Statistical Models and Causal Inference A Dialogue with the Social Sciences 1st Edition by David Collier, Jasjeet Sekhon, Philip Stark 0521195004 9780521195003
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ISBN 10: 0521195004
ISBN 13: 9780521195003
Author: David A. Collier, Jasjeet S. Sekhon, Philip B. Stark
David A. Freedman presents here a definitive synthesis of his approach to causal inference in the social sciences. He explores the foundations and limitations of statistical modeling, illustrating basic arguments with examples from political science, public policy, law, and epidemiology. Freedman maintains that many new technical approaches to statistical modeling constitute not progress, but regress. Instead, he advocates a ‘shoe leather’ methodology, which exploits natural variation to mitigate confounding and relies on intimate knowledge of the subject matter to develop meticulous research designs and eliminate rival explanations. When Freedman first enunciated this position, he was met with scepticism, in part because it was hard to believe that a mathematical statistician of his stature would favor ‘low-tech’ approaches. But the tide is turning. Many social scientists now agree that statistical technique cannot substitute for good research design and subject matter knowledge. This book offers an integrated presentation of Freedman’s views.
Table of contents:
Part I Statistical Modeling: Foundations and Limitations
1 Issues in the Foundations of Statistics: Probability and Statistical Models
1.1 What is probability?
1.2 The objectivist position
1.3 The subjectivist position
1.3.1 Probability and relative frequency
1.3.2 Labels do not settle the issue
1.4 A critique of the subjectivist position
1.4.1 Other arguments for the Bayesian position
1.4.2 To sum up
1.5 Statistical models
1.5.1 Examples
1.5.2 Standard errors, t-statistics, and statistical significance
1.5.3 Statistical models and the problem of induction
1.6 Conclusions
Notes
Acknowledgments
2 Statistical Assumptions as Empirical Commitments
2.1 Introduction
2.2 Treating the data as a population
2.3 Assuming a real population and an imaginary sampling mechanism
2.4 An imaginary population and imaginary sampling mechanism
2.5 When the statistical issues are substantive
2.6 Does the random-sampling assumption make any difference?
2.6.1 Violations of independence
2.7 Dependence in other settings
2.7.1 Spatial dependence
2.7.2 Regression models
2.7.3 Time series models
2.7.4 Meta-analysis
2.7.5 Observational studies and experiments
2.8 Recommendations for practice
2.9 Conclusions
Notes
3 Statistical Models and Shoe Leather
3.1 Introduction
3.2 Some examples from Epidemiology
3.3 Some examples from the Social Sciences
3.4 Summary of the position
3.5 Can technical fixes rescue the models?
3.6 Other literature
3.7 Conclusion
Acknowledgments
Part II Studies in Political Science, Public Policy, and Epidemiology
4 Methods for Census 2000 and Statistical Adjustments
4.1 Introduction
4.2 The census
4.3 Demographic analysis
4.4 DSE—Dual System Estimator
4.5 Small-area estimation
4.6 State shares
4.7 The 1990 adjustment decision
4.8 Census 2000
4.9 The adjustment decision for Census 2000
4.10 Gross or net?
4.11 Heterogeneity in 2000
4.12 Loss function analysis
4.13 Pointers to the literature
4.14 Litigation
4.15 Other countries
4.16 Summary and conclusion
Note
5 On “Solutions” to the Ecological Inference Problem
5.1 Introduction
5.2 The test data
5.3 Empirical results
5.4 Diagnostics
5.5 Summary on diagnostics
5.6 Summary of empirical findings
5.7 Counting success
5.8 A checklist
5.9 Other literature
5.10 Some details
5.11 The extended model
5.12 Identifiability and other a priori arguments
5.13 Summary and conclusions
6 Rejoinder to King
6.1 Introduction
6.2 Model comparisons
6.3 Diagnostics
6.4 Other issues
6.5 Making the data available
6.6 Summary and conclusions
7 Black Ravens, White Shoes, and Case Selection: Inference with Categorical Variables
7.1 Introduction
7.2 The paradox
7.3 Case selection
7.A Appendix
7.A.1 Good’s example
7.A.2 Simple random samples
7.A.3 Other possibilities
7.A.4 Samples and inductive inference
7.A.5 The ravens and causal inference
7.A.6 Ambiguity in the rules
7.A.7 The odds ratio
Notes
Acknowledgments
8 What is the Chance of an Earthquake?
8.1 Introduction
8.2 Interpreting probability
8.2.1 Symmetryand equallylik elyoutcomes
8.2.2 The frequentist approach
8.2.3 The Bayesian approach
8.2.4 The principle of insufficient reason
8.2.5 Earthquake forecasts and weather forecasts
8.2.6 Mathematical probability: Kolmogorov’s axioms
8.2.7 Probabilitymodels
8.3 The USGS earthquake forecast
