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Modeling Binary Correlated Responses using SAS, SPSS and R
von: Jeffrey R. Wilson, Kent A. Lorenz
Springer-Verlag, 2015
ISBN: 9783319238050 , 283 Seiten
Format: PDF, Online Lesen
Kopierschutz: Wasserzeichen
Preis: 53,49 EUR
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Preface
8
Part I: Introduction and Review of Modeling Uncorrelated Observations
10
Part II: Analyzing Correlated Data Through Random Component
11
Part III: Analyzing Correlated Data Through Systematic Components
15
Part IV: Analyzing Correlated Data Through the Joint Modeling of Mean and Variance
16
Contents
18
Part I: Introduction and Review of Modeling Uncorrelated Observations
25
Chapter 1: Introduction to Binary Logistic Regression
26
1.1 Motivating Example
26
1.2 Definition and Notation
27
1.2.1 Notations
27
1.2.2 Definitions
27
Categorical Variable in the Form of a Series of Binary Variables
28
Relationship Between Response and Predictor Variables
29
1.3 Exploratory Analyses
29
1.4 Statistical Models
31
1.4.1 Chapter 3: Standard Binary Logistic Regression Model
31
1.4.2 Chapter 4: Overdispersed Logistic Regression Model
31
1.4.3 Chapter 5: Survey Data Logistic Regression Model
32
1.4.4 Chapter 6: Generalized Estimating Equations Logistic Regression Model
32
1.4.5 Chapter 7: Generalized Method of Moments Logistic Regression Model
32
1.4.6 Chapter 8: Exact Logistic Regression Model
32
1.4.7 Chapter 9: Two-Level Nested Logistic Regression Model
33
1.4.8 Chapter 10: Hierarchical Logistic Regression Model
33
1.4.9 Chapter 11: Fixed Effects Logistic Regression Model
33
1.4.10 Chapter 12: Heteroscedastic Logistic Regression Model
33
1.5 Analysis of Data
34
1.5.1 SAS Programming
35
1.5.2 SPSS Programming
35
1.5.3 R Programming
35
1.6 Conclusions
36
1.7 Related Examples
37
1.7.1 Medicare Data
37
1.7.2 Philippines Data
37
1.7.3 Household Satisfaction Survey
38
1.7.4 NHANES: Treatment for Osteoporosis
38
References
39
Chapter 2: Short History of the Logistic Regression Model
40
2.1 Motivating Example
40
2.2 Definition and Notation
41
2.2.1 Notation
41
2.2.2 Definition
41
2.3 Exploratory Analyses
42
2.4 Statistical Model
43
2.5 Analysis of Data
45
2.6 Conclusions
45
References
46
Chapter 3: Standard Binary Logistic Regression Model
48
3.1 Motivating Example
49
3.1.1 Study Hypotheses
49
3.2 Definition and Notation
49
3.3 Exploratory Analyses
51
3.4 Statistical Models
54
3.4.1 Probability
55
3.4.2 Odds
55
3.4.3 Logits
56
3.4.4 Logistic Regression Versus Ordinary Least Squares
56
3.4.5 Generalized Linear Models
57
3.4.6 Response Probability Distributions
58
3.4.7 Log-Likelihood Functions
58
3.4.8 Maximum Likelihood Fitting
58
3.4.9 Goodness of Fit
59
3.4.10 Other Fit Statistics
59
3.4.11 Assumptions for Logistic Regression Model
60
3.4.12 Interpretation of Coefficients
60
3.4.13 Interpretation of Odds Ratio (OR)
60
3.4.14 Model Fit
61
3.4.15 Null Hypothesis
61
3.4.16 Predicted Probabilities
62
3.4.17 Computational Issues Encountered with Logistic Regression
63
3.5 Analysis of Data
63
3.5.1 Medicare Data
64
SAS Output
69
SAS Output
69
3.6 Conclusions
74
3.7 Related Examples
74
Appendix: Partial Medicare Data time=1
75
References
76
