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E-raamat: Generalized Linear Models for Categorical and Continuous Limited Dependent Variables

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(The Australian National University, Canberra), (University of Missouri, Columbia, USA)
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Generalized Linear Models for Categorical and Continuous Limited Dependent VariablesSuurem pilt
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"Designed for graduate students and researchers in the behavioral, social, health, and medical sciences, this text employs generalized linear models, including mixed models, for categorical and limited dependent variables. Categorical variables include both nominal and ordinal variables. Discrete or continuous limited dependent variables have restricted support, whether through censorship or truncation or by their nature. The book incorporates examples of truncated counts, censored continuous variables, and doubly bounded continuous variables, such as percentages. "--

"This book is devoted to dependent variables other than those for which linear regression is appropriate. The authors argue that such dependent variables are, if anything, more common throughout the human sciences than the kind that suit linear regression. Presenting a broader but unified coverage in which the authors attempt to integrate concepts and ideas shared across models and types of data broader but unified coverage in which we attempt to integrate the concepts and ideas shared across models and types of data, especially regarding conceptual links between discrete and continuous limited dependent variables"--

Designed for graduate students and researchers in the behavioral, social, health, and medical sciences, this text employs generalized linear models, including mixed models, for categorical and limited dependent variables. Categorical variables include both nominal and ordinal variables. Discrete or continuous limited dependent variables have restricted support, whether through censorship or truncation or by their nature. The book incorporates examples of truncated counts, censored continuous variables, and doubly bounded continuous variables, such as percentages.

Arvustused

" a very useful contribution for anyone who needs modern extensions of statistical modeling tools. I was also impressed with the elegant way in which the authors went about the demanding task of explaining complex methods to readers." International Statistical Review, 2015

"What new perspective or emphasis could be brought to this crowded market? This contribution from Smithson and Merkle is distinctive in several respects. It is geared toward a social-science audience The authors cover an impressive amount of ground in one book, the authors cover many different models for a wide array of discrete and limited dependent variables (LDVs). a valuable resource for graduate students and practitioners in psychology, political science, international relations, anthropology, sociology, education, and communication . The Beta GLM and some of the models for censored and truncated responses are much newer and more exotic than say, logistic regression or count models, making Smithson and Merkles book a welcome addition even for seasoned practitioners ." Journal of the American Statistical Association, June 2015

