Quantifying the Impact of Local SUTVA Violations in Spatiotemporal Causal Models Open Access
Noreen, Samantha (Spring 2018)
Abstract
Various causal frameworks have been built upon and extended to deal with the complexities and intricacies that arise when quantifying causal relationships that may exist in natural or quasi-experimental settings. Particular care is needed when data are sensitive to or defined by spatial differences and dependencies, as fundamental causal assumptions may be violated. Interaction and heterogeneity frequently witnessed as part of spatial data settings, such as in health-related policy or program evaluation and event point data, can often violate the Stable Unit Treatment Value Assumption (SUTVA), a key assumption in the counterfactual causal framework. With such a violation, it is diffcult to assess treatment effects that are at the heart of the problem of interest.
We propose a potential outcomes framework in the context of spatio-temporal point processes, developing a theoretical spatial framework that extends existing methods of causal inference with spatial point process theory. Specifically, we focus on bringing this viewpoint to event point data looking at conflict in Afghanistan, used as the illustrative setting for the matched wake analysis (MWA) approach. We reshape the causal hypothesis that indiscriminate insurgent violence using improvised explosive devices (IEDs) increases civilian handover events of unexploded ordnances to U.S. troops, compared to selective insurgent violence from a focus on counting events to quantify a causal effect, to interpreting the intensity, representing the expected events per unit volume of space-time, to quantify a local causal effect. Framing the effect of changing rates of an outcome event over time under treatment or control intervention in a stochastic point process perspective allows us to take advantage of convenient properties to inform the estimation and specification of spatio-temporal areas of influence for each unit. This impacts the definition of the units themselves in addition to estimation of an unbiased causal effect.
By bringing together two methological and computational approaches, we consider the misspecification of the radius of spatial influence that is needed to define the spatio-temporal wakes of each intervention event in the MWA approach. The assignment mechanism is based on geography, where changes can occur in one place and time but not another. As such, it is important to consider the local impact and spatial definitions of the causal relationship that is being quantified. This approach raises methodological challenges; however, we illustrate how a space-time point process stochastic framework allows novel insight as well as a theoretical basis for heuristic approaches for determining the local space-time scale of effects.
In order to address the violations of SUTVA that occur in this spatio-temporal setting due to interference and the treatment definition based on geography, we propose a novel approach considering a space-time point process stochastic framework combined with the structure of interference with geographic features. This solution to the challenges posed by spatial interaction allows for a more in-depth examination of the underlying causal relationships of intervention efficacy. This problem is of interest due the spatial and temporal nature of the data and motivating questions of interest in the conflict data set. Geographic impact analysis accounting for selection bias, spatial dependence and spillovers, and spatial heterogeneity is becoming more and more necessary in this age of increasingly available observational, natural, and quasi-experimental data. This work contributes to an on-going conversation and area of focus that continues to grow across multiple disciplines.
Table of Contents
Introduction and Background 1
1.1 Literature Review 2
1.1.1 Observational studies 2
1.1.2 Causal Inference Framework 2
1.1.3 Controlling for Pre-Treatment Confounders 5
1.1.4 Controlling for Post-Treatment Confounders 7
1.1.5 Spatial Point Processes 7
1.1.6 Motivating Problem: Conflict Analysis of Civilian Collaboration in the Afghanistan War 10
1.2 Outline 12
Causal Inference and Spatial Settings 13
2.1 Introduction 14
2.1.1 Causal Effects of Spatial Events 14
2.1.1.1 Spatially Defined Treatment 15
2.1.1.2 Motivating Problem: Conflict Data Analysis 15
2.2 Motivation: Adapting Causal Inference to a Spatial Setting 16
2.2.1 Notation and Framework 16
2.2.2 Assumptions 17
2.2.3 Our Goals 18
2.3 Current Methods 19
2.3.1 Matched Wake Analysis 19
2.3.2 Spatial Complications in Definitions of Elements of Standard Causal Framework 21
2.3.3 Spatio-temporal Point Processes 22
Linking Spatial Point Process Theory and Causal Inference 24
3.1 Proposed Spatial Point Process Causal Framework 25
3.1.1 Scenario 1: Constant, Known Spatio-temporal Cylinder Radius 25
3.1.2 Scenario 2: Constant, Unknown Spatio-temporal Cylinder Radius 28
3.2 Results 33
3.2.1 Simulations 33
3.2.2 Conflict Data: Civilian Collaboration in Afghanistan 38
3.2.2.1 Results 42
3.2.2.2 Conclusions 50
3.3 Discussion 51
Defining the Interference Effect With Spatial Point Process Theory 52
4.1 Introduction 53
4.1.1 Spatial-Causal Setting 53
4.1.2 Types of Questions of Interest 53
4.1.3 Spatially Defined Treatment 54
4.2 Causal Inference in a Spatio-temporal or Spatial Setting 54
4.2.1 Notation and Framework 54
4.2.2 Definition of SUTVA, SUTVA Violations 56
4.2.3 Geographic Regression Discontinuity 59
4.2.4 Our Goals 61
4.3 Spatio-temporal Manifestations of SUTVA Violations 61
4.3.1 Complications of Spatial Setting for Definitions of Elements of Standard Causal Framework: SUTVA, Interference, and Spillover 62
4.3.2 Scenario 1A: When the Spatio-temporal Wake Radius is Known 63
4.3.3 Scenario 1B: Accounting for Potential Overlap as Interference 66
4.3.3.1 Derivation of Spatio-temporal Overlap Where the Interference Effect Lives 70
4.3.4 Scenario 2A: Proposing the Spatio-temporal Wake Radius 74
4.3.5 Scenario 2B: How to Account for Potential Overlap as Interference with a Proposed Spatio-temporal Wake Radius 75
4.3.5.1 Further Considerations Regarding Wake Overlap 75
4.4 Numerical Studies 77
4.4.1 Simulations 77
4.4.2 Conflict Data: Civilian Collaboration in Afghanistan 85
4.5 Discussion 86
Conclusions 88
5.1 Spatial-Causal Setting 89
5.1.1 Spatially Defined Treatment 89
5.1.2 Methods for Proposed Specific Questions 90
5.2 Example Applications 91
5.2.1 Voting 91
5.2.2 Alcohol Sales 93
5.2.3 Air Pollution 93
5.2.4 Conflict Analysis 94
5.3 Review of Current Methods for Spatial-Causal Inference 95
5.3.1 Matched Wake Analysis 95
5.3.2 Geographic Regression Discontinuity 97
5.4 Comparing and Contrasting Approaches to Spatial Causal Inference 98
5.4.1 Complications of Spatial Setting for Definitions of Elements of Standard Causal Framework 101
5.5 Future Work 102
Appendix A: Linking Spatial Point Process Theory and Causal Inference 106
Appendix B: Defining the Interference Effect With Spatial Point Process Theory 114
Bibliography 118
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