8.3.1 What does the uncertaintyestimate mean?
8.4 A view from the past
8.5 Conclusions
Notes
9 Salt and Blood Pressure: Conventional Wisdom Reconsidered
9.1 Animal studies
9.2 The Intersalt study
9.3 Units for salt and blood pressure
9.4 Patterns in the Intersalt data
9.5 P-values
9.6 The protocol
9.7 Human experiments
9.8 Publication bias
9.9 DASH—Dietary Approaches to Stop Hypertension
9.10 Health effects of salt
9.11 Back to Intersalt
9.12 The salt epidemiologists respond
9.13 Policy implications
Acknowledgments
10 The Swine Flu Vaccine and Guillain-Barré Syndrome: A Case Study in Relative Riskand Specific Cau
10.1 Introduction
10.2 The swine flu vaccine and GBS
10.3 The Manko case
10.3.1 Completeness of reporting
10.3.2 Discovery issues
10.3.3 Individual differences
10.4 Summary and conclusions
Notes
Acknowledgments
11 Survival Analysis: An Epidemiological Hazard?
11.1 Cross-sectional life tables
11.2 Hazard rates
11.3 The Kaplan-Meier estimator
11.4 An application of the Kaplan-Meier estimator
11.5 The proportional-hazards model in brief
11.5.1 A mathematical diversion
11.6 An application of the proportional-hazards model
11.6.1 The crucial questions
11.7 Does HRT prevent heart disease?
11.7.1 Nurses’ Health Study: Observational
11.7.2 Women’s Health Initiative: Experimental
11.7.3 Were the observational studies right, or the experiments?
11.8 Simulations
11.8.1 The model works
11.8.2 The model does not work
11.9 Causal inference from observational data
11.10 What is the bottom line?
11.11 Where do we go from here?
11.12 Some pointers to the literature
11.A Appendix: The delta method in more detail
Acknowledgments
Part III New Developments: Progress or Regress?
12 On Regression Adjustments in Experiments with Several Treatments
12.1 Introduction
12.2 Asymptotics for multiple-regression estimators
12.3 Asymptotic nominal variances
12.4 The gain from adjustment
12.5 Finite-sample results
12.6 Recommendations for practice
12.A Technical appendix
Acknowledgments
13 Randomization Does Not Justify Logistic Regression
13.1 Introduction
13.2 Neyman
13.2.1 The intention-to-treat principle
13.3 The logit model
13.3.1 Interpreting the coefficients in the model
13.3.2 Application to experimental data
13.3.3 What if the logit model is right?
13.3.4 From Neyman to logits
13.4 A plug-in estimator for the log odds
13.5 Simulations
13.6 Extensions and implications
13.7 Literature review
13.8 Sketch of proofs
13.8.1 Additional detail on boundedness
13.8.2 Summing up
13.8.3 Estimating individual-level parameters
13.9 An inequality
Acknowledgments
14 The Grand Leap
Notes
15 On Specifying Graphical Models for Causation, and the Identification Problem
15.1 A first example: Simple regression
15.2 Conditionals
15.3 Two linear regressions
15.4 Simultaneous equations
15.5 Nonlinear models: Figure 15.1 revisited
15.6 Technical notes
15.7 More complicated examples
15.8 Parametric nonlinear models
15.9 Concomitants
15.10 The story behind Figures 15.3 and 15.4
15.11 Models and kernels revisited
15.12 Literature review
Acknowledgments
16 Weighting Regressions by Propensity Scores
16.1 Simulation #1
16.2 Results for Simulation #2
16.3 Covariate balance
16.4 Discussion
16.5 Literature review
16.6 Theory
16.7 Non-parametric estimation
16.8 Contrasts
16.9 Contrasts vs structural equations
16.10 Conclusions
Acknowledgments
17 On The So-Called “Huber Sandwich Estimator” and “Robust Standard Errors”
17.1 Introduction
17.2 Robust standard errors
17.3 Why not assume IID variables?
17.4 A possible extension
17.5 Cluster samples
17.6 The linear case
17.7 An example
17.8 What about Huber?
17.9 Summary and conclusions
Acknowledgments
18 Endogeneity in Probit Response Models
18.1 Introduction
18.2 Aprobit response model with an endogenous regressor
18.3 Aprobit model with endogenous sample selection
18.4 Numerical issues
18.5 Implications for practice
18.6 Motivating the estimator
18.7 Identifiability
18.8 Some relevant literature
Acknowledgments
19 Diagnostics Cannot Have Much Power Against General Alternatives
19.1. Introduction
19.2. Specific models
19.3. Discussion
19.4. What about forecasting?
19.5. Recommendations
Acknowledgments
Part IV Shoe Leather Revisited
20 On Types of Scientific Inquiry: The Role of Qualitative Reasoning
20.1 Jenner and vaccination
20.2 Semmelweis and puerperal fever
20.3 Snow and cholera
20.4 Eijkman and beriberi
20.5 Goldberger and pellagra
20.6 McKay and fluoridation
20.7 Flemingand penicillin
20.8 Gregg and German measles
20.9 Herbst and DES
20.10 Conclusions
20.11 Further reading
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Tags: David Collier, Jasjeet Sekhon, Philip Stark, Statistical