Preface xiii
List of Figures
xvii
List of Tables
xix
Notation xxi
About the Authors xxiii
1 Introduction and Overview
1(14)
1.1 The Nature of Limited Dependent Variables
1(1)
1.2 Overview of GLMs
2(4)
1.2.1 Definition
2(2)
1.2.2 Extensions
4(2)
1.3 Estimation Methods and Model Evaluation
6(6)
1.3.1 Model Evaluation and Diagnosis
6(3)
1.3.2 Model Selection and Interpretation Issues
9(3)
1.4 Organization of This Book
12(3)
I Discrete Variables
15(136)
2 Binary Variables
17(34)
2.1 Logistic Regression
18(2)
2.2 The Binomial GLM
20(12)
2.2.1 Latent Variable Interpretation
22(1)
2.2.2 Interpretation of Coefficients
22(3)
2.2.3 Example
25(2)
2.2.4 Extension to n > 1
27(3)
2.2.5 Alternative Link Functions
30(2)
2.3 Estimation Methods and Issues
32(8)
2.3.1 Model Evaluation and Diagnostics
32(6)
2.3.2 Overdispersion
38(1)
2.3.3 Relationships to Other Models
39(1)
2.4 Analyses in R and Stata
40(9)
2.4.1 Analyses in R
40(5)
2.4.2 Analyses in Stata
45(4)
2.5 Exercises
49(2)
3 Nominal Polytomous Variables
51(30)
3.1 Multinomial Logit Model
51(7)
3.2 Conditional Logit and Choice Models
58(3)
3.3 Multinomial Processing Tree Models
61(5)
3.4 Estimation Methods and Model Evaluation
66(5)
3.4.1 Estimation Methods and Model Comparison
66(1)
3.4.2 Model Evaluation and Diagnosis
67(4)
3.5 Analyses in R and Stata
71(9)
3.5.1 Analyses in R
71(6)
3.5.2 Analyses in Stata
77(3)
3.6 Exercises
80(1)
4 Ordinal Categorical Variables
81(32)
4.1 Modeling Ordinal Variables: Common Practice versus Best Practice
81(1)
4.2 Ordinal Model Alternatives
82(2)
4.2.1 The Proportional Odds Assumption
82(1)
4.2.2 Modeling Relative Probabilities
83(1)
4.3 Cumulative Models
84(5)
4.3.1 The Proportional Odds Model
84(2)
4.3.2 Example
86(3)
4.4 Adjacent Models
89(2)
4.4.1 The Adjacent Categories Model
89(1)
4.4.2 Example
90(1)
4.5 Stage Models
91(6)
4.5.1 The Continuation Ratio Model
92(2)
4.5.2 Example
94(3)
4.6 Estimation Methods and Issues
97(5)
4.6.1 Model Choice
98(1)
4.6.2 Model Diagnostics
98(4)
4.7 Analyses in R and Stata
102(9)
4.7.1 Analyses in R
102(5)
4.7.2 Analyses in Stata
107(4)
4.8 Exercises
111(2)
5 Count Variables
113(38)
5.1 Distributions for Count Data
113(3)
5.2 Poisson Regression Models
116(7)
5.2.1 Model Definition
116(2)
5.2.2 Example
118(1)
5.2.3 Exposure
119(1)
5.2.4 Overdispersion and Quasi-Poisson Models
120(3)
5.3 Negative Binomial Models
123(2)
5.3.1 Model Definition
123(2)
5.3.2 Example
125(1)
5.4 Truncated and Censored Models
125(2)
5.5 Zero-Inflated and Hurdle Models
127(6)
5.5.1 Hurdle Models
127(3)
5.5.2 Zero-Inflated Models
130(3)
5.6 Estimation Methods and Issues
133(4)
5.6.1 Negative Binomial Model Estimation
133(1)
5.6.2 Model Diagnostics
133(4)
5.7 Analyses in R and Stata
137(11)
5.7.1 Analyses in R
138(6)
5.7.2 Analyses in Stata
144(4)
5.8 Exercises
148(3)
II Continuous Variables
151(110)
6 Doubly Bounded Continuous Variables
153(40)
6.1 Doubly Bounded versus Censored
153(1)
6.2 The beta GLM
153(6)
6.3 Modeling Location and Dispersion
159(7)
6.3.1 Judged Probability of Guilt
160(2)
6.3.2 Reading Accuracy for Dyslexic and Non-Dyslexic Readers
162(2)
6.3.3 Model Comparison
164(2)
6.4 Estimation Methods and Issues
166(10)
6.4.1 Estimator Bias
168(3)
6.4.2 Model Diagnostics
171(5)
6.5 Zero- and One-Inflated Models
176(2)
6.6 Finite Mixture Models
178(4)
6.6.1 Car Dealership Example
180(2)
6.7 Analyses in R and Stata
182(9)
6.7.1 Analyses in R
182(4)
6.7.2 Analyses in Stata
186(5)
6.8 Exercises
191(2)
7 Censoring and Truncation
193(42)
7.1 Models for Censored and Truncated Variables
193(10)
7.1.1 Tobit Models
197(6)
7.2 Non-Gaussian Censored Regression
203(5)
7.3 Estimation Methods, Model Comparison, and Diagnostics
208(3)
7.4 Extensions of Censored Regression Models
211(11)
7.4.1 Proportional Hazard and Proportional Odds Models
212(2)
7.4.2 Double and Interval Censoring
214(6)
7.4.3 Censored Quantile Regression
220(2)
7.5 Analyses in R and Stata
222(10)
7.5.1 Analyses in R
222(6)
7.5.2 Analyses in Stata
228(4)
7.6 Exercises
232(3)
8 Extensions
235(26)
8.1 Extensions and Generalizations
235(1)
8.2 Multilevel Models
236(9)
8.2.1 Multilevel Binary Logistic Regression
236(3)
8.2.2 Multilevel Count Models
239(2)
8.2.3 Multilevel Beta Regression
241(4)
8.3 Bayesian Estimation
245(11)
8.3.1 Bayesian Binomial GLM
247(3)
8.3.2 Bayesian Beta Regression
250(3)
8.3.3 Modeling Random Sums
253(3)
8.4 Evaluating Relative Importance of Predictors in GLMs
256(5)
References 261(14)
Author Index 275(6)
Subject Index 281
Michael Smithson, Edgar C. Merkle
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