Regression for categorical data:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2012
|
| Series: | Cambridge series in statistical and probabilistic mathematics
[34] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | X, 561 S. graph. Darst., Kt. |
| ISBN: | 9781107009653 |
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Record in the Search Index
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| adam_text | Contents
Preface
ix
1
Introduction
1
1.1
Categorical Data: Examples and Basic Concepts
................. 1
1.2
Organization of This Book
............................ 5
1.3
Basic Components of Structured Regression
................... 6
1.4
Classical Linear Regression
............................ 15
1.5
Exercises
..................................... 27
2
Binary Regression: The Logit Model
29
2.1
Distribution Models for Binary Responses and Basic Concepts
......... 29
2.2
Linking Response and Explanatory Variables
.................. 33
2.3
The Logit Model
................................. 37
2.4
The Origins of the Logistic Function and the Logit Model
............ 48
2.5
Exercises
..................................... 49
3
Generalized Linear Models
51
3.1
Basic Structure
.................................. 51
3.2
Generalized Linear Models for Continuous Responses
.............. 53
3.3
GLMs for Discrete Responses
.......................... 56
3.4
Further Concepts
................................. 60
3.5
Modeling of Grouped Data
............................ 62
3.6
Maximum Likelihood Estimation
......................... 63
3.7
Inference
..................................... 67
3.8
Goodness-of-Fit for Grouped Observations
................... 72
3.9
Computation of Maximum Likelihood Estimates
................ 75
3.10
Hat Matrix for Generalized Linear Models
.................... 76
3.11
Quasi-Likelihood Modeling
............................ 78
3.12
Further Reading
.................................. 79
3.13
Exercises
..................................... 79
4
Modeling of Binary Data
81
4.1
Maximum Likelihood Estimation
......................... 82
4.2
Discrepancy between Data and Fit
........................ 87
4.3
Diagnostic Checks
................................ 93
4.4
Structuring the Linear Predictor
......................... 101
4.5
Comparing Non-Nested Models
......................... 113
4.6
Explanatory Value of Covariates
......................... 114
4.7
Further Reading
.................................. 119
4.8
Exercises
..................................... 120
vi
CONTENTS
5
Alternative
Binary Regression Models
123
5.1
Alternative Links in Binary Regression
...................... 123
5.2
The Missing Link
................................. 130
5.3
Overdispersion
.................................. 132
5.4
Conditional Likelihood
.............................. 138
5.5
Further Reading
.................................. 140
5.6
Exercises
..................................... 140
6
Regularizaron
and Variable Selection for Parametric Models
143
6.1
Classical Subset Selection
............................ 144
6.2
Regularization by Penalization
.......................... 145
6.3
Boosting Methods
................................. 163
6.4
Simultaneous Selection of Link Function and Predictors
............. 170
6.5
Categorical Predictors
............................... 173
6.6
Bayesian Approach
................................ 178
6.7
Further Reading
.................................. 179
6.8
Exercises
..................................... 179
7
Regression Analysis of Count Data
181
7.1
The
Poisson
Distribution
............................. 182
7.2
Poisson
Regression Model
............................ 185
7.3
Inference for the
Poisson
Regression Model
................... 186
7.4
Poisson
Regression with an Offset
........................ 190
7.5
Poisson
Regression with Overdispersion
..................... 192
7.6
Negative Binomial Model and Alternatives
.................... 194
7.7
Zero-Inflated Counts
............................... 198
7.8
Hurdle Models
.................................. 200
7.9
Further Reading
.................................. 203
7.10
Exercises
..................................... 204
8
Multinomial Response Models
207
8.1
The Multinomial Distribution
........................... 209
8.2
The Multinomial Logit Model
.......................... 210
8.3
Multinomial Model as Random Utility Model
.................. 215
8.4
Structuring the Predictor
............................. 215
8.5
Logit Model as Multivariate Generalized Linear Model
............. 217
8.6
Inference for Multicategorical Response Models
................. 218
8.7
Multinomial Models with Hierarchically Structured Response
......... 223
8.8
Discrete Choice Models
.............................. 226
8.9
Nested Logit Model
................................ 231
8.10
Regularization for the Multinomial Model
.................... 233
8.11
Further Reading
.................................. 238
8.12
Exercises
..................................... 239
9
Ordinal Response Models
241
9.1
Cumulative Models
................................ 243
9.2
Sequential Models
................................ 252
9.3
Further Properties and Comparison of Models
.................. 255
9.4
Alternative Models
