Permutation tests for inference on causal effects: a simulation study comparing a new approach to existing methods
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| Format: | Thesis Book |
| Language: | English |
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[2015?]
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| Online Access: | Inhaltsverzeichnis |
| Item Description: | Enthält CD-Rom mit digitalen Anhängen |
| Physical Description: | XIV, 201 Seiten Diagramme 1 CD-Rom |
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| 245 | 1 | 0 | |a Permutation tests for inference on causal effects |b a simulation study comparing a new approach to existing methods |c von Dipl. Psych. Sonja Hahn (geb. Falk) |
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| adam_text | Titel: Permutation tests for inference on causal effects
Autor: Hahn, Sonja
Jahr: 2015
Contents
1 Introduction 1
1.1 Motivation...................................... 1
1.2 Introductory Example................................ 3
1.3 Overview...................................... 6
2 Theory of Causal Effects 7
2.1 Background..................................... 7
2.1.1 A single-unit trial.............................. 8
2.1.2 Notation and assumptions......................... 9
2.1.3 Defining causal effects........................... 10
2.1.4 Unbiasedness................................ 11
2.1.5 Conditions implying unbiasedness..................... 13
2.1.6 Identification................................ 13
2.1.7 Illustration of the Theory of Causal Effects ................ 14
2.1.8 Summary and outlook........................... 18
2.2 Excursion: Stochasticity of Regressors....................... 21
2.2.1 Design of (quasi-)experiments....................... 21
2.2.2 Relevance for data analysis and hypothesis testing............ 24
2.2.3 Summary and some remarks........................ 28
2.3 Parametric Procedures ............................... 29
2.3.1 Standard approaches (f-test/ANOVA) ................... 29
2.3.2 ANCOVA approaches........................... 36
2.3.3 Further Procedures.............................. 42
2.3.4 Summary.................................. 43
3 Permutation Tests 44
3.1 Background..................................... 44
3.1.1 An introduction to permutation tests.................... 45
VII
CONTENTS
3.1.2 Exchangeability............................... 46
3.1.3 Some terms describing properties of significance tests .......... 50
3.1.4 Simulation studies on permutation tests.................. 51
3.1.5 Mixed practical issues........................... 53
3.2 Permutation tests and causality........................... 54
3.2.1 Rosenbaum................................. 55
3.2.2 Approaches recommended by other authors................ 58
3.2.3 Permutation tests and the Theory of Causal Effects............. 59
3.2.4 Summary.................................. 65
3.3 Permutation procedures .............................. 66
3.3.1 Standard approaches............................ 67
3.3.2 Permutation procedures that use a special test statistic .......... 68
3.3.3 Permutation procedures that permute residuals .............. 70
3.3.4 Permutation procedures that use stratification............... 74
4 Comparison of Procedures: Research Questions 77
4.1 Research Questions................................. 77
4.2 Settings and Parameters............................... 79
4.3 Predictions ..................................... 82
4.3.1 Parametric procedures........................... 82
4.3.2 Permutation procedures .......................... 84
4.3.3 Summary.................................. 86
5 Comparison of Procedures: Design of the Simulation Study 89
5.1 Simulation of Data Sets............................... 89
5.1.1 Total sample size.............................. 90
5.1.2 Distributions of the covariate and the treatment variable ......... 90
5.1.3 Simulation of the outcome variable.................... 93
5.1.4 Summary.................................. 95
5.2 Procedures and Algorithms............................. 95
5.2.1 A design matrix .............................. 96
5.2.2 Parametric part............................... 97
5.2.3 Permutation procedures .......................... 99
6 Comparison of Procedures: Results 103
6.1 Parametric Approaches under ATE = 0 ...................... 103
6.1.1 Standard approaches (Mest/ANOVA)................... 103
6.1.2 ANCOVA approaches ........................... 105
6.1.3 Further procedures............................. 107
VIII
CONTENTS
6.1.4 Summary and discussion.......................... 107
6.2 Permutation Approaches under ATE = 0...................... 112
6.2.1 Standard approaches............................ 112
6.2.2 Procedures that use a special test statistic ................. 112
6.2.3 Procedures that permute residuals..................... 115
6.2.4 Procedures that use stratification...................... 118
6.2.5 Summary and discussion.......................... 118
6.3 Power........................................ 122
6.3.1 Experimental settings............................ 123
6.3.2 Quasi-experimental settings........................ 123
6.3.3 Summary and discussion.......................... 130
7 Small Sample Investigations 135
7.1 Background and Research Questions........................ 135
7.2 Design of the Simulation Study........................... 136
7.2.1 Simulated data sets............................. 136
7.2.2 Procedure.................................. 136
7.2.3 Outcome criteria.............................. 136
7.3 Results......................................... 137
7.3.1 Cumulative distributions functions..................... 137
