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Causality in a Social World introduces innovative new statistical research and strategies for investigating moderated intervention effects, mediated intervention effects, and spill-over effects using experimental or quasi-experimental data.
The book uses potential outcomes to define causal effects, explains and evaluates identification assumptions using application examples, and compares innovative statistical strategies with conventional analysis methods. Whilst highlighting the crucial role of good research design and the evaluation of assumptions required for identifying causal effects…mehr
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Causality in a Social World introduces innovative new statistical research and strategies for investigating moderated intervention effects, mediated intervention effects, and spill-over effects using experimental or quasi-experimental data.
The book uses potential outcomes to define causal effects, explains and evaluates identification assumptions using application examples, and compares innovative statistical strategies with conventional analysis methods. Whilst highlighting the crucial role of good research design and the evaluation of assumptions required for identifying causal effects in the context of each application, the author demonstrates that improved statistical procedures will greatly enhance the empirical study of causal relationship theory.
Applications focus on interventions designed to improve outcomes for participants who are embedded in social settings, including families, classrooms, schools, neighbourhoods, and workplaces.
The book uses potential outcomes to define causal effects, explains and evaluates identification assumptions using application examples, and compares innovative statistical strategies with conventional analysis methods. Whilst highlighting the crucial role of good research design and the evaluation of assumptions required for identifying causal effects in the context of each application, the author demonstrates that improved statistical procedures will greatly enhance the empirical study of causal relationship theory.
Applications focus on interventions designed to improve outcomes for participants who are embedded in social settings, including families, classrooms, schools, neighbourhoods, and workplaces.
Produktdetails
- Produktdetails
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 448
- Erscheinungstermin: 17. August 2015
- Englisch
- Abmessung: 250mm x 175mm x 28mm
- Gewicht: 942g
- ISBN-13: 9781118332566
- ISBN-10: 1118332563
- Artikelnr.: 41771643
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 448
- Erscheinungstermin: 17. August 2015
- Englisch
- Abmessung: 250mm x 175mm x 28mm
- Gewicht: 942g
- ISBN-13: 9781118332566
- ISBN-10: 1118332563
- Artikelnr.: 41771643
Guanglei Hong, University of Chicago, Department of Comparative Human Development, USA.
Preface xv Part I Overview 1 1 Introduction 3 1.1 Concepts of moderation,
mediation, and spill-over 3 1.1.1 Moderated treatment effects 5 1.1.2
Mediated treatment effects 7 1.1.3 Spill-over effects of a treatment 8 1.2
Weighting methods for causal inference 10 1.3 Objectives and organization
of the book 11 1.4 How is this book situated among other publications on
related topics? 12 2 Review of causal inference concepts and methods 18 2.1
Causal inference theory 18 2.1.1 Attributes versus causes 18 2.1.2
Potential outcomes and individual-specific causal effects 19 2.1.3
Inference about population average causal effects 22 2.2 Applications to
Lord's paradox and Simpson's paradox 27 2.2.1 Lord's paradox 27 2.2.2
Simpson's paradox 31 2.3 Identification and estimation 34 2.3.1 Selection
bias 35 2.3.2 Sampling bias 35 2.3.3 Estimation efficiency 36 Appendix 2.1:
Potential bias in a prima facie effect 36 Appendix 2.2: Application of the
causal inference theory to Lord's paradox 37 3 Review of causal inference
designs and analytic methods 40 3.1 Experimental designs 40 3.1.1
Completely randomized designs 40 3.1.2 Randomized block designs 41 3.1.3
Covariance adjustment for improving efficiency 43 3.1.4 Multilevel
experimental designs 43 3.2 Quasiexperimental designs 44 3.2.1
Nonequivalent comparison group designs 44 3.2.2 Other quasiexperimental
designs 45 3.3 Statistical adjustment methods 46 3.3.1 ANCOVA and multiple
regression 46 3.3.2 Matching and stratification 50 3.3.3 Other statistical
adjustment methods 51 3.4 Propensity score 55 3.4.1 What is a propensity
score? 56 3.4.2 Balancing property of the propensity score 57 3.4.3 Pooling
conditional treatment effect estimate: Matching, stratification, and
covariance adjustment 60 Appendix 3.A: Potential bias due to the omission
of treatment-by-covariate interaction 70 Appendix 3.B: Variable selection
for the propensity score model 71 4 Adjustment for selection bias through
weighting 76 4.1 Weighted estimation of population parameters in survey
sampling 77 4.1.1 Simple random sample 77 4.1.2 Proportionate sample 78
4.1.3 Disproportionate sample 79 4.2 Weighting adjustment for selection
bias in causal inference 80 4.2.1 Experimental result 81 4.2.2
Quasiexperimental result 81 4.2.3 Sample weight for bias removal 82 4.2.4
IPTW for bias removal 84 4.3 MMWS 86 4.3.1 Theoretical rationale 86 4.3.2
MMWS analytic procedure 91 4.3.3 Inherent connection and major distinctions
between MMWS and IPTW 93 Appendix 4.A: Proof of MMWS-adjusted mean observed
outcome being unbiased for the population average potential outcome 95
Appendix 4.B: Derivation of MMWS for estimating the treatment effect on the
treated 96 Appendix 4.C: Theoretical equivalence of MMWS and IPTW 97
Appendix 4.D: Simulations comparing MMWS and IPTW under misspecifications
of the functional form of a propensity score model 97 5 Evaluations of
multivalued treatments 100 5.1 Defining the causal effects of multivalued
treatments 100 5.2 Existing designs and analytic methods for evaluating
multivalued treatments 102 5.2.1 Experimental designs and analysis 102
5.2.2 Quasiexperimental designs and analysis 105 5.3 MMWS for evaluating
multivalued treatments 112 5.3.1 Basic rationale 113 5.3.2 Analytic
procedure 114 5.3.3 Identification assumptions 121 5.4 Summary 123 Appendix
5.A: Multiple IV for evaluating multivalued treatments 124 Part II
Moderation 127 6 Moderated treatment effects: concepts and existing
analytic methods 129 6.1 What is moderation? 129 6.1.1 Past discussions of
moderation 130 6.1.2 Definition of moderated treatment effects 133 6.2
Experimental designs and analytic methods for investigating explicit
moderators 136 6.2.1 Randomized block designs 137 6.2.2 Factorial designs
140 6.3 Existing research designs and analytic methods for investigating
implicit moderators 142 6.3.1 Multisite randomized trials 143 6.3.2
Principal stratification 149 Appendix 6.A: Derivation of bias in the
fixed-effects estimator when the treatment effect is heterogeneous in
multisite randomized trials 151 Appendix 6.B: Derivation of bias in the
mixed-effects estimator when the probability of treatment assignment varies
across sites 153 Appendix 6.C: Derivation and proof of the population
weight applied to mixed-effects models for eliminating bias in multisite
randomized trials 153 7 Marginal mean weighting through stratification for
investigating moderated treatment effects 159 7.1 Existing methods for
moderation analyses with quasiexperimental data 159 7.1.1 Analysis of
covariance and regression-based adjustment 161 7.1.2 Propensity score-based
adjustment 165 7.2 MMWS estimation of treatment effects moderated by
