European University Institute Library

Regression for categorical data, Gerhard Tutz

eng

Includes bibliographical references and indexes

illustrations

index present

non fiction

Regression for categorical data

bibliography

700468349

Gerhard Tutz

Cambridge series in statistical and probabilistic mathematics

"Categorical data play an important role in many statistical analyses. They appear whenever the outcomes of one or more categorical variables are observed. A categorical variable can be seen as a variable for which the possible values form a set of categories, which can be finite or, in the case of count data, infinite. These categories can be records of answers (yes/no) in a questionnaire, diagnoses like normal/abnormal resulting from a medical examination or choices of brands in consumer behaviour. Data of this type are common in all sciences that use quantitative research tools, for example social sciences, economics, biology, genetics and medicine, but also engineering and agriculture. In some applications all of the observed variables are categorical and the resulting data can be summarized in contingency tables which contain the counts for combinations of possible outcomes. In other applications categorical data are collected together with continuous variables and one wants to investigate the dependence of one or more categorical variables on continuous and/or categorical variables"--, Provided by publisher

ch. 1 Introduction -- 1.1 Categorical Data: Examples and Basic Concepts -- 1.1.1 Some Examples -- 1.1.2 Classification of Variables -- Scale Levels: Nominal and Ordinal Variables -- Discrete and Continuous Variables -- 1.2 Organization of This Book -- 1.3 Basic Components of Structured Regression -- 1.3.1 Structured Univariate Regression -- Structuring the Dependent Variable -- Structuring the Influential Term -- Linear Predictor -- Categorical Explanatory Variables -- Additive Predictor -- Tree-Based Methods -- The Link between Covariates and Response1.3.2 Structured Multicategorical Regression -- 1.3.3 Multivariate Regression -- Structuring the Dependent Variables -- Structuring the Influential Term -- 1.3.4 Statistical Modeling -- 1.4 Classical Linear Regression -- 1.4.1 Interpretation and Coding of Covariates -- Quantitative Explanatory Variables -- Binary Explanatory Variables -- Multicategorical Explanatory Variables or Factors -- 1.4.2 Linear Regression in Matrix Notation -- 1.4.3 Estimation -- Least-Squares Estimation -- Maximum Likelihood Estimation -- Properties of Estimates -- 1.4.4 Residuals and Hat Matrix -- Case Deletion as Diagnostic Tool1.4.5 Decomposition of Variance and Coefficient of Determination -- 1.4.6 Testing in Multiple Linear Regression -- Submodels and the Testing of Linear Hypotheses -- 1.5 Exercises -- ch. 2 Binary Regression: The Logit Model -- 2.1 Distribution Models for Binary Responses and Basic Concepts -- 2.1.1 Single Binary Variables -- 2.1.2 The Binomial Distribution -- Odds, Logits, and Odds Ratios -- Comparing Two Groups -- 2.2 Linking Response and Explanatory Variables -- 2.2.1 Deficiencies of Linear Models -- 2.2.2 Modeling Binary Responses -- Binary Responses as Dichotomized Latent VariablesModeling the Common Distribution of a Binary and a Continuous Distribution -- Basic Form of Binary Regression Models -- 2.3 The Logit Model -- 2.3.1 Model Representations -- 2.3.2 Logit Model with Continuous Predictor -- Multivariate Predictor -- 2.3.3 Logit Model with Binary Predictor -- Logit Model with (0-1)-Coding of Covariates -- Logit Model with Effect Coding -- 2.3.4 Logit Model with Categorical Predictor -- Logit Model with (0-1)-Coding -- Logit Model with Effect Coding -- Logit Model with Several Categorical Predictors -- 2.3.5 Logit Model with Linear Predictor -- 2.4 The Origins of the Logistic Function and the Logit Model2.5 Exercises -- ch. 3 Generalized Linear Models -- 3.1 Basic Structure -- 3.2 Generalized Linear Models for Continuous Responses -- 3.2.1 Normal Linear Regression -- 3.2.2 Exponential Distribution -- 3.2.3 Gamma-Distributed Responses -- 3.2.4 Inverse Gaussian Distribution -- 3.3 GLMs for Discrete Responses -- 3.3.1 Models for Binary Data -- 3.3.2 Models for Binomial Data -- 3.3.3 Poisson Model for Count Data -- 3.3.4 Negative Binomial Distribution -- 3.4 Further Concepts -- 3.4.1 Means and Variances -- 3.4.2 Canonical Link -- 3.4.3 Extensions Including Offsets