................................ 257
9.5
Inference for Ordinal Models
........................... 261
CONTENTS
VU
9.6
Further Reading
.................................. 265
9.7
Exercises
..................................... 265
10
Semi- and Non-Parametric Generalized Regression
269
10.1
Univariate Generalized Non-Parametric Regression
............... 269
10.2
Non-Parametric Regression with Multiple Covariates
.............. 285
10.3
Structured Additive Regression
.......................... 289
10.4
Functional Data and Signal Regression
...................... 307
10.5
Further Reading
.................................. 313
10.6
Exercises
..................................... 314
11
Tree-Based Methods
317
11.1
Regression and Classification Trees
....................... 317
11.2
Multivariate Adaptive Regression Splines
.................... 328
11.3
Further Reading
.................................. 329
11.4
Exercises
..................................... 329
12
The Analysis of Contingency Tables: Log-Linear and Graphical Models
331
12.1
Types of Contingency Tables
........................... 332
12.2
Log-Linear Models for Two-Way Tables
..................... 335
12.3
Log-Linear Models for Three-Way Tables
.................... 338
12.4
Specific Log-Linear Models
........................... 341
12.5
Log-Linear and Graphical Models for Higher Dimensions
............ 345
12.6
Collapsibility
................................... 348
12.7
Log-Linear Models and the Logit Model
..................... 349
12.8
Inference for Log-Linear Models
......................... 350
12.9
Model Selection and Regularization
....................... 354
12.10
Mosaic Plots
................................... 357
12.11
Further Reading
................................. 358
12.12
Exercises
..................................... 359
13
Multivariate Response Models
363
13.1
Conditional Modeling
............................... 365
13.2
Marginal Parametrization and Generalized Log-Linear Models
......... 370
13.3
General Marginal Models: Association as Nuisance and GEEs
......... 371
13.4
Marginal Homogeneity
.............................. 385
13.5
Further Reading
.................................. 392
13.6
Exercises
..................................... 393
14
Random Effects Models and Finite Mixtures
395
14.1
Linear Random Effects Models for Gaussian Data
................ 396
14.2
Generalized Linear Mixed Models
........................ 402
14.3
Estimation Methods for Generalized Mixed Models
............... 407
14.4
Multicategorical Response Models
........................ 416
14.5
The Marginalized Random Effects Model
.................... 419
14.6
Latent Trait Models and Conditional ML
..................... 420
14.7
Semiparametric Mixed Models
.......................... 420
14.8
Finite Mixture Models
.............................. 422
14.9
Further Reading
.................................. 426
14.10
Exercises
..................................... 427
viii CONTENTS
15
Prediction and Classification
429
15.1
Basic Concepts of Prediction
........................... 430
15.2
Methods for Optimal Classification
........................ 438
15.3
Basics of Estimated Classification Rules
..................... 445
15.4
Parametric Classification Methods
........................ 451
15.5
Non-Parametric Methods
............................. 457
15.6
Neural Networks
................................. 468
15.7
Examples
..................................... 471
15.8
Variable Selection in Classification
........................ 473
15.9
Prediction of Ordinal Outcomes
......................... 474
15.10
Model-Based Prediction
............................. 480
15.11
Further Reading
................................. 481
15.12
Exercises
..................................... 482
A Distributions
485
A.
1
Discrete Distributions
............................... 485
A.2 Continuous Distributions
............................. 487
В
Some Basic Tools
490
B.I Linear Algebra
.................................. 490
B.2 Taylor Approximation
............................... 491
B.3 Conditional Expectation, Distribution
...................... 493
B.4 EM Algorithm
................................... 494
С
Constrained Estimation
496
C.I Simplification of Penalties
............................ 496
C.2 Linear Constraints
................................. 498
C.3 Fisher Scoring with Penalty Term
........................ 499
D Kullback-Leibler
Distance and Information-Based Criteria of Model Fit
500
D.I Kullback-Leibler Distance
............................ 500
E
Numerical Integration and Tools for Random Effects Modeling
504
E.I Laplace Approximation
.............................. 504
E.2 Gauss-Hermite Integration
............................ 505
E.3 Inversion of Pseudo-Fisher Matrix
........................ 507
List of Examples
509
Bibliography
513
Author Index
545
Subject Index
554
This book introduces basic and advanced concepts of categorical regression with
a focus on the structuring constituents of regression. Meant for statisticians,
applied researchers, and students, it includes topics not normally included in books
on categorical data analysis, including recent developments in flexible and high-
dimensional regression.