individual or contextual characteristics 168 7.2.1 Application example 170
7.2.2 Analytic procedure 170 7.3 MMWS estimation of the joint effects of
concurrent treatments 174 7.3.1 Application example 174 7.3.2 Analytic
procedure 175 7.3.3 Joint treatment effects moderated by individual or
contextual characteristics 179 8 Cumulative effects of time-varying
treatments 185 8.1 Causal effects of treatment sequences 186 8.1.1
Application example 186 8.1.2 Causal parameters 187 8.2 Existing strategies
for evaluating time-varying treatments 190 8.2.1 The endogeneity problem in
nonexperimental data 190 8.2.2 SEM 191 8.2.3 Fixed-effects econometric
models 192 8.2.4 Sequential randomization 192 8.2.5 Dynamic treatment
regimes 193 8.2.6 Marginal structural models and structural nested models
194 8.3 MMWS for evaluating 2-year treatment sequences 195 8.3.1 Sequential
ignorability 195 8.3.2 Propensity scores 196 8.3.3 MMWS computation 197
8.3.4 Two-year growth model specification 199 8.4 MMWS for evaluating
multiyear sequences of multivalued treatments 204 8.4.1 Sequential
ignorability of multiyear treatment sequences 204 8.4.2 Propensity scores
for multiyear treatment sequences 204 8.4.3 MMWS computation 205 8.4.4
Weighted multiyear growth model 205 8.4.5 Issues of sample size 206 8.5
Conclusion 207 Appendix 8.A: A saturated model for evaluating multivalued
treatments over multiple time periods 207 Part III Mediation 211 9 Concepts
of mediated treatment effects and experimental designs for investigating
causal mechanisms 213 9.1 Introduction 214 9.2 Path coefficients 215 9.3
Potential outcomes and potential mediators 216 9.3.1 Controlled direct
effects 217 9.3.2 Controlled treatment-by-mediator interaction effect 217
9.4 Causal effects with counterfactual mediators 219 9.4.1 Natural direct
effect 219 9.4.2 Natural indirect effect 220 9.4.3 Natural
treatment-by-mediator interaction effect 220 9.4.4 Unstable unit treatment
value 221 9.5 Population causal parameters 222 9.5.1 Population average
natural direct effect 224 9.5.2 Population average natural indirect effect
225 9.6 Experimental designs for studying causal mediation 225 9.6.1
Sequentially randomized designs 228 9.6.2 Two-phase experimental designs
228 9.6.3 Three- and four-treatment arm designs 230 9.6.4 Experimental
causal-chain designs 231 9.6.5 Moderation-of-process designs 231 9.6.6
Augmented encouragement designs 232 9.6.7 Parallel experimental designs and
parallel encouragement designs 232 9.6.8 Crossover experimental designs and
crossover encouragement designs 233 9.6.9 Summary 234 10 Existing analytic
methods for investigating causal mediation mechanisms 238 10.1 Path
analysis and SEM 239 10.1.1 Analytic procedure for continuous outcomes 239
10.1.2 Identification assumptions 242 10.1.3 Analytic procedure for
discrete outcomes 245 10.2 Modified regression approach 246 10.2.1 Analytic
procedure for continuous outcomes 246 10.2.2 Identification assumptions 247
10.2.3 Analytic procedure for binary outcomes 248 10.3 Marginal structural
models 250 10.3.1 Analytic procedure 250 10.3.2 Identification assumptions
252 10.4 Conditional structural models 252 10.4.1 Analytic procedure 252
10.4.2 Identification assumptions 253 10.5 Alternative weighting methods
254 10.5.1 Analytic procedure 254 10.5.2 Identification assumptions 256
10.6 Resampling approach 256 10.6.1 Analytic procedure 256 10.6.2
Identification assumptions 257 10.7 IV method 257 10.7.1 Rationale and
analytic procedure 257 10.7.2 Identification assumptions 258 10.8 Principal
stratification 259 10.8.1 Rationale and analytic procedure 259 10.8.2
Identification assumptions 260 10.9 Sensitivity analysis 261 10.9.1
Unadjusted confounding as a product of hypothetical regression coefficients
261 10.9.2 Unadjusted confounding reflected in a hypothetical correlation
coefficient 262 10.9.3 Limitations when the selection mechanism differs by
treatment 264 10.9.4 Other sensitivity analyses 265 10.10 Conclusion 265
10.10.1 The essentiality of sequential ignorability 265 10.10.2
Treatment-by-mediator interactions 266 10.10.3 Homogeneous versus
heterogeneous causal effects 266 10.10.4 Model-based assumptions 266
Appendix 10.A: Bias in path analysis estimation due to the omission of
treatment-by-mediator interaction 267 11 Investigations of a simple
mediation mechanism 273 11.1 Application example: national evaluation of
welfare-to-work strategies 274 11.1.1 Historical context 274 11.1.2
Research questions 275 11.1.3 Causal parameters 275 11.1.4 NEWWS Riverside
data 277 11.2 RMPW rationale 277 11.2.1 RMPW in a sequentially randomized
design 278 11.2.2 RMPW in a sequentially randomized block design 283 11.2.3
RMPW in a standard randomized experiment 285 11.2.4 Identification
assumptions 286 11.3 Parametric RMPW procedure 287 11.4 Nonparametric RMPW
procedure 290 11.5 Simulation results 292 11.5.1 Correctly specified
propensity score models 292 11.5.2 Misspecified propensity score models 294
11.5.3 Comparisons with path analysis and IV results 294 11.6 Discussion
295 11.6.1 Advantages of the RMPW strategy 295 11.6.2 Limitations of the
RMPW strategy 295 Appendix 11.A: Causal effect estimation through the RMPW
procedure 296 Appendix 11.B: Proof of the consistency of RMPW estimation
297 12 RMPW extensions to alternative designs and measurement 301 12.1 RMPW
extensions to mediators and outcomes of alternative distributions 301
12.1.1 Extensions to a multicategory mediator 302 12.1.2 Extensions to a
continuous mediator 304 12.1.3 Extensions to a binary outcome 306 12.2 RMPW
extensions to alternative research designs 306 12.2.1 Extensions to
quasiexperimental data 307 12.2.2 Extensions to data from cluster
randomized trials 308 12.2.3 Extensions to data from multisite randomized
trials 313 12.3 Alternative decomposition of the treatment effect 321 13
RMPW extensions to studies of complex mediation mechanisms 325 13.1 RMPW
extensions to moderated mediation 325 13.1.1 RMPW analytic procedure for
estimating and testing moderated mediation 326 13.1.2 Path analysis/SEM
approach to analyzing moderated mediation 327 13.1.3 Principal
stratification and moderated mediation 328 13.2 RMPW extensions to
concurrent mediators 328 13.2.1 Treatment effect decomposition 329 13.2.2
Identification assumptions 333 13.2.3 RMPW procedure 333 13.2.4 Contrast
with the linear SEM approach 338 13.2.5 Contrast with the multivariate IV
approach 339 13.3 RMPW extensions to consecutive mediators 340 13.3.1
Treatment effect decomposition 341 13.3.2 Identification assumptions 345
13.3.3 RMPW procedure 347 13.3.4 Contrast with the linear SEM approach 353
13.3.5 Contrast with the sensitivity-based estimation of bounds for causal
effects 354 13.4 Discussion 355 Appendix 13.A: Derivation of RMPW for
estimating population average counterfactual outcomes of two concurrent
mediators 355 Appendix 13.B: Derivation of RMPW for estimating population
average counterfactual outcomes of consecutive mediators 358 Part IV
Spill-over 363 14 Spill-over of treatment effects: concepts and methods 365
14.1 Spill-over: A nuisance, a trifle, or a focus? 365 14.2 Stable versus
unstable potential outcome values: An example from agriculture 367 14.3
Consequences for causal inference when spill-over is overlooked 369 14.4
Modified framework of causal inference 371 14.4.1 Treatment settings 371
14.4.2 Simplified characterization of treatment settings 373 14.4.3 Causal
effects of individual treatment assignment and of peer treatment assignment
375 14.5 Identification: Challenges and solutions 376 14.5.1 Hypothetical
experiments for identifying average treatment effects in the presence of
