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Introduction to the Statistical Analysis of Categorical Data


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Table of Contents

Introduction: The two-way Table.- Basic Theory: Exponential families; Statistical inference in an exponential family; The binomial distribution; The Poisson distribution; Composite hypotheses; Applications to the multinomial distribution; Log-linear models; The two-way contingency table; The numerical solution of the likelihood equations for the log-linear model.- Three-way contingency tables: Log-linear models; Log-linear hypotheses; Estimation; testing hypotheses; Interpretation of the log-linear parameters; Choice of model; Detection of model deviations.- Multi-dimensional contingency tables: The log-linear-model; Classification and interpretation of log-linear models; Choice of model; Diagnostics; Model search strategies.- Incomplete Tables: Random and structural zeros; Counting th number of degrees of freedom; Validity of the X2-approximation.- The Logit Model: The Logit model; Hypothesis testing in the logit model; Logit models with higher order interactions; The Logit model as a regression model.- Logistic Regression Analysis: The logistic regression model; Estimation in the logistic regression model; Numerical solution of the likelihood equations; Checking the fit of the model; Hypothesis testing; Diagnostics; Predictions; Dummy variables; Polytomous response variables.- Association Models: Symmetry models; Marginal homogeneity; RC-association models; Correspondence analysis.- Appendix: Solutions and output to selected excercises.

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