihood equations
3.8 Exercises
4. Two-way Contingency Tables
4.1 Three models
4.2 The 2x2 table
4.3 The log-linear parameterization
4.4 The hypothesis of no interaction
4.5 Residual analysis
4.6 Exercises
5. Three-way Contingency Tables
5.1 The log-linear parameterization
5.2 Hypothesis in a three-way table
5.3 Hypothesis testing
5.4 Decomposition of the test statistic
5.5 Detection of model departures
5.6 Exercises
6. Multi-dimension Contingency Tables
6.1 The log-linear model
6.2 Interpretation of log-linear models
6.3 Search for a model
6.4 Diagnostics for model departures
6.5 Exercises
7. Incomplete Tables, Separability and Collapsibility
7.1 Incomplete tables
7.2 Two-way tables and quasi-independence
7.3 Higher order tables. Separability
7.4 Collapsibility
7.5 Exercises
8. The Logit Model
8.1 The logit-model with binary explanatory variables
8.2 The logit model with polytomous explanatory variables
8.3 Exercises
9. Logistic Regression Analysis
9.1 The logistic regression model
9.2 Regression diagnostics
9.3 Predictions
9.4 Polytomous response variables
9.5 Exercises
10. Models for the Interactions
10.1 Introduction
10.2 Symmetry models
10.3 Marginal homogeneity
10.4 Models for mobility tables
10.5 Association models
10.6 RC-association models
10.7 Log-linear association models
10.8 Exercises
11. Correspondence Analysis
11.1 Correspondence analysis for two-way tables
11.2 Correspondence analysis for multi-way tables
11.3 Comparison of models
11.4 Exercises
12. Latent Structure Analysis
12.1 Latent structure models
12.2 Latent class models
12.3 Continuous latent structure models
12.4 The EM-algorithm
12.5 Estimation in the latent class model
12.6 Estimation in the continuous latent structure model
12.7 Testing the goodness of fit
12.8 Diagnostics
12.9 Score models with varying discriminating powers
12.10 Comparison of latent structure models
12.11 Estimation of the latent variable
12.12 Exercises
13. Computer Programs
References
Author Index
Examples with Data.
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登録日 2020.06.27
更新日 2020.06.28