social interactions 376 14.5.2 Hypothetical experiments for identifying the
impact of social interactions 380 14.5.3 Application to an evaluation of
kindergarten retention 382 14.6 Analytic strategies for experimental and
quasiexperimental data 384 14.6.1 Estimation with experimental data 384
14.6.2 Propensity score stratification 385 14.6.3 MMWS 386 14.7 Summary 387
15 Mediation through spill-over 391 15.1 Definition of mediated effects
through spill-over in a cluster randomized trial 393 15.1.1 Notation 393
15.1.2 Treatment effect mediated by a focal individual's compliance 394
15.1.3 Treatment effect mediated by peers' compliance through spill-over
394 15.1.4 Decomposition of the total treatment effect 395 15.2
Identification and estimation of the spill-over effect in a cluster
randomized design 395 15.2.1 Identification in an ideal experiment 395
15.2.2 Identification when the mediators are not randomized 398 15.2.3
Estimation of mediated effects through spill-over 400 15.3 Definition of
mediated effects through spill-over in a multisite trial 402 15.3.1
Notation 402 15.3.2 Treatment effect mediated by a focal individual's
compliance 404 15.3.3 Treatment effect mediated by peers' compliance
through spill-over 404 15.3.4 Direct effect of individual treatment
assignment on the outcome 405 15.3.5 Direct effect of peer treatment
assignment on the outcome 405 15.3.6 Decomposition of the total treatment
effect 405 15.4 Identification and estimation of spill-over effects in a
multisite trial 406 15.4.1 Identification in an ideal experiment 407 15.4.2
Identification when the mediators are not randomized 409 15.4.3 Estimation
of mediated effects through spill-over 410 15.5 Consequences of omitting
spill-over effects in causal mediation analyses 412 15.5.1 Biased inference
in a cluster randomized trial 413 15.5.2 Biased inference in a multisite
randomized trial 413 15.5.3 Biased inference of the local average treatment
effect 415 15.6 Quasiexperimental application 416 15.7 Summary 419 Appendix
15.1: Derivation of the weight for estimating the population average
counterfactual outcome E[Y(1, p, 0,M.( p))] 419 Appendix 15.2: Derivation
of bias in the ITT effect due to the omission of spill-over effects 420
Index 423
mediation, and spill-over 3 1.1.1 Moderated treatment effects 5 1.1.2
Mediated treatment effects 7 1.1.3 Spill-over effects of a treatment 8 1.2
Weighting methods for causal inference 10 1.3 Objectives and organization
of the book 11 1.4 How is this book situated among other publications on
related topics? 12 2 Review of causal inference concepts and methods 18 2.1
Causal inference theory 18 2.1.1 Attributes versus causes 18 2.1.2
Potential outcomes and individual-specific causal effects 19 2.1.3
Inference about population average causal effects 22 2.2 Applications to
Lord's paradox and Simpson's paradox 27 2.2.1 Lord's paradox 27 2.2.2
Simpson's paradox 31 2.3 Identification and estimation 34 2.3.1 Selection
bias 35 2.3.2 Sampling bias 35 2.3.3 Estimation efficiency 36 Appendix 2.1:
Potential bias in a prima facie effect 36 Appendix 2.2: Application of the
causal inference theory to Lord's paradox 37 3 Review of causal inference
designs and analytic methods 40 3.1 Experimental designs 40 3.1.1
Completely randomized designs 40 3.1.2 Randomized block designs 41 3.1.3
Covariance adjustment for improving efficiency 43 3.1.4 Multilevel
experimental designs 43 3.2 Quasiexperimental designs 44 3.2.1
Nonequivalent comparison group designs 44 3.2.2 Other quasiexperimental
designs 45 3.3 Statistical adjustment methods 46 3.3.1 ANCOVA and multiple
regression 46 3.3.2 Matching and stratification 50 3.3.3 Other statistical
adjustment methods 51 3.4 Propensity score 55 3.4.1 What is a propensity
score? 56 3.4.2 Balancing property of the propensity score 57 3.4.3 Pooling
conditional treatment effect estimate: Matching, stratification, and
covariance adjustment 60 Appendix 3.A: Potential bias due to the omission
of treatment-by-covariate interaction 70 Appendix 3.B: Variable selection
for the propensity score model 71 4 Adjustment for selection bias through
weighting 76 4.1 Weighted estimation of population parameters in survey
sampling 77 4.1.1 Simple random sample 77 4.1.2 Proportionate sample 78
4.1.3 Disproportionate sample 79 4.2 Weighting adjustment for selection
bias in causal inference 80 4.2.1 Experimental result 81 4.2.2
Quasiexperimental result 81 4.2.3 Sample weight for bias removal 82 4.2.4
IPTW for bias removal 84 4.3 MMWS 86 4.3.1 Theoretical rationale 86 4.3.2
MMWS analytic procedure 91 4.3.3 Inherent connection and major distinctions
between MMWS and IPTW 93 Appendix 4.A: Proof of MMWS-adjusted mean observed
outcome being unbiased for the population average potential outcome 95
Appendix 4.B: Derivation of MMWS for estimating the treatment effect on the
treated 96 Appendix 4.C: Theoretical equivalence of MMWS and IPTW 97
Appendix 4.D: Simulations comparing MMWS and IPTW under misspecifications
of the functional form of a propensity score model 97 5 Evaluations of
multivalued treatments 100 5.1 Defining the causal effects of multivalued
treatments 100 5.2 Existing designs and analytic methods for evaluating
multivalued treatments 102 5.2.1 Experimental designs and analysis 102
5.2.2 Quasiexperimental designs and analysis 105 5.3 MMWS for evaluating
multivalued treatments 112 5.3.1 Basic rationale 113 5.3.2 Analytic
procedure 114 5.3.3 Identification assumptions 121 5.4 Summary 123 Appendix
5.A: Multiple IV for evaluating multivalued treatments 124 Part II
Moderation 127 6 Moderated treatment effects: concepts and existing
analytic methods 129 6.1 What is moderation? 129 6.1.1 Past discussions of
moderation 130 6.1.2 Definition of moderated treatment effects 133 6.2
Experimental designs and analytic methods for investigating explicit
moderators 136 6.2.1 Randomized block designs 137 6.2.2 Factorial designs
140 6.3 Existing research designs and analytic methods for investigating
implicit moderators 142 6.3.1 Multisite randomized trials 143 6.3.2
Principal stratification 149 Appendix 6.A: Derivation of bias in the
fixed-effects estimator when the treatment effect is heterogeneous in
multisite randomized trials 151 Appendix 6.B: Derivation of bias in the
mixed-effects estimator when the probability of treatment assignment varies
across sites 153 Appendix 6.C: Derivation and proof of the population
weight applied to mixed-effects models for eliminating bias in multisite
randomized trials 153 7 Marginal mean weighting through stratification for
investigating moderated treatment effects 159 7.1 Existing methods for
moderation analyses with quasiexperimental data 159 7.1.1 Analysis of
covariance and regression-based adjustment 161 7.1.2 Propensity score-based
adjustment 165 7.2 MMWS estimation of treatment effects moderated by
individual or contextual characteristics 168 7.2.1 Application example 170
7.2.2 Analytic procedure 170 7.3 MMWS estimation of the joint effects of
concurrent treatments 174 7.3.1 Application example 174 7.3.2 Analytic
procedure 175 7.3.3 Joint treatment effects moderated by individual or
contextual characteristics 179 8 Cumulative effects of time-varying
treatments 185 8.1 Causal effects of treatment sequences 186 8.1.1
Application example 186 8.1.2 Causal parameters 187 8.2 Existing strategies
for evaluating time-varying treatments 190 8.2.1 The endogeneity problem in
nonexperimental data 190 8.2.2 SEM 191 8.2.3 Fixed-effects econometric
models 192 8.2.4 Sequential randomization 192 8.2.5 Dynamic treatment
regimes 193 8.2.6 Marginal structural models and structural nested models
