Regression for categorical data /

"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 cas...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Tutz, Gerhard
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, 2012.
Colección:Cambridge series on statistical and probabilistic mathematics.
Temas:
Regression analysis.
Categories (Mathematics)
Regression Analysis
Analyse de régression.
Catégories (Mathématiques)
MATHEMATICS > Probability & Statistics > Regression Analysis.
Regression analysis
Kategoriale Daten
Regressionsanalyse
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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