Introduction to the Statistical Analysis of Categorical Data

1 Introduction.- 1.1 The two-way table.- 2 Basic Theory.- 2.1 Introduction.- 2.2 Exponential families.- 2.3 Statistical inference in an exponential family.- 2.4 The binomial distribution.- 2.5 The multinomial distribution.- 2.6 The Poisson distribution.- 2.7 Composite hypotheses.- 2.8 Applications to the multinomial distribution.- 2.9 Log-linear models.- 2.10 The two-way contingency table.- 2.11 The numerical solution of the likelihood equations for the log-linear model.- 2.12 Bibliographical notes.- 2.13 Exercises.- 3 Three-way contingency tables.- 3.1 Log-linear models.- 3.2 Log-linear hypotheses.- 3.3 Estimation.- 3.4 Testing hypotheses.- 3.5 Interpretation of the log-linear parameters.- 3.6 Choice of model.- 3.7 Detection of model deviations.- 3.8 Bibliographical notes.- 3.9 Exercises.- 4 Multi-dimensional contingency tables.- 4.1 The log-linear model.- 4.2 Classification and interpretation of log-linear models.- 4.3 Choice of model.- 4.4 Diagnostics.- 4.5 Model search strategies.- 4.6 Bibliographical notes.- 4.7 Exercises.- 5 Incomplete Tables.- 5.1 Random and structural zeros.- 5.2 Counting the number of degrees of freedom.- 5.3 Validity of the X2-approximation.- 5.4 Exercises.- 6 The Logit Model.- 6.1 The logit model.- 6.2 Hypothesis testing in the logit model.- 6.3 Logit models with higher order interactions.- 6.4 The logit model as a regression model.- 6.5 Bibliographical notes.- 6.6 Exercises.- 7 Logistic Regression Analysis.- 7.1 The logistic regression model.- 7.2 Estimation in the logistic regression model.- 7.3 Numerical solution of the likelihood equations.- 7.4 Checking the fit of the model.- 7.5 Hypothesis testing.- 7.6 Diagnostics.- 7.7 Predictions.- 7.8 Dummy variables.- 7.9 Polytomous response variables.- 7.10 Bibliographical notes.- 7.11 Exercises.-8 Association Models.- 8.1 Introduction.- 8.2 Symmetry models.- 8.3 Marginal homogeneity.- 8.4 RC-association models.- 8.5 Correspondence analysis.- 8.6 Bibliographical notes.- 8.5 Exercises.- Appendix Solutions and output to selected exercises.- References.