Cover image for Monte Carlo simulation and resampling methods for social  science
Title:
Monte Carlo simulation and resampling methods for social science
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Publication Information:
Los Angeles : Sage, 2014
Physical Description:
x, 293 pages : illustrations ; 24 cm.
ISBN:
9781452288901
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35000000003027 HA29 C37 2014 Open Access Book Book
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Summary

Summary

Taking the topics of a quantitative methodology course and illustrating them through Monte Carlo simulation, this book examines abstract principles, such as bias, efficiency, and measures of uncertainty in an intuitive, visual way. Instead of thinking in the abstract about what would happen to a particular estimator "in repeated samples," the book uses simulation to actually create those repeated samples and summarize the results. The book includes basic examples appropriate for readers learning the material for the first time, as well as more advanced examples that a researcher might use to evaluate an estimator he or she was using in an actual research project. The book also covers a wide range of topics related to Monte Carlo simulation, such as resampling methods, simulations of substantive theory, simulation of quantities of interest (QI) from model results, and cross-validation. Complete R code from all examples is provided so readers can replicate every analysis presented using R.


Table of Contents

Acknowledgmentsp. ix
1 Introductionp. 1
1.1 Can You Repeat That Please?p. 2
1.2 Simulation and Resampling Methodsp. 4
1.2.1 Simulations as Experimentsp. 4
1.2.2 Simulations Help Develop Intuitionp. 5
1.2.3 An Overview of Simulationp. 6
1.2.4 Resampling Methods as Simulationp. 7
1.3 OLS as a Motivating Examplep. 8
1.4 Two Brief Examplesp. 12
1.4.1 Example 1: A Statistical Simulationp. 13
1.4.2 Example 2: A Substantive Theory Simulationp. 15
1.5 Looking Aheadp. 15
1.5.1 Assumed Knowledgep. 16
1.5.2 A Preview of the Bookp. 16
1.6 R Packagesp. 17
2 Probabilityp. 19
2.1 Introductionp. 19
2.2 Some Basic Rules of Probabilityp. 20
2.2.1 Introduction to Set Theoryp. 20
2.2.2 Properties of Probabilityp. 22
2.2.3 Conditional Probabilityp. 22
2.2.4 Simple Math With Probabilitiesp. 23
2.3 Random Variables and Probability Distributionsp. 24
2.4 Discrete Random Variablesp. 29
2.4.1 Some Common Discrete Distributionsp. 30
2.5 Continuous Random Variablesp. 33
2.5.1 Two Common Continuous Distributionsp. 36
2.5.2 Other Continuous Distributionsp. 39
2.6 Conclusionsp. 43
3 Introduction to Rp. 45
3.1 Introductionp. 45
3.2 What Is R?p. 45
3.2.1 Resourcesp. 46
3.3 Using R With a Text Editorp. 46
3.4 First Stepsp. 47
3.4.1 Creating Objectsp. 47
3.5 Basic Manipulation of Objectsp. 48
3.5.1 Vectors and Sequencesp. 48
3.5.2 Matricesp. 49
3.6 Functionsp. 50
3.6.1 Matrix Algebra Functionsp. 51
3.6.2 Creating New Functionsp. 51
3.7 Working With Datap. 52
3.7.1 Loading Datap. 52
3.7.2 Exploring the Datap. 53
3.7.3 Statistical Modelsp. 54
3.7.4 Generalized Linear Modelsp. 57