194 8.3 MMWS for evaluating 2-year treatment sequences 195 8.3.1 Sequential
ignorability 195 8.3.2 Propensity scores 196 8.3.3 MMWS computation 197
8.3.4 Two-year growth model specification 199 8.4 MMWS for evaluating
multiyear sequences of multivalued treatments 204 8.4.1 Sequential
ignorability of multiyear treatment sequences 204 8.4.2 Propensity scores
for multiyear treatment sequences 204 8.4.3 MMWS computation 205 8.4.4
Weighted multiyear growth model 205 8.4.5 Issues of sample size 206 8.5
Conclusion 207 Appendix 8.A: A saturated model for evaluating multivalued
treatments over multiple time periods 207 Part III Mediation 211 9 Concepts
of mediated treatment effects and experimental designs for investigating
causal mechanisms 213 9.1 Introduction 214 9.2 Path coefficients 215 9.3
Potential outcomes and potential mediators 216 9.3.1 Controlled direct
effects 217 9.3.2 Controlled treatment-by-mediator interaction effect 217
9.4 Causal effects with counterfactual mediators 219 9.4.1 Natural direct
effect 219 9.4.2 Natural indirect effect 220 9.4.3 Natural
treatment-by-mediator interaction effect 220 9.4.4 Unstable unit treatment
value 221 9.5 Population causal parameters 222 9.5.1 Population average
natural direct effect 224 9.5.2 Population average natural indirect effect
225 9.6 Experimental designs for studying causal mediation 225 9.6.1
Sequentially randomized designs 228 9.6.2 Two-phase experimental designs
228 9.6.3 Three- and four-treatment arm designs 230 9.6.4 Experimental
causal-chain designs 231 9.6.5 Moderation-of-process designs 231 9.6.6
Augmented encouragement designs 232 9.6.7 Parallel experimental designs and
parallel encouragement designs 232 9.6.8 Crossover experimental designs and
crossover encouragement designs 233 9.6.9 Summary 234 10 Existing analytic
methods for investigating causal mediation mechanisms 238 10.1 Path
analysis and SEM 239 10.1.1 Analytic procedure for continuous outcomes 239
10.1.2 Identification assumptions 242 10.1.3 Analytic procedure for
discrete outcomes 245 10.2 Modified regression approach 246 10.2.1 Analytic
procedure for continuous outcomes 246 10.2.2 Identification assumptions 247
10.2.3 Analytic procedure for binary outcomes 248 10.3 Marginal structural
models 250 10.3.1 Analytic procedure 250 10.3.2 Identification assumptions
252 10.4 Conditional structural models 252 10.4.1 Analytic procedure 252
10.4.2 Identification assumptions 253 10.5 Alternative weighting methods
254 10.5.1 Analytic procedure 254 10.5.2 Identification assumptions 256
10.6 Resampling approach 256 10.6.1 Analytic procedure 256 10.6.2
Identification assumptions 257 10.7 IV method 257 10.7.1 Rationale and
analytic procedure 257 10.7.2 Identification assumptions 258 10.8 Principal
stratification 259 10.8.1 Rationale and analytic procedure 259 10.8.2
Identification assumptions 260 10.9 Sensitivity analysis 261 10.9.1
Unadjusted confounding as a product of hypothetical regression coefficients
261 10.9.2 Unadjusted confounding reflected in a hypothetical correlation
coefficient 262 10.9.3 Limitations when the selection mechanism differs by
treatment 264 10.9.4 Other sensitivity analyses 265 10.10 Conclusion 265
10.10.1 The essentiality of sequential ignorability 265 10.10.2
Treatment-by-mediator interactions 266 10.10.3 Homogeneous versus
heterogeneous causal effects 266 10.10.4 Model-based assumptions 266
Appendix 10.A: Bias in path analysis estimation due to the omission of
treatment-by-mediator interaction 267 11 Investigations of a simple
mediation mechanism 273 11.1 Application example: national evaluation of
welfare-to-work strategies 274 11.1.1 Historical context 274 11.1.2
Research questions 275 11.1.3 Causal parameters 275 11.1.4 NEWWS Riverside
data 277 11.2 RMPW rationale 277 11.2.1 RMPW in a sequentially randomized
design 278 11.2.2 RMPW in a sequentially randomized block design 283 11.2.3
RMPW in a standard randomized experiment 285 11.2.4 Identification
assumptions 286 11.3 Parametric RMPW procedure 287 11.4 Nonparametric RMPW
procedure 290 11.5 Simulation results 292 11.5.1 Correctly specified
propensity score models 292 11.5.2 Misspecified propensity score models 294
11.5.3 Comparisons with path analysis and IV results 294 11.6 Discussion
295 11.6.1 Advantages of the RMPW strategy 295 11.6.2 Limitations of the
RMPW strategy 295 Appendix 11.A: Causal effect estimation through the RMPW
procedure 296 Appendix 11.B: Proof of the consistency of RMPW estimation
297 12 RMPW extensions to alternative designs and measurement 301 12.1 RMPW
extensions to mediators and outcomes of alternative distributions 301
12.1.1 Extensions to a multicategory mediator 302 12.1.2 Extensions to a
continuous mediator 304 12.1.3 Extensions to a binary outcome 306 12.2 RMPW
extensions to alternative research designs 306 12.2.1 Extensions to
quasiexperimental data 307 12.2.2 Extensions to data from cluster
randomized trials 308 12.2.3 Extensions to data from multisite randomized
trials 313 12.3 Alternative decomposition of the treatment effect 321 13
RMPW extensions to studies of complex mediation mechanisms 325 13.1 RMPW
extensions to moderated mediation 325 13.1.1 RMPW analytic procedure for
estimating and testing moderated mediation 326 13.1.2 Path analysis/SEM
approach to analyzing moderated mediation 327 13.1.3 Principal
stratification and moderated mediation 328 13.2 RMPW extensions to
concurrent mediators 328 13.2.1 Treatment effect decomposition 329 13.2.2
Identification assumptions 333 13.2.3 RMPW procedure 333 13.2.4 Contrast
with the linear SEM approach 338 13.2.5 Contrast with the multivariate IV
approach 339 13.3 RMPW extensions to consecutive mediators 340 13.3.1
Treatment effect decomposition 341 13.3.2 Identification assumptions 345
13.3.3 RMPW procedure 347 13.3.4 Contrast with the linear SEM approach 353
13.3.5 Contrast with the sensitivity-based estimation of bounds for causal
effects 354 13.4 Discussion 355 Appendix 13.A: Derivation of RMPW for
estimating population average counterfactual outcomes of two concurrent
mediators 355 Appendix 13.B: Derivation of RMPW for estimating population
average counterfactual outcomes of consecutive mediators 358 Part IV
Spill-over 363 14 Spill-over of treatment effects: concepts and methods 365
14.1 Spill-over: A nuisance, a trifle, or a focus? 365 14.2 Stable versus
unstable potential outcome values: An example from agriculture 367 14.3
Consequences for causal inference when spill-over is overlooked 369 14.4
Modified framework of causal inference 371 14.4.1 Treatment settings 371
14.4.2 Simplified characterization of treatment settings 373 14.4.3 Causal
effects of individual treatment assignment and of peer treatment assignment
375 14.5 Identification: Challenges and solutions 376 14.5.1 Hypothetical
experiments for identifying average treatment effects in the presence of
social interactions 376 14.5.2 Hypothetical experiments for identifying the
impact of social interactions 380 14.5.3 Application to an evaluation of
kindergarten retention 382 14.6 Analytic strategies for experimental and
quasiexperimental data 384 14.6.1 Estimation with experimental data 384
14.6.2 Propensity score stratification 385 14.6.3 MMWS 386 14.7 Summary 387
15 Mediation through spill-over 391 15.1 Definition of mediated effects
through spill-over in a cluster randomized trial 393 15.1.1 Notation 393
15.1.2 Treatment effect mediated by a focal individual's compliance 394
15.1.3 Treatment effect mediated by peers' compliance through spill-over
394 15.1.4 Decomposition of the total treatment effect 395 15.2
Identification and estimation of the spill-over effect in a cluster
