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 |  موضوع: كتاب Methods of Statistical Model Estimation الخميس 13 مارس 2014, 12:07 pm | |
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Methods of Statistical Model Estimation
Joseph M. Hilbe
Jet Propulsion Laboratory
California Institute of Technology, USA and
Arizona State Univeristy, USA
Andrew P. Robinson
ACERA & Department of Mathematics and Statistics
The University of Melbourne, Australia
ويتناول الموضوعات الأتية :
1 Programming and R 1
1.1 Introduction 1
1.2 R Specifics 1
1.2.1 Objects 3
1.2.1.1 Vectors 3
1.2.1.2 Subsetting 7
1.2.2 Container Objects 7
1.2.2.1 Lists 8
1.2.2.2 Dataframes 9
1.2.3 Functions 10
1.2.3.1 Arguments 11
1.2.3.2 Body 13
1.2.3.3 Environments and Scope 14
1.2.4 Matrices 16
1.2.5 Probability Families 19
1.2.6 Flow Control 22
1.2.6.1 Conditional Execution 23
1.2.6.2 Loops 23
1.2.7 Numerical Optimization 25
1.3 Programming 27
1.3.1 Programming Style 27
1.3.2 Debugging 28
1.3.2.1 Debugging in Batch 29
1.3.3 Object-Oriented Programming 30
1.3.4 S3 Classes 30
1.4 Making R Packages 34
1.4.1 Building a Package 35
1.4.2 Testing 36
1.4.3 Installation 36
1.5 Further Reading 37
1.6 Exercises 37
2 Statistics and Likelihood-Based Estimation 39
2.1 Introduction 39
2.2 Statistical Models 39
2.3 Maximum Likelihood Estimation 41
2.3.1 Process 41
2.3.2 Estimation 45
2.3.2.1 Exponential Family 46
2.3.3 Properties 47
2.4 Interval Estimates 49
2.4.1 Wald Intervals 49
2.4.2 Inverting the LRT: Profile Likelihood 50
2.4.3 Nuisance Parameters 52
2.5 Simulation for Fun and Profit 56
2.5.1 Pseudo-Random Number Generators 56
2.6 Exercises 59
3 Ordinary Regression 61
3.1 Introduction 61
3.2 Least-Squares Regression 62
3.2.1 Properties 64
3.2.2 Matrix Representation 66
3.2.3 QR Decomposition 69
3.2.4 Example 71
3.3 Maximum-Likelihood Regression 74
3.4 Infrastructure 76
3.4.1 Easing Model Specification 76
3.4.2 Missing Data 77
3.4.3 Link Function 78
3.4.4 Initializing the Search 78
3.4.5 Making Failure Informative 79
3.4.6 Reporting Asymptotic SE and CI 79
3.4.7 The Regression Function 80
3.4.8 S3 Classes 82
3.4.8.1 Print 82
3.4.8.2 Fitted Values 83
3.4.8.3 Residuals 84
3.4.8.4 Diagnostics 85
3.4.8.5 Metrics of Fit 87
3.4.8.6 Presenting a Summary 89
3.4.9 Example Redux 91
3.4.10 Follow-up 94
3.5 Conclusion 94
3.6 Exercises 94
4 Generalized Linear Models 97
4.1 Introduction 97
4.2 GLM: Families and Terms 99
4.3 The Exponential Family 102
4.4 The IRLS Fitting Algorithm 104
4.5 Bernoulli or Binary Logistic Regression 105
4.5.1 IRLS 111
4.6 Grouped Binomial Models 114
4.7 Constructing a GLM Function 120
4.7.1 A Summary Function 125
4.7.2 Other Link Functions 128
4.8 GLM Negative Binomial Model 129
4.9 Offsets 133
4.10 Dispersion, Over- and Under- 136
4.11 Goodness-of-Fit and Residual Analysis 139
4.11.1 Goodness-of-Fit 139
4.11.2 Residual Analysis 141
4.12 Weights 143
4.13 Conclusion 143
4.14 Exercises 144
5 Maximum Likelihood Estimation 145
5.1 Introduction 145
5.2 MLE for GLM 146
5.2.1 The Log-Likelihood 146
5.2.2 Parameter Estimation 148
5.2.3 Residuals 149
5.2.4 Deviance 150
5.2.5 Initial Values 151
5.2.6 Printing the Object 151
5.2.7 GLM Function 153
5.2.8 Fitting for a New Family 157
5.3 Two-Parameter MLE 160
5.3.1 The Log-Likelihood 160
5.3.2 Parameter Estimation 162
5.3.3 Deviance and Deviance Residuals 163
5.3.4 Initial Values 165
5.3.5 Printing and Summarizing the Object 165
5.3.6 GLM Function 165
5.3.7 Building on the Model 171
5.3.8 Fitting for a New Family 173
5.4 Exercises 176
6 Panel Data 177
6.1 What Is a Panel Model? 177
6.1.1 Fixed- or Random-Effects Models 181
6.2 Fixed-Effects Model 181
6.2.1 Unconditional Fixed-Effects Models 181
6.2.2 Conditional Fixed-Effects Models 183
6.2.3 Coding a Conditional Fixed-Effects Negative Binomial 185
6.3 Random-Intercept Model 188
6.3.1 Random-Effects Models 188
6.3.2 Coding a Random-Intercept Gaussian Model 191
6.4 Handling More Advanced Models 194
6.5 The EM Algorithm 194
6.5.1 A Simple Example 196
6.5.2 The Random-Intercept Model 197
6.6 Further Reading 201
6.7 Exercises 202
7 Model Estimation Using Simulation 203
7.1 Simulation: Why and When? 203
7.2 Synthetic Statistical Models 205
7.2.1 Developing Synthetic Models 205
7.2.2 Monte Carlo Estimation 209
7.2.3 Reference Distributions 216
7.3 Bayesian Parameter Estimation 219
7.3.1 Gibbs Sampling 229
7.4 Discussion 230
7.5 Exercises 231
Bibliography 233
Index 239
Preface
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