Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Binary Regression: The Logit Model
- 3 Generalized Linear Models
- 4 Modeling of Binary Data
- 5 Alternative Binary Regression Models
- 6 Regularization and Variable Selection for Parametric Models
- 7 Regression Analysis of Count Data
- 8 Multinomial Response Models
- 9 Ordinal Response Models
- 10 Semi- and Non-Parametric Generalized Regression
- 11 Tree-Based Methods
- 12 The Analysis of Contingency Tables: Log-Linear and Graphical Models
- 13 Multivariate Response Models
- 14 Random Effects Models and Finite Mixtures
- 15 Prediction and Classification
- A Distributions
- B Some Basic Tools
- C Constrained Estimation
- D Kullback-Leibler Distance and Information-Based Criteria of Model Fit
- E Numerical Integration and Tools for Random Effects Modeling
- List of Examples
- Bibliography
- Author Index
- Subject Index
8 - Multinomial Response Models
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 Binary Regression: The Logit Model
- 3 Generalized Linear Models
- 4 Modeling of Binary Data
- 5 Alternative Binary Regression Models
- 6 Regularization and Variable Selection for Parametric Models
- 7 Regression Analysis of Count Data
- 8 Multinomial Response Models
- 9 Ordinal Response Models
- 10 Semi- and Non-Parametric Generalized Regression
- 11 Tree-Based Methods
- 12 The Analysis of Contingency Tables: Log-Linear and Graphical Models
- 13 Multivariate Response Models
- 14 Random Effects Models and Finite Mixtures
- 15 Prediction and Classification
- A Distributions
- B Some Basic Tools
- C Constrained Estimation
- D Kullback-Leibler Distance and Information-Based Criteria of Model Fit
- E Numerical Integration and Tools for Random Effects Modeling
- List of Examples
- Bibliography
- Author Index
- Subject Index
Summary
In many regression problems the response is restricted to a fixed set of possible values, the so-called response categories. Response variables of this type are called polytomous or multicategory responses. In economical applications, the response categories may refer to the choice of different brands or to the choice of the transport mode (Example 1.3). In medical applications, the response categories may represent different side effects of medical treatment or several types of infection that may follow an operation. Most rating scales have fixed response categories that measure, for example, the medical condition after some treatment in categories like good, fair, and poor or the severeness of symptoms in categories like none, mild, moderate, marked. These examples show that there are at least two cases to be distinguished, namely, the case where response categories are mere labels that have no inherent ordering and the case where categories are ordered. In the first case, the response Y is measured on a nominal scale. Instead of using the numbers 1, …, k for the response categories, any set of k numbers would do. In the latter case, the response is measured on an ordinal scale, where the ordering of the categories and the corresponding numbers may be interpreted but not the distance or spacing between categories. Figures 8.1 and 8.2 illustrate different scalings of response categories. In the nominal case the response categories are given in an unsystematic way, while in the ordinal case the response categories are given on a straight line, thus illustrating the ordering of the categories.
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- Regression for Categorical Data , pp. 207 - 240Publisher: Cambridge University PressPrint publication year: 2011
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