In addition to standard methods such as logit and
probit
models and their
extensions to multivariate settings, the author presents more recent developments
in regularized regression with a focus on the seleciton of predictors; tools for flexible
non-parametric regression that yield fits that are closer to the data; advanced models
for count data; non-standard tree-based ensemble methods; and tools for the
handling of both nominal and ordered
categorial
predictors. Issues of prediction are
explicitly considered in a chapter that introduces standard and newer classification
techniques.
Software including an
R
package that contains
datasets
and code for most of
the examples is available from http://www.stat.uni-muenchen.de/~tutz/catdata.
Dr. Gerhard Tutz is a Professor in the Department of Statistics at
Ludwig-Maximilians
University, Munich. He was formerly a Professor at the Technical University Berlin. He
is the author or co-author of nine books and more than
100
papers.
CAMBRIDGE SERIES IN STATISTICAL AND PROBABILISTIC MATHEMATICS
Editorial Board:
Z. Ghahramani, Department of Engineering, University of Cambridge
R. Gill, Mathematical Institute, Leiden University
F. Kelly, Statistical Laboratory, University of Cambridge
B. D.
Ripley, Department of Statistics, University of Oxford
S. Ross, Department of Industrial
&
Systems Engineering, University of Southern
California
M. Stein, Department of Statistics, University of Chicago
This series of high-quality upper-division textbooks and expository monographs
covers all aspects of stochastic applicable mathematics. The topics range from pure
and applied statistics to probability theory, operations research, optimization,
and mathematical programming. The books contain clear presentations of new
developments in the field and also of the state of the art in classical methods. While
emphasizing rigorous treatment of theoretical methods, the books also contain
applications and discussions of new techniques made possible by advances in com¬
putational practice.
Cambridge
UNIVERSITY FRLSS
www Cambridge.org
ÌH
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107-00965-
|
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| indexdate | 2024-07-10T00:08:50Z |
| institution | BVB |
| isbn | 9781107009653 |
| language | English |
| lccn | 2011000390 |
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| spelling | Tutz, Gerhard 1950- Verfasser (DE-588)172422973 aut Regression for categorical data Gerhard Tutz Cambridge [u.a.] Cambridge Univ. Press 2012 X, 561 S. graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics [34] Regression analysis Categories (Mathematics) Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Kategoriale Daten (DE-588)4327512-6 gnd rswk-swf Kategoriale Daten (DE-588)4327512-6 s Regressionsanalyse (DE-588)4129903-6 s 1\p DE-604 Cambridge series in statistical and probabilistic mathematics [34] (DE-604)BV011442366 34 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024529798&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024529798&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tutz, Gerhard 1950- Regression for categorical data Cambridge series in statistical and probabilistic mathematics Regression analysis Categories (Mathematics) Regressionsanalyse (DE-588)4129903-6 gnd Kategoriale Daten (DE-588)4327512-6 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4327512-6 |
| title | Regression for categorical data |
| title_auth | Regression for categorical data |
| title_exact_search | Regression for categorical data |
| title_full | Regression for categorical data Gerhard Tutz |
| title_fullStr | Regression for categorical data Gerhard Tutz |
| title_full_unstemmed | Regression for categorical data Gerhard Tutz |
| title_short | Regression for categorical data |
| title_sort | regression for categorical data |
| topic | Regression analysis Categories (Mathematics) Regressionsanalyse (DE-588)4129903-6 gnd Kategoriale Daten (DE-588)4327512-6 gnd |
| topic_facet | Regression analysis Categories (Mathematics) Regressionsanalyse Kategoriale Daten |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024529798&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024529798&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011442366 |
| work_keys_str_mv | AT tutzgerhard regressionforcategoricaldata |