Part II: Analyzing Correlated Data Through Random Component
78
Chapter 4: Overdispersed Logistic Regression Model
79
4.1 Motivating Example
79
4.2 Definition and Notation
80
4.3 Exploratory Data Analyses
81
4.4 Statistical Model
82
4.4.1 Williams Method of Analysis
83
4.4.2 Overdispersion Factor
84
4.4.3 Datasets
85
4.4.4 Housing Satisfaction Survey
85
4.5 Analysis of Data
85
4.5.1 Standard Logistic Regression Model
86
4.5.2 Overdispersed Logistic Regression Model
89
4.5.3 Exchangeability Logistic Regression Model
95
4.6 Conclusions
99
4.7 Related Example
100
4.7.1 Use of Word Einai
100
References
100
Chapter 5: Weighted Logistic Regression Model
102
5.1 Motivating Example
103
5.2 Definition and Notation
103
5.3 Exploratory Analyses
104
5.3.1 Treatment for Osteoporosis
105
5.4 Statistical Model
106
5.5 Analysis of Data
107
5.5.1 Weighted Logistic Regression Model with Survey Weights
107
SAS Program
108
5.5.2 Weighted Logistic Regression Model with Strata and Clusters Identified
118
5.5.3 Comparison of Weighted Logistic Regression Models
121
5.6 Conclusions
121
5.7 Related Examples
121
References
122
Chapter 6: Generalized Estimating Equations Logistic Regression
124
6.1 Motivating Example
124
6.1.1 Description of the Rehospitalization Issues
124
Study Hypotheses
125
6.2 Definition and Notation
125
6.3 Exploratory Analyses
127
6.4 Statistical Models: GEE Logistic Regression
130
6.4.1 Medicare Data
130
6.4.2 Generalized Linear Model
131
6.4.3 Generalized Estimating Equations
131
6.4.4 Marginal Model
132
6.4.5 Working Correlation Matrices
132
6.4.6 Model Fit
133
6.4.7 Properties of GEE Estimates
134
6.5 Data Analysis
134
6.5.1 GEE Logistic Regression Model
134
SAS Output
139
GEE with INDEP and EXCH CORR structure
139
6.6 Conclusions
149
6.7 Related Examples
150
References
151
Chapter 7: Generalized Method of Moments Logistic Regression Model
152
7.1 Motivating Example
152
7.1.1 Description of the Case Study
152
Study Hypotheses
153
7.2 Definition and Notation
153
7.3 Exploratory Analyses
154
7.4 Statistical Model
157
7.4.1 GEE Models for Time-Dependent Covariates
158
7.4.2 Lai and Small GMM Method
159
Types of Classification of Time-Dependent Covariates
159
7.4.3 Lalonde Wilson and Yin Method
161
7.5 Analysis of Data
162
7.5.1 Modeling Probability of Rehospitalization
162
7.5.2 SAS Results
163
7.5.3 SAS OUTPUT (Partial)
164
7.6 Conclusions
165
7.7 Related Examples
166
References
166
Chapter 8: Exact Logistic Regression Model
168
8.1 Motivating Example
168
8.2 Definition and Notation
169
8.3 Exploratory Analysis
170
8.3.1 Artificial Data for Clustering
170
8.3.2 Standard Logistic Regression
171
Sparse and Skewed Correlated Binary Data
171
8.3.3 Two-Stage Clustered Data
172
8.4 Statistical Models
173
8.4.1 Independent Observations
173
8.4.2 One-Stage Cluster Model
173
8.4.3 Two-Stage Cluster Exact Logistic Regression Model
175
8.5 Analysis of Data
176
8.5.1 Exact Logistic Regression for Independent Observations
176
8.5.2 Exact Logistic Regression for One-Stage Clustered Data
183
8.5.3 Exact Logistic Regression for Two-Stage Clustered Data
184
8.6 Conclusions
184
8.7 Related Examples
185
8.7.1 Description of the Data
185
8.7.2 Clustering
185
References
186