3.8 Basic Graphicsp. 59
3.9 Conclusionsp. 61
4 Random Number Generationp. 63
4.1 Introductionp. 63
4.2 Probability Distributionsp. 63
4.2.1 Drawing Random Numbersp. 65
4.2.2 Creating Your Own Distribution Functionsp. 67
4.3 Systematic and Stochasticp. 68
4.3.1 The Systematic Componentp. 69
4.3.2 The Stochastic Componentp. 70
4.3.3 Repeating the Processp. 71
4.4 Programming in Rp. 72
4.4.1 for Loopsp. 73
4.4.2 Efficient Programmingp. 74
4.4.3 If-Elsep. 76
4.5 Completing the OLS Simulationp. 77
4.5.1 Anatomy of a Script Filep. 80
5 Statistical Simulation of the Linear Modelp. 83
5.1 Introductionp. 83
5.2 Evaluating Statistical Estimatorsp. 84
5.2.1 Bias, Efficiency, and Consistencyp. 84
5.2.2 Measuring Estimator Performance in Rp. 87
5.3 Simulations as Experimentsp. 96
5.3.1 Heteroskedasticityp. 96
5.3.2 Multicollinearityp. 103
5.3.3 Measurement Errorp. 105
5.3.4 Omitted Variablep. 109
5.3.5 Serial Correlationp. 112
5.3.6 Clustered Datap. 114
5.3.7 Heavy-Tailed Errorsp. 118
5.4 Conclusionsp. 125
6 Simulating Generalized Linear Modelsp. 127
6.1 Introductionp. 127
6.2 Simulating OLS as a Probability Modelp. 128
6.3 Simulating GLMsp. 130
6.3.1 Binary Modelsp. 130
6.3.2 Ordered Modelsp. 135
6.3.3 Multinomial Modelsp. 141
6.4 Extended Examplesp. 145
6.4.1 Ordered or Multinomial?p. 145
6.4.2 Count Modelsp. 150
6.4.3 Duration Modelsp. 157
6.5 Computational Issues for Simulationsp. 162
6.5.1 Research Computingp. 162
6.5.2 Parallel Processingp. 163
6.6 Conclusionsp. 167
7 Testing Theory Using Simulationp. 169
7.1 Introductionp. 169
7.2 What Is a Theory?p. 169
7.3 Zipf's Lawp. 171
7.3.1 Testing Zipf's Law With Frankensteinp. 171
7.3.2 From Patterns to Explanationsp. 174
7.4 Punctuated Equilibrium and Policy Responsivenessp. 181
7.4.1 Testing Punctuated Equilibrium Theoryp. 183
7.4.2 From Patterns to Explanationsp. 185
7.5 Dynamic Learningp. 190
7.5.1 Reward and Punishmentp. 193
7.5.2 Damned If You Do, Damned If You Don'tp. 195
7.5.3 The Midas Touchp. 197
7.6 Conclusionsp. 200
8 Resampling Methodsp. 201
8.1 Introductionp. 201
8.2 Permutation and Randomization Testsp. 202
8.2.1 A Basic Permutation Testp. 203
8.2.2 Randomization Testsp. 205
8.2.3 Permutation/Randomization and Multiple Regression Modelsp. 208
8.3 Jackknifingp. 209
8.3.1 An Examplep. 210
8.3.2 An Application: Simulating Heteroskedasticityp. 213
8.3.3 Pros and Cons of Jackknifingp. 214
8.4 Bootstrappingp. 215
8.4.1 Bootstrapping Basicsp. 217
8.4.2 Bootstrapping With Multiple Regression Modelsp. 220
8.4.3 Adding Complexity: Clustered Bootstrappingp. 225
8.5 Conclusionsp. 228
9 Other Simulation-Based Methodsp. 231
9.1 Introductionp. 231
9.2 QI Simulationp. 232
9.2.1 Statistical Overviewp. 232
9.2.2 Examplesp. 235
9.2.3 Simulating QI With Zeligp. 245
9.2.4 Average Case Versus Observed Valuesp. 249
9.2.5 The Benefits of QI Simulationp. 254
9.3 Cross-Validationp. 255
9.3.1 How CV Can Helpp. 257
9.3.2 An Examplep. 258
9.3.3 Using R Functions for CVp. 266
9.4 Conclusionsp. 267
10 Final Thoughtsp. 269
10.1 A Summary of the Bookp. 270
10.2 Going Forwardp. 271
10.3 Conclusionsp. 272
Referencesp. 275
Indexp. 283