Regression for categorical data
لتكبير النص لتصغير النص- كتاب
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.
العنوان |
Regression for categorical data / Gerhard Tutz. [electronic resource] |
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الناشر |
Cambridge : Cambridge University Press |
تاريخ الإصدار |
2012 |
ملاحظات |
Title from publisher's bibliographic system (viewed on 05 Oct 2015). Includes bibliographical references and indexes. English |
رقم الرف |
Cover Regression for Categorical Data Title Copyright Contents Preface 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 Response1.3.2 Structured Multicategorical Regression 1.3.3 Multivariate Regression Structuring the Dependent Variables 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 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 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 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 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 |
سلسلة |
Cambridge series on statistical and probabilistic mathematics 34 |
الشكل |
1 online resource (x, 561 pages) : digital, PDF file(s). |
اللغة |
الانكليزية |
رقم النظام |
997010707358005171 |
MARC RECORDS
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