randomized design 395 15.2.1 Identification in an ideal experiment 395
15.2.2 Identification when the mediators are not randomized 398 15.2.3
Estimation of mediated effects through spill-over 400 15.3 Definition of
mediated effects through spill-over in a multisite trial 402 15.3.1
Notation 402 15.3.2 Treatment effect mediated by a focal individual's
compliance 404 15.3.3 Treatment effect mediated by peers' compliance
through spill-over 404 15.3.4 Direct effect of individual treatment
assignment on the outcome 405 15.3.5 Direct effect of peer treatment
assignment on the outcome 405 15.3.6 Decomposition of the total treatment
effect 405 15.4 Identification and estimation of spill-over effects in a
multisite trial 406 15.4.1 Identification in an ideal experiment 407 15.4.2
Identification when the mediators are not randomized 409 15.4.3 Estimation
of mediated effects through spill-over 410 15.5 Consequences of omitting
spill-over effects in causal mediation analyses 412 15.5.1 Biased inference
in a cluster randomized trial 413 15.5.2 Biased inference in a multisite
randomized trial 413 15.5.3 Biased inference of the local average treatment
effect 415 15.6 Quasiexperimental application 416 15.7 Summary 419 Appendix
15.1: Derivation of the weight for estimating the population average
counterfactual outcome E[Y(1, p, 0,M.( p))] 419 Appendix 15.2: Derivation
of bias in the ITT effect due to the omission of spill-over effects 420
Index 423
Preface xv Part I Overview 1 1 Introduction 3 1.1 Concepts of moderation,
mediation, and spill-over 3 1.1.1 Moderated treatment effects 5 1.1.2
Mediated treatment effects 7 1.1.3 Spill-over effects of a treatment 8 1.2
Weighting methods for causal inference 10 1.3 Objectives and organization
of the book 11 1.4 How is this book situated among other publications on
related topics? 12 2 Review of causal inference concepts and methods 18 2.1
Causal inference theory 18 2.1.1 Attributes versus causes 18 2.1.2
Potential outcomes and individual-specific causal effects 19 2.1.3
Inference about population average causal effects 22 2.2 Applications to
Lord's paradox and Simpson's paradox 27 2.2.1 Lord's paradox 27 2.2.2
Simpson's paradox 31 2.3 Identification and estimation 34 2.3.1 Selection
bias 35 2.3.2 Sampling bias 35 2.3.3 Estimation efficiency 36 Appendix 2.1:
Potential bias in a prima facie effect 36 Appendix 2.2: Application of the
causal inference theory to Lord's paradox 37 3 Review of causal inference
designs and analytic methods 40 3.1 Experimental designs 40 3.1.1
Completely randomized designs 40 3.1.2 Randomized block designs 41 3.1.3
Covariance adjustment for improving efficiency 43 3.1.4 Multilevel
experimental designs 43 3.2 Quasiexperimental designs 44 3.2.1
Nonequivalent comparison group designs 44 3.2.2 Other quasiexperimental
designs 45 3.3 Statistical adjustment methods 46 3.3.1 ANCOVA and multiple
regression 46 3.3.2 Matching and stratification 50 3.3.3 Other statistical
adjustment methods 51 3.4 Propensity score 55 3.4.1 What is a propensity
score? 56 3.4.2 Balancing property of the propensity score 57 3.4.3 Pooling
conditional treatment effect estimate: Matching, stratification, and
covariance adjustment 60 Appendix 3.A: Potential bias due to the omission
of treatment-by-covariate interaction 70 Appendix 3.B: Variable selection
for the propensity score model 71 4 Adjustment for selection bias through
weighting 76 4.1 Weighted estimation of population parameters in survey
sampling 77 4.1.1 Simple random sample 77 4.1.2 Proportionate sample 78
4.1.3 Disproportionate sample 79 4.2 Weighting adjustment for selection
bias in causal inference 80 4.2.1 Experimental result 81 4.2.2
Quasiexperimental result 81 4.2.3 Sample weight for bias removal 82 4.2.4
IPTW for bias removal 84 4.3 MMWS 86 4.3.1 Theoretical rationale 86 4.3.2
MMWS analytic procedure 91 4.3.3 Inherent connection and major distinctions
between MMWS and IPTW 93 Appendix 4.A: Proof of MMWS-adjusted mean observed
outcome being unbiased for the population average potential outcome 95
Appendix 4.B: Derivation of MMWS for estimating the treatment effect on the
treated 96 Appendix 4.C: Theoretical equivalence of MMWS and IPTW 97
Appendix 4.D: Simulations comparing MMWS and IPTW under misspecifications
of the functional form of a propensity score model 97 5 Evaluations of
multivalued treatments 100 5.1 Defining the causal effects of multivalued
treatments 100 5.2 Existing designs and analytic methods for evaluating
multivalued treatments 102 5.2.1 Experimental designs and analysis 102
5.2.2 Quasiexperimental designs and analysis 105 5.3 MMWS for evaluating
multivalued treatments 112 5.3.1 Basic rationale 113 5.3.2 Analytic
procedure 114 5.3.3 Identification assumptions 121 5.4 Summary 123 Appendix
5.A: Multiple IV for evaluating multivalued treatments 124 Part II
Moderation 127 6 Moderated treatment effects: concepts and existing
analytic methods 129 6.1 What is moderation? 129 6.1.1 Past discussions of
moderation 130 6.1.2 Definition of moderated treatment effects 133 6.2
Experimental designs and analytic methods for investigating explicit
moderators 136 6.2.1 Randomized block designs 137 6.2.2 Factorial designs
140 6.3 Existing research designs and analytic methods for investigating
implicit moderators 142 6.3.1 Multisite randomized trials 143 6.3.2
Principal stratification 149 Appendix 6.A: Derivation of bias in the
fixed-effects estimator when the treatment effect is heterogeneous in
multisite randomized trials 151 Appendix 6.B: Derivation of bias in the
mixed-effects estimator when the probability of treatment assignment varies
across sites 153 Appendix 6.C: Derivation and proof of the population
weight applied to mixed-effects models for eliminating bias in multisite
randomized trials 153 7 Marginal mean weighting through stratification for
investigating moderated treatment effects 159 7.1 Existing methods for
moderation analyses with quasiexperimental data 159 7.1.1 Analysis of
covariance and regression-based adjustment 161 7.1.2 Propensity score-based
adjustment 165 7.2 MMWS estimation of treatment effects moderated by
individual or contextual characteristics 168 7.2.1 Application example 170
7.2.2 Analytic procedure 170 7.3 MMWS estimation of the joint effects of
concurrent treatments 174 7.3.1 Application example 174 7.3.2 Analytic
procedure 175 7.3.3 Joint treatment effects moderated by individual or
contextual characteristics 179 8 Cumulative effects of time-varying
treatments 185 8.1 Causal effects of treatment sequences 186 8.1.1
Application example 186 8.1.2 Causal parameters 187 8.2 Existing strategies
for evaluating time-varying treatments 190 8.2.1 The endogeneity problem in
nonexperimental data 190 8.2.2 SEM 191 8.2.3 Fixed-effects econometric
models 192 8.2.4 Sequential randomization 192 8.2.5 Dynamic treatment
regimes 193 8.2.6 Marginal structural models and structural nested models
194 8.3 MMWS for evaluating 2-year treatment sequences 195 8.3.1 Sequential
ignorability 195 8.3.2 Propensity scores 196 8.3.3 MMWS computation 197
8.3.4 Two-year growth model specification 199 8.4 MMWS for evaluating
multiyear sequences of multivalued treatments 204 8.4.1 Sequential
ignorability of multiyear treatment sequences 204 8.4.2 Propensity scores
for multiyear treatment sequences 204 8.4.3 MMWS computation 205 8.4.4
Weighted multiyear growth model 205 8.4.5 Issues of sample size 206 8.5
Conclusion 207 Appendix 8.A: A saturated model for evaluating multivalued
treatments over multiple time periods 207 Part III Mediation 211 9 Concepts
of mediated treatment effects and experimental designs for investigating
