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Regression for Categorical Data 1st Edition by Gerhard Tutz ISBN 1107009650 9781107009653

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Author(s): Gerhard Tutz, Ludwig-Maximilians-Universität Munchen
ISBN(s): 9781107009653, 1107009650
Edition: 1st edition
File Details: PDF, 6.05 MB
Year: 2012
Language: english
SKU: EB-7314984 Category: Tags: ,

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ISBN 10: 1107009650 
ISBN 13: 9781107009653
Author: Gerhard Tutz

This book introduces basic and advanced concepts of categorical regression with a focus on the structuring constituents of regression, including regularization techniques to structure predictors. In addition to standard methods such as the logit and probit model and extensions to multivariate settings, the author presents more recent developments in flexible and high-dimensional regression, which allow weakening of assumptions on the structuring of the predictor and yield fits that are closer to the data. A generalized linear model is used as a unifying framework whenever possible in particular parametric models that are treated within this framework. Many topics not normally included in books on categorical data analysis are treated here, such as nonparametric regression; selection of predictors by regularized estimation procedures; ternative models like the hurdle model and zero-inflated regression models for count data; and non-standard tree-based ensemble methods. The book is accompanied by an R package that contains data sets and code for all the examples.

Regression for Categorical Data 1st Table of contents:

Chapter 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 Response
1.3.2 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 Tool
1.4.5 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

Chapter 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 Variables
Modeling 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 Model
2.5 Exercises

Chapter 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
3.5 Modeling of Grouped Data
3.6 Maximum Likelihood Estimation
Log-Likelihood and Score Function
Information Matrix
3.7 Inference
3.7.1 The Deviance
3.7.2 Analysis of Deviance and the Testing of Hypotheses
Analysis of Deviance
3.7.3 Alternative Test Statistics for Linear Hypotheses
3.8 Goodness-of-Fit for Grouped Observations
3.8.1 The Deviance for Grouped Observations
3.8.2 Pearson Statistic
3.9 Computation of Maximum Likelihood Estimates
3.10 Hat Matrix for Generalized Linear Models
3.11 Quasi-Likelihood Modeling
3.12 Further Reading
3.13 Exercises

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