An empirical evaluation of approximate and exact regression-based causal mediation approaches for a binary outcome and a continuous or a binary mediator for case-control study designs

BACKGROUND

In the causal mediation analysis framework, several parametric regression-based approaches have been introduced in past years for decomposing the total effect of an exposure on a binary outcome into a direct effect and an indirect effect through a target mediator. In this context, a well-known strategy involves specifying a logistic model for the outcome and invoking the rare outcome assumption (ROA) to simplify estimation. Recently, exact estimators for natural direct and indirect effects have been introduced to circumvent the challenges prompted by the ROA. As for the approximate approaches relying on the ROA, these exact approaches cannot be used as is on case-control data where the sampling mechanism depends on the outcome.

METHODS

Considering a continuous or a binary mediator, we empirically compare the approximate and exact approaches using simulated data under various case-control scenarios. An illustration of these approaches on case-control data is provided, where the natural mediation effects of long-term use of oral contraceptives on ovarian cancer, with lifetime number of ovulatory cycles as the mediator, are estimated.

RESULTS

In the simulations, we found few differences between the performances of the approximate and exact approaches when the outcome was rare, both marginally and conditionally on variables. However, the performance of the approximate approaches degraded as the prevalence of the outcome increased in at least one stratum of variables. Differences in behavior were also observed among the approximate approaches. In the data analysis, all studied approaches were in agreement with respect to the natural direct and indirect effects estimates.

CONCLUSIONS

In the case where a violation of the ROA applies or is expected, approximate mediation approaches should be avoided or used with caution, and exact estimators favored.

Calculated Comparisons: Manufacturing Societal Causal Judgments by Implying Different Counterfactual Outcomes

How do people come to opposite causal judgments about societal problems, such as whether a public health policy reduced COVID-19 cases? The current research tests an understudied cognitive mechanism in which people may agree about what actually happened (e.g., that a public health policy was implemented and COVID-19 cases declined), but can be made to disagree about the counterfactual, or what would have happened otherwise (e.g., whether COVID-19 cases would have declined naturally without intervention) via comparison cases. Across two preregistered studies (total N = 480), participants reasoned about the implementation of a public policy that was followed by an immediate decline in novel virus cases. Study 1 shows that people's judgments about the causal impact of the policy could be pushed in opposite directions by emphasizing comparison cases that imply different counterfactual outcomes. Study 2 finds that people recognize they can use such information to influence others. Specifically, in service of persuading others to support or reject a public health policy, people systematically showed comparison cases implying the counterfactual outcome that aligned with their position. These findings were robust across samples of U.S. college students and politically and socioeconomically diverse U.S. adults. Together, these studies suggest that implied counterfactuals are a powerful tool that individuals can use to manufacture others' causal judgments and warrant further investigation as a mechanism contributing to belief polarization.

CLARUS: An interactive explainable AI platform for manual counterfactuals in graph neural networks

BACKGROUND

Lack of trust in artificial intelligence (AI) models in medicine is still the key blockage for the use of AI in clinical decision support systems (CDSS). Although AI models are already performing excellently in systems medicine, their black-box nature entails that patient-specific decisions are incomprehensible for the physician. Explainable AI (XAI) algorithms aim to "explain" to a human domain expert, which input features influenced a specific recommendation. However, in the clinical domain, these explanations must lead to some degree of causal understanding by a clinician.

RESULTS

We developed the CLARUS platform, aiming to promote human understanding of graph neural network (GNN) predictions. CLARUS enables the visualisation of patient-specific networks, as well as, relevance values for genes and interactions, computed by XAI methods, such as GNNExplainer. This enables domain experts to gain deeper insights into the network and more importantly, the expert can interactively alter the patient-specific network based on the acquired understanding and initiate re-prediction or retraining. This interactivity allows us to ask manual counterfactual questions and analyse the effects on the GNN prediction.

CONCLUSION

We present the first interactive XAI platform prototype, CLARUS, that allows not only the evaluation of specific human counterfactual questions based on user-defined alterations of patient networks and a re-prediction of the clinical outcome but also a retraining of the entire GNN after changing the underlying graph structures. The platform is currently hosted by the GWDG on https://rshiny.gwdg.de/apps/clarus/.

Close counterfactuals and almost doing the impossible

Can we feel that an unrealized outcome nearly happened if it was never possible in the first place? People often consider counterfactual events that did not happen, and some counterfactuals seem so close to reality that people say they "almost" or "easily could have" happened. Across four preregistered experiments (total N = 1,228), we investigated how judgments of counterfactual closeness depend on possibility, and whether this varies across two kinds of close counterfactuals. In judging whether outcomes almost happened, participants were more strongly impacted by possibility than by incremental manipulations of probability. In contrast, when judging whether outcomes easily could have happened, participants treated the distinction between impossible and possible like any other variation in probability. Both kinds of judgments were also impacted by propensity, though these effects were comparatively small. Together, these findings reveal novel differences between the two kinds of close counterfactuals and suggest that while possibility is privileged when judging what almost happened, probability is the focus when judging what easily could have happened.