causal mechanisms 213 9.1 Introduction 214 9.2 Path coefficients 215 9.3
Potential outcomes and potential mediators 216 9.3.1 Controlled direct
effects 217 9.3.2 Controlled treatment-by-mediator interaction effect 217
9.4 Causal effects with counterfactual mediators 219 9.4.1 Natural direct
effect 219 9.4.2 Natural indirect effect 220 9.4.3 Natural
treatment-by-mediator interaction effect 220 9.4.4 Unstable unit treatment
value 221 9.5 Population causal parameters 222 9.5.1 Population average
natural direct effect 224 9.5.2 Population average natural indirect effect
225 9.6 Experimental designs for studying causal mediation 225 9.6.1
Sequentially randomized designs 228 9.6.2 Two-phase experimental designs
228 9.6.3 Three- and four-treatment arm designs 230 9.6.4 Experimental
causal-chain designs 231 9.6.5 Moderation-of-process designs 231 9.6.6
Augmented encouragement designs 232 9.6.7 Parallel experimental designs and
parallel encouragement designs 232 9.6.8 Crossover experimental designs and
crossover encouragement designs 233 9.6.9 Summary 234 10 Existing analytic
methods for investigating causal mediation mechanisms 238 10.1 Path
analysis and SEM 239 10.1.1 Analytic procedure for continuous outcomes 239
10.1.2 Identification assumptions 242 10.1.3 Analytic procedure for
discrete outcomes 245 10.2 Modified regression approach 246 10.2.1 Analytic
procedure for continuous outcomes 246 10.2.2 Identification assumptions 247
10.2.3 Analytic procedure for binary outcomes 248 10.3 Marginal structural
models 250 10.3.1 Analytic procedure 250 10.3.2 Identification assumptions
252 10.4 Conditional structural models 252 10.4.1 Analytic procedure 252
10.4.2 Identification assumptions 253 10.5 Alternative weighting methods
254 10.5.1 Analytic procedure 254 10.5.2 Identification assumptions 256
10.6 Resampling approach 256 10.6.1 Analytic procedure 256 10.6.2
Identification assumptions 257 10.7 IV method 257 10.7.1 Rationale and
analytic procedure 257 10.7.2 Identification assumptions 258 10.8 Principal
stratification 259 10.8.1 Rationale and analytic procedure 259 10.8.2
Identification assumptions 260 10.9 Sensitivity analysis 261 10.9.1
Unadjusted confounding as a product of hypothetical regression coefficients
261 10.9.2 Unadjusted confounding reflected in a hypothetical correlation
coefficient 262 10.9.3 Limitations when the selection mechanism differs by
treatment 264 10.9.4 Other sensitivity analyses 265 10.10 Conclusion 265
10.10.1 The essentiality of sequential ignorability 265 10.10.2
Treatment-by-mediator interactions 266 10.10.3 Homogeneous versus
heterogeneous causal effects 266 10.10.4 Model-based assumptions 266
Appendix 10.A: Bias in path analysis estimation due to the omission of
treatment-by-mediator interaction 267 11 Investigations of a simple
mediation mechanism 273 11.1 Application example: national evaluation of
welfare-to-work strategies 274 11.1.1 Historical context 274 11.1.2
Research questions 275 11.1.3 Causal parameters 275 11.1.4 NEWWS Riverside
data 277 11.2 RMPW rationale 277 11.2.1 RMPW in a sequentially randomized
design 278 11.2.2 RMPW in a sequentially randomized block design 283 11.2.3
RMPW in a standard randomized experiment 285 11.2.4 Identification
assumptions 286 11.3 Parametric RMPW procedure 287 11.4 Nonparametric RMPW
procedure 290 11.5 Simulation results 292 11.5.1 Correctly specified
propensity score models 292 11.5.2 Misspecified propensity score models 294
11.5.3 Comparisons with path analysis and IV results 294 11.6 Discussion
295 11.6.1 Advantages of the RMPW strategy 295 11.6.2 Limitations of the
RMPW strategy 295 Appendix 11.A: Causal effect estimation through the RMPW
procedure 296 Appendix 11.B: Proof of the consistency of RMPW estimation
297 12 RMPW extensions to alternative designs and measurement 301 12.1 RMPW
extensions to mediators and outcomes of alternative distributions 301
12.1.1 Extensions to a multicategory mediator 302 12.1.2 Extensions to a
continuous mediator 304 12.1.3 Extensions to a binary outcome 306 12.2 RMPW
extensions to alternative research designs 306 12.2.1 Extensions to
quasiexperimental data 307 12.2.2 Extensions to data from cluster
randomized trials 308 12.2.3 Extensions to data from multisite randomized
trials 313 12.3 Alternative decomposition of the treatment effect 321 13
RMPW extensions to studies of complex mediation mechanisms 325 13.1 RMPW
extensions to moderated mediation 325 13.1.1 RMPW analytic procedure for
estimating and testing moderated mediation 326 13.1.2 Path analysis/SEM
approach to analyzing moderated mediation 327 13.1.3 Principal
stratification and moderated mediation 328 13.2 RMPW extensions to
concurrent mediators 328 13.2.1 Treatment effect decomposition 329 13.2.2
Identification assumptions 333 13.2.3 RMPW procedure 333 13.2.4 Contrast
with the linear SEM approach 338 13.2.5 Contrast with the multivariate IV
approach 339 13.3 RMPW extensions to consecutive mediators 340 13.3.1
Treatment effect decomposition 341 13.3.2 Identification assumptions 345
13.3.3 RMPW procedure 347 13.3.4 Contrast with the linear SEM approach 353
13.3.5 Contrast with the sensitivity-based estimation of bounds for causal
effects 354 13.4 Discussion 355 Appendix 13.A: Derivation of RMPW for
estimating population average counterfactual outcomes of two concurrent
mediators 355 Appendix 13.B: Derivation of RMPW for estimating population
average counterfactual outcomes of consecutive mediators 358 Part IV
Spill-over 363 14 Spill-over of treatment effects: concepts and methods 365
14.1 Spill-over: A nuisance, a trifle, or a focus? 365 14.2 Stable versus
unstable potential outcome values: An example from agriculture 367 14.3
Consequences for causal inference when spill-over is overlooked 369 14.4
Modified framework of causal inference 371 14.4.1 Treatment settings 371
14.4.2 Simplified characterization of treatment settings 373 14.4.3 Causal
effects of individual treatment assignment and of peer treatment assignment
375 14.5 Identification: Challenges and solutions 376 14.5.1 Hypothetical
experiments for identifying average treatment effects in the presence of
social interactions 376 14.5.2 Hypothetical experiments for identifying the
impact of social interactions 380 14.5.3 Application to an evaluation of
kindergarten retention 382 14.6 Analytic strategies for experimental and
quasiexperimental data 384 14.6.1 Estimation with experimental data 384
14.6.2 Propensity score stratification 385 14.6.3 MMWS 386 14.7 Summary 387
15 Mediation through spill-over 391 15.1 Definition of mediated effects
through spill-over in a cluster randomized trial 393 15.1.1 Notation 393
15.1.2 Treatment effect mediated by a focal individual's compliance 394
15.1.3 Treatment effect mediated by peers' compliance through spill-over
394 15.1.4 Decomposition of the total treatment effect 395 15.2
Identification and estimation of the spill-over effect in a cluster
randomized design 395 15.2.1 Identification in an ideal experiment 395
15.2.2 Identification when the mediators are not randomized 398 15.2.3
Estimation of mediated effects through spill-over 400 15.3 Definition of
mediated effects through spill-over in a multisite trial 402 15.3.1
Notation 402 15.3.2 Treatment effect mediated by a focal individual's
compliance 404 15.3.3 Treatment effect mediated by peers' compliance
through spill-over 404 15.3.4 Direct effect of individual treatment
assignment on the outcome 405 15.3.5 Direct effect of peer treatment
assignment on the outcome 405 15.3.6 Decomposition of the total treatment
effect 405 15.4 Identification and estimation of spill-over effects in a