7.3.2 Comparison at a fixed value of the test statistic.............. 137
7.4 Summary and Discussion.............................. 140
8 Different Error Distributions 142
8.1 Background and Research Questions........................ 142
8.2 Design of the Simulation Study........................... 144
8.2.1 Simulated data sets............................. 144
8.2.2 Procedures................................. 145
8.2.3 Outcome criterion ............................. 145
8.3 Results........................................ 146
8.4 Summary and Discussion.............................. 146
9 Discussion 149
9.1 Comparison of Procedures.............................149
9.1.1 Parametric procedures...........................149
9.1.2 Permutation procedures ..........................150
9.1.3 Power....................................150
9.2 Small Sample Investigations............................151
9.3 Different Error Distributions............................151
IX
CONTENTS___________________________________________________________
9.4 Limitations of the Simulation Studies ....................... 152
9.4.1 Simulated data settings........................... 152
9.4.2 Investigated procedures........................... 156
9.4.3 Outcome criteria and related technical aspects............... 157
9.4.4 Furtherpoints................................ 157
9.4.5 Summary.................................. 158
9.5 Recommendations for data analysis ........................ 158
9.6 Illustrative Example................................. 159
9.6.1 Description of the data set......................... 159
9.6.2 Statistical procedures............................ 160
9.6.3 Results................................... 162
9.7 Open Questions and Conclusion.......................... 164
9.7.1 Extending the permutation counterpart of EffecfLite ........... 164
9.7.2 Stochasticity of regressors......................... 166
9.7.3 Conclusion................................. 168
A Theoretical Derivations 169
A.l ANOVA Approaches................................ 169
A.l.l ANOVA 1.................................. 170
A.1.2 ANOVA 2.................................. 171
A. 1.3 ANOVA 3.................................. 173
A.1.4 Summary and discussion.......................... 173
A.2 Rosenbaum s residuals............................... 174
B Appendix to the First Simulation Study 175
B.l R Syntax....................................... 175
B.l.l Data simulation............................... 175
B.1.2 Statistical procedures............................ 176
B.1.3 Processing results and graphical display.................. 180
B.2 Additional Results ................................. 180
B.2.1 A self-programmed algorithm....................... 180
B.2.2 Permutation tests that use rank transformation............... 182
B.2.3 Procedures that incorporate the expectation of the covariate........ 184
C Appendix to the Second Simulation Study 186
Cl R syntax....................................... 186
C.2 Additional Results ................................. 186
CONTENTS
D Appendix to the Third Simulation Study 188
D.l R syntax....................................... 188
D.2 Additional Results ................................. 188
Bibliography 190
XI
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| discipline | Mathematik |
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| spelling | Hahn, Sonja 1982- Verfasser (DE-588)1076575404 aut Permutation tests for inference on causal effects a simulation study comparing a new approach to existing methods von Dipl. Psych. Sonja Hahn (geb. Falk) Jena [2015?] XIV, 201 Seiten Diagramme 1 CD-Rom txt rdacontent n rdamedia nc rdacarrier Enthält CD-Rom mit digitalen Anhängen Dissertation Friedrich-Schiller-Universität Jena 2015 Randomisierter Test (DE-588)4294178-7 gnd rswk-swf Kausalität (DE-588)4030102-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Randomisierter Test (DE-588)4294178-7 s Kausalität (DE-588)4030102-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029625124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hahn, Sonja 1982- Permutation tests for inference on causal effects a simulation study comparing a new approach to existing methods Randomisierter Test (DE-588)4294178-7 gnd Kausalität (DE-588)4030102-3 gnd |
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| title | Permutation tests for inference on causal effects a simulation study comparing a new approach to existing methods |
| title_auth | Permutation tests for inference on causal effects a simulation study comparing a new approach to existing methods |
| title_exact_search | Permutation tests for inference on causal effects a simulation study comparing a new approach to existing methods |
| title_full | Permutation tests for inference on causal effects a simulation study comparing a new approach to existing methods von Dipl. Psych. Sonja Hahn (geb. Falk) |
| title_fullStr | Permutation tests for inference on causal effects a simulation study comparing a new approach to existing methods von Dipl. Psych. Sonja Hahn (geb. Falk) |
| title_full_unstemmed | Permutation tests for inference on causal effects a simulation study comparing a new approach to existing methods von Dipl. Psych. Sonja Hahn (geb. Falk) |
| title_short | Permutation tests for inference on causal effects |
| title_sort | permutation tests for inference on causal effects a simulation study comparing a new approach to existing methods |
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| topic | Randomisierter Test (DE-588)4294178-7 gnd Kausalität (DE-588)4030102-3 gnd |
| topic_facet | Randomisierter Test Kausalität Hochschulschrift |
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