Part III: Analyzing Correlated Data Through Systematic Components
188
Chapter 9: Two-Level Nested Logistic Regression Model
189
9.1 Motivating Example
189
9.1.1 Description of the Case Study
189
9.1.2 Study Hypotheses
190
9.2 Definition and Notation
190
9.3 Exploratory Analyses
191
9.3.1 Medicare
193
9.4 Statistical Model
193
9.4.1 Marginal and Conditional Models
194
9.4.2 Two-Level Nested Logistic Regression with Random Intercept Model
195
9.4.3 Interpretation of Parameter Estimates
196
9.4.4 Two-Level Nested Logistic Regression Model with Random Intercept and Slope
197
9.4.5 Analysis of Data
198
9.4.6 Comparisons of Procedures (PROC NLMIXED Versus PROC GLIMMIX)
198
9.4.7 Model 1: Two-Level Nested Logistic Regression Model with Random Intercepts
199
SPSS Model 1: Logistic Regression Model with Random Intercepts
207
9.4.8 Two-Level Nested Logistic Regression Model Random Intercept and Slope
211
9.4.9 Model 2: Logistic Regression with Random Intercept/Random Slope for LOS
217
9.5 Conclusions
218
9.6 Related Examples
218
9.6.1 Multicenter Randomized Controlled Data (Beitler and Landis, 1985)
218
References
219
Chapter 10: Hierarchical Logistic Regression Models
221
10.1 Motivation
221
10.1.1 Description of Case Study
221
10.1.2 Study Hypotheses
222
10.2 Definitions and Notations
222
10.3 Exploratory Analyses
223
10.4 Statistical Model
224
10.4.1 Multilevel Modeling Approaches with Binary Outcomes
225
10.4.2 Potential Problems
225
10.4.3 Three-Level Logistic Regression Models with Multiple Random Intercepts
226
10.4.4 Three-Level Logistic Regression Models with Random Intercepts and Random Slopes
227
10.4.5 Nested Higher Level Logistic Regression Models
229
10.4.6 Cluster Sizes and Number of Clusters
229
10.4.7 Parameter Estimations
229
10.5 Analysis of Data
230
10.5.1 Modeling Random Intercepts for Levels 2 and 3
230
Graphical Representation
235
Three-Level Logistic Regression Model with Random Slopes
235
Graphical Representation
240
10.5.2 Interpretation
241
Binary Outcomes
242
10.6 Conclusions
242
10.7 Related Examples
243
References
244
Chapter 11: Fixed Effects Logistic Regression Model
245
11.1 Motivating Example
245
11.2 Definition and Notation
246
11.3 Exploratory Analysis
247
11.3.1 Philippine´s Data
247
11.4 Statistical Models
248
11.4.1 Fixed Effects Regression Models with Two Observations per Unit
249
11.4.2 Modeling More than Two Observations per Unit: Conditional Logistic
250
11.5 Analysis of Data
251
11.5.1 Fixed Effects Logistic Regression Model with Two Observations per Unit
251
Fixed Effects Logistic Regression Model with More than Two Observations
260
11.6 Conclusions
264
11.7 Related Examples
265
References
265
Part IV: Analyzing Correlated Data Through the Joint Modeling of Mean and Variance
267
Chapter 12: Heteroscedastic Logistic Regression Model
268
12.1 Motivating Example
268
12.2 Definitions and Notations
269
12.3 Exploratory Analyses
270
12.3.1 Dispersion Sub-model
273
12.4 Statistical Model
274
12.5 Analysis of Data
276
12.5.1 Heteroscedastic Logistic Regression Model
276
12.5.2 Standard Logistic Regression Model
279
12.5.3 Model Comparisons Mean Sub-model Versus Joint Modeling
280
12.6 Conclusions
281
12.7 Related Examples
281
References
283