multisite trial 406 15.4.1 Identification in an ideal experiment 407 15.4.2
Identification when the mediators are not randomized 409 15.4.3 Estimation
of mediated effects through spill-over 410 15.5 Consequences of omitting
spill-over effects in causal mediation analyses 412 15.5.1 Biased inference
in a cluster randomized trial 413 15.5.2 Biased inference in a multisite
randomized trial 413 15.5.3 Biased inference of the local average treatment
effect 415 15.6 Quasiexperimental application 416 15.7 Summary 419 Appendix
15.1: Derivation of the weight for estimating the population average
counterfactual outcome E[Y(1, p, 0,M.( p))] 419 Appendix 15.2: Derivation
of bias in the ITT effect due to the omission of spill-over effects 420
Index 423
mediation, and spill-over 3 1.1.1 Moderated treatment effects 5 1.1.2
Mediated treatment effects 7 1.1.3 Spill-over effects of a treatment 8 1.2
Weighting methods for causal inference 10 1.3 Objectives and organization
of the book 11 1.4 How is this book situated among other publications on
related topics? 12 2 Review of causal inference concepts and methods 18 2.1
Causal inference theory 18 2.1.1 Attributes versus causes 18 2.1.2
Potential outcomes and individual-specific causal effects 19 2.1.3
Inference about population average causal effects 22 2.2 Applications to
Lord's paradox and Simpson's paradox 27 2.2.1 Lord's paradox 27 2.2.2
Simpson's paradox 31 2.3 Identification and estimation 34 2.3.1 Selection
bias 35 2.3.2 Sampling bias 35 2.3.3 Estimation efficiency 36 Appendix 2.1:
Potential bias in a prima facie effect 36 Appendix 2.2: Application of the
causal inference theory to Lord's paradox 37 3 Review of causal inference
designs and analytic methods 40 3.1 Experimental designs 40 3.1.1
Completely randomized designs 40 3.1.2 Randomized block designs 41 3.1.3
Covariance adjustment for improving efficiency 43 3.1.4 Multilevel
experimental designs 43 3.2 Quasiexperimental designs 44 3.2.1
Nonequivalent comparison group designs 44 3.2.2 Other quasiexperimental
designs 45 3.3 Statistical adjustment methods 46 3.3.1 ANCOVA and multiple
regression 46 3.3.2 Matching and stratification 50 3.3.3 Other statistical
adjustment methods 51 3.4 Propensity score 55 3.4.1 What is a propensity
score? 56 3.4.2 Balancing property of the propensity score 57 3.4.3 Pooling
conditional treatment effect estimate: Matching, stratification, and
covariance adjustment 60 Appendix 3.A: Potential bias due to the omission
of treatment-by-covariate interaction 70 Appendix 3.B: Variable selection
for the propensity score model 71 4 Adjustment for selection bias through
weighting 76 4.1 Weighted estimation of population parameters in survey
sampling 77 4.1.1 Simple random sample 77 4.1.2 Proportionate sample 78
4.1.3 Disproportionate sample 79 4.2 Weighting adjustment for selection
bias in causal inference 80 4.2.1 Experimental result 81 4.2.2
Quasiexperimental result 81 4.2.3 Sample weight for bias removal 82 4.2.4
IPTW for bias removal 84 4.3 MMWS 86 4.3.1 Theoretical rationale 86 4.3.2
MMWS analytic procedure 91 4.3.3 Inherent connection and major distinctions
between MMWS and IPTW 93 Appendix 4.A: Proof of MMWS-adjusted mean observed
outcome being unbiased for the population average potential outcome 95
Appendix 4.B: Derivation of MMWS for estimating the treatment effect on the
treated 96 Appendix 4.C: Theoretical equivalence of MMWS and IPTW 97
Appendix 4.D: Simulations comparing MMWS and IPTW under misspecifications
of the functional form of a propensity score model 97 5 Evaluations of
multivalued treatments 100 5.1 Defining the causal effects of multivalued
treatments 100 5.2 Existing designs and analytic methods for evaluating
multivalued treatments 102 5.2.1 Experimental designs and analysis 102
5.2.2 Quasiexperimental designs and analysis 105 5.3 MMWS for evaluating
multivalued treatments 112 5.3.1 Basic rationale 113 5.3.2 Analytic
procedure 114 5.3.3 Identification assumptions 121 5.4 Summary 123 Appendix
5.A: Multiple IV for evaluating multivalued treatments 124 Part II
Moderation 127 6 Moderated treatment effects: concepts and existing
analytic methods 129 6.1 What is moderation? 129 6.1.1 Past discussions of
moderation 130 6.1.2 Definition of moderated treatment effects 133 6.2
Experimental designs and analytic methods for investigating explicit
moderators 136 6.2.1 Randomized block designs 137 6.2.2 Factorial designs
140 6.3 Existing research designs and analytic methods for investigating
implicit moderators 142 6.3.1 Multisite randomized trials 143 6.3.2
Principal stratification 149 Appendix 6.A: Derivation of bias in the
fixed-effects estimator when the treatment effect is heterogeneous in
multisite randomized trials 151 Appendix 6.B: Derivation of bias in the
mixed-effects estimator when the probability of treatment assignment varies
across sites 153 Appendix 6.C: Derivation and proof of the population
weight applied to mixed-effects models for eliminating bias in multisite
randomized trials 153 7 Marginal mean weighting through stratification for
investigating moderated treatment effects 159 7.1 Existing methods for
moderation analyses with quasiexperimental data 159 7.1.1 Analysis of
covariance and regression-based adjustment 161 7.1.2 Propensity score-based
adjustment 165 7.2 MMWS estimation of treatment effects moderated by
individual or contextual characteristics 168 7.2.1 Application example 170
7.2.2 Analytic procedure 170 7.3 MMWS estimation of the joint effects of
concurrent treatments 174 7.3.1 Application example 174 7.3.2 Analytic
procedure 175 7.3.3 Joint treatment effects moderated by individual or
contextual characteristics 179 8 Cumulative effects of time-varying
treatments 185 8.1 Causal effects of treatment sequences 186 8.1.1
Application example 186 8.1.2 Causal parameters 187 8.2 Existing strategies
for evaluating time-varying treatments 190 8.2.1 The endogeneity problem in
nonexperimental data 190 8.2.2 SEM 191 8.2.3 Fixed-effects econometric
models 192 8.2.4 Sequential randomization 192 8.2.5 Dynamic treatment
regimes 193 8.2.6 Marginal structural models and structural nested models
194 8.3 MMWS for evaluating 2-year treatment sequences 195 8.3.1 Sequential
ignorability 195 8.3.2 Propensity scores 196 8.3.3 MMWS computation 197
8.3.4 Two-year growth model specification 199 8.4 MMWS for evaluating
multiyear sequences of multivalued treatments 204 8.4.1 Sequential
ignorability of multiyear treatment sequences 204 8.4.2 Propensity scores
for multiyear treatment sequences 204 8.4.3 MMWS computation 205 8.4.4
Weighted multiyear growth model 205 8.4.5 Issues of sample size 206 8.5
Conclusion 207 Appendix 8.A: A saturated model for evaluating multivalued
treatments over multiple time periods 207 Part III Mediation 211 9 Concepts
of mediated treatment effects and experimental designs for investigating
causal mechanisms 213 9.1 Introduction 214 9.2 Path coefficients 215 9.3
Potential outcomes and potential mediators 216 9.3.1 Controlled direct
effects 217 9.3.2 Controlled treatment-by-mediator interaction effect 217
9.4 Causal effects with counterfactual mediators 219 9.4.1 Natural direct
effect 219 9.4.2 Natural indirect effect 220 9.4.3 Natural
treatment-by-mediator interaction effect 220 9.4.4 Unstable unit treatment
value 221 9.5 Population causal parameters 222 9.5.1 Population average
natural direct effect 224 9.5.2 Population average natural indirect effect
225 9.6 Experimental designs for studying causal mediation 225 9.6.1
Sequentially randomized designs 228 9.6.2 Two-phase experimental designs
228 9.6.3 Three- and four-treatment arm designs 230 9.6.4 Experimental
causal-chain designs 231 9.6.5 Moderation-of-process designs 231 9.6.6
Augmented encouragement designs 232 9.6.7 Parallel experimental designs and
parallel encouragement designs 232 9.6.8 Crossover experimental designs and
crossover encouragement designs 233 9.6.9 Summary 234 10 Existing analytic
methods for investigating causal mediation mechanisms 238 10.1 Path
analysis and SEM 239 10.1.1 Analytic procedure for continuous outcomes 239
10.1.2 Identification assumptions 242 10.1.3 Analytic procedure for
discrete outcomes 245 10.2 Modified regression approach 246 10.2.1 Analytic
procedure for continuous outcomes 246 10.2.2 Identification assumptions 247
10.2.3 Analytic procedure for binary outcomes 248 10.3 Marginal structural
models 250 10.3.1 Analytic procedure 250 10.3.2 Identification assumptions
252 10.4 Conditional structural models 252 10.4.1 Analytic procedure 252
10.4.2 Identification assumptions 253 10.5 Alternative weighting methods
254 10.5.1 Analytic procedure 254 10.5.2 Identification assumptions 256
10.6 Resampling approach 256 10.6.1 Analytic procedure 256 10.6.2
Identification assumptions 257 10.7 IV method 257 10.7.1 Rationale and
analytic procedure 257 10.7.2 Identification assumptions 258 10.8 Principal
stratification 259 10.8.1 Rationale and analytic procedure 259 10.8.2
Identification assumptions 260 10.9 Sensitivity analysis 261 10.9.1
Unadjusted confounding as a product of hypothetical regression coefficients
261 10.9.2 Unadjusted confounding reflected in a hypothetical correlation
coefficient 262 10.9.3 Limitations when the selection mechanism differs by
treatment 264 10.9.4 Other sensitivity analyses 265 10.10 Conclusion 265
10.10.1 The essentiality of sequential ignorability 265 10.10.2
Treatment-by-mediator interactions 266 10.10.3 Homogeneous versus
heterogeneous causal effects 266 10.10.4 Model-based assumptions 266
Appendix 10.A: Bias in path analysis estimation due to the omission of
treatment-by-mediator interaction 267 11 Investigations of a simple
mediation mechanism 273 11.1 Application example: national evaluation of
welfare-to-work strategies 274 11.1.1 Historical context 274 11.1.2
Research questions 275 11.1.3 Causal parameters 275 11.1.4 NEWWS Riverside
data 277 11.2 RMPW rationale 277 11.2.1 RMPW in a sequentially randomized
design 278 11.2.2 RMPW in a sequentially randomized block design 283 11.2.3
RMPW in a standard randomized experiment 285 11.2.4 Identification
assumptions 286 11.3 Parametric RMPW procedure 287 11.4 Nonparametric RMPW
procedure 290 11.5 Simulation results 292 11.5.1 Correctly specified
propensity score models 292 11.5.2 Misspecified propensity score models 294
11.5.3 Comparisons with path analysis and IV results 294 11.6 Discussion
295 11.6.1 Advantages of the RMPW strategy 295 11.6.2 Limitations of the
RMPW strategy 295 Appendix 11.A: Causal effect estimation through the RMPW
procedure 296 Appendix 11.B: Proof of the consistency of RMPW estimation
297 12 RMPW extensions to alternative designs and measurement 301 12.1 RMPW
extensions to mediators and outcomes of alternative distributions 301
12.1.1 Extensions to a multicategory mediator 302 12.1.2 Extensions to a
continuous mediator 304 12.1.3 Extensions to a binary outcome 306 12.2 RMPW
extensions to alternative research designs 306 12.2.1 Extensions to
quasiexperimental data 307 12.2.2 Extensions to data from cluster
randomized trials 308 12.2.3 Extensions to data from multisite randomized
trials 313 12.3 Alternative decomposition of the treatment effect 321 13
RMPW extensions to studies of complex mediation mechanisms 325 13.1 RMPW
extensions to moderated mediation 325 13.1.1 RMPW analytic procedure for
estimating and testing moderated mediation 326 13.1.2 Path analysis/SEM
approach to analyzing moderated mediation 327 13.1.3 Principal
stratification and moderated mediation 328 13.2 RMPW extensions to
concurrent mediators 328 13.2.1 Treatment effect decomposition 329 13.2.2
Identification assumptions 333 13.2.3 RMPW procedure 333 13.2.4 Contrast
with the linear SEM approach 338 13.2.5 Contrast with the multivariate IV
approach 339 13.3 RMPW extensions to consecutive mediators 340 13.3.1
Treatment effect decomposition 341 13.3.2 Identification assumptions 345
13.3.3 RMPW procedure 347 13.3.4 Contrast with the linear SEM approach 353
13.3.5 Contrast with the sensitivity-based estimation of bounds for causal
effects 354 13.4 Discussion 355 Appendix 13.A: Derivation of RMPW for
estimating population average counterfactual outcomes of two concurrent
mediators 355 Appendix 13.B: Derivation of RMPW for estimating population
average counterfactual outcomes of consecutive mediators 358 Part IV
Spill-over 363 14 Spill-over of treatment effects: concepts and methods 365
14.1 Spill-over: A nuisance, a trifle, or a focus? 365 14.2 Stable versus
unstable potential outcome values: An example from agriculture 367 14.3
Consequences for causal inference when spill-over is overlooked 369 14.4
Modified framework of causal inference 371 14.4.1 Treatment settings 371
14.4.2 Simplified characterization of treatment settings 373 14.4.3 Causal
effects of individual treatment assignment and of peer treatment assignment
375 14.5 Identification: Challenges and solutions 376 14.5.1 Hypothetical
experiments for identifying average treatment effects in the presence of
social interactions 376 14.5.2 Hypothetical experiments for identifying the
impact of social interactions 380 14.5.3 Application to an evaluation of
kindergarten retention 382 14.6 Analytic strategies for experimental and
quasiexperimental data 384 14.6.1 Estimation with experimental data 384
14.6.2 Propensity score stratification 385 14.6.3 MMWS 386 14.7 Summary 387
15 Mediation through spill-over 391 15.1 Definition of mediated effects
through spill-over in a cluster randomized trial 393 15.1.1 Notation 393
15.1.2 Treatment effect mediated by a focal individual's compliance 394
15.1.3 Treatment effect mediated by peers' compliance through spill-over
394 15.1.4 Decomposition of the total treatment effect 395 15.2
Identification and estimation of the spill-over effect in a cluster
randomized design 395 15.2.1 Identification in an ideal experiment 395
15.2.2 Identification when the mediators are not randomized 398 15.2.3
Estimation of mediated effects through spill-over 400 15.3 Definition of
mediated effects through spill-over in a multisite trial 402 15.3.1
Notation 402 15.3.2 Treatment effect mediated by a focal individual's
compliance 404 15.3.3 Treatment effect mediated by peers' compliance
through spill-over 404 15.3.4 Direct effect of individual treatment
assignment on the outcome 405 15.3.5 Direct effect of peer treatment
assignment on the outcome 405 15.3.6 Decomposition of the total treatment
effect 405 15.4 Identification and estimation of spill-over effects in a
multisite trial 406 15.4.1 Identification in an ideal experiment 407 15.4.2
Identification when the mediators are not randomized 409 15.4.3 Estimation
of mediated effects through spill-over 410 15.5 Consequences of omitting
spill-over effects in causal mediation analyses 412 15.5.1 Biased inference
in a cluster randomized trial 413 15.5.2 Biased inference in a multisite
randomized trial 413 15.5.3 Biased inference of the local average treatment
effect 415 15.6 Quasiexperimental application 416 15.7 Summary 419 Appendix
15.1: Derivation of the weight for estimating the population average
counterfactual outcome E[Y(1, p, 0,M.( p))] 419 Appendix 15.2: Derivation
of bias in the ITT effect due to the omission of spill-over effects 420
Index 423