How people reason with counterfactual and causal explanations for Artificial Intelligence decisions in familiar and unfamiliar domains

Few empirical studies have examined how people understand counterfactual explanations for other people's decisions, for example, "if you had asked for a lower amount, your loan application would have been approved". Yet many current Artificial Intelligence (AI) decision support systems rely on counterfactual explanations to improve human understanding and trust. We compared counterfactual explanations to causal ones, i.e., "because you asked for a high amount, your loan application was not approved", for an AI's decisions in a familiar domain (alcohol and driving) and an unfamiliar one (chemical safety) in four experiments (n = 731). Participants were shown inputs to an AI system, its decisions, and an explanation for each decision; they attempted to predict the AI's decisions, or to make their own decisions. Participants judged counterfactual explanations more helpful than causal ones, but counterfactuals did not improve the accuracy of their predictions of the AI's decisions more than causals (Experiment 1). However, counterfactuals improved the accuracy of participants' own decisions more than causals (Experiment 2). When the AI's decisions were correct (Experiments 1 and 2), participants considered explanations more helpful and made more accurate judgements in the familiar domain than in the unfamiliar one; but when the AI's decisions were incorrect, they considered explanations less helpful and made fewer accurate judgements in the familiar domain than the unfamiliar one, whether they predicted the AI's decisions (Experiment 3a) or made their own decisions (Experiment 3b). The results corroborate the proposal that counterfactuals provide richer information than causals, because their mental representation includes more possibilities.

Making a positive difference: Criticality in groups

How critical are individual members perceived to be for their group's performance? In this paper, we show that judgments of criticality are intimately linked to considering responsibility. Prospective responsibility attributions in groups are relevant across many domains and situations, and have the potential to influence motivation, performance, and allocation of resources. We develop various models that differ in how the relationship between criticality and responsibility is conceptualized. To test our models, we experimentally vary the task structure (disjunctive, conjunctive, and mixed) and the abilities of the group members (which affects their probability of success). We show that both factors influence criticality judgments, and that a model which construes criticality as anticipated credit best explains participants' judgments. Unlike prior work that has defined criticality as anticipated responsibility for both success and failures, our results suggest that people only consider the possible outcomes in which an individual contributed to a group success, but disregard group failure.

How I Would have been Differently Treated. Discrimination Through the Lens of Counterfactual Fairness

The widespread use of algorithms for prediction-based decisions urges us to consider the question of what it means for a given act or practice to be discriminatory. Building upon work by Kusner and colleagues in the field of machine learning, we propose a counterfactual condition as a necessary requirement on discrimination. To demonstrate the philosophical relevance of the proposed condition, we consider two prominent accounts of discrimination in the recent literature, by Lippert-Rasmussen and Hellman respectively, that do not logically imply our condition and show that they face important objections. Specifically, Lippert-Rasmussen's definition proves to be over-inclusive, as it classifies some acts or practices as discriminatory when they are not, whereas Hellman's account turns out to lack explanatory power precisely insofar as it does not countenance a counterfactual condition on discrimination. By defending the necessity of our counterfactual condition, we set the conceptual limits for justified claims about the occurrence of discriminatory acts or practices in society, with immediate applications to the ethics of algorithmic decision-making.

Should I have been more careful or less careless? The comparative nature of counterfactual thoughts alters judgments of their impact

Counterfactual thoughts inherently imply a comparison of a given reality to an alternative state of affairs. Previous research mainly considered consequences of different counterfactual types, namely focus (other vs. self), structure (additive vs. subtractive), and direction (upward vs. downward). The current work investigates whether a 'more-than' versus 'less-than' comparative nature of counterfactual thoughts alters judgments of their impact. Four experiments demonstrated that self-generated other- (Studies 1 and 3) and self-focused (Study 2) upward counterfactuals are judged more impactful when they entail 'more-than' rather than 'less-than' comparisons. Judgments include plausibility and persuasiveness, as well as counterfactuals' likelihood to change future behavior and feelings. Self-reported ease of thought generation and (dis)fluency gauged by difficulty in thought generation was similarly affected. This more-less asymmetry reversed in Study 3 for downward counterfactual thoughts, with 'less-than' counterfactuals being judged more impactful and easier to generate. Further attesting to the role of ease, when spontaneously generating comparative counterfactuals, participants correctly provided more 'more-than' upward counterfactuals, but more 'less-than' downward counterfactuals (Study 4). These findings delineate one of the to date few conditions for a reversal of the more-less asymmetry and provide support for a correspondence principle, the simulation heuristic, and thus the role of ease in counterfactual thinking. They suggest that especially 'more-than' counterfactuals following negative events, and 'less-than' counterfactuals following positive events, are likely to have an important impact on people. (226 words).

The modal basis of scientific modelling

The practice of scientific modelling often resorts to hypothetical, false, idealised, targetless, partial, generalised, and other types of modelling that appear to have at least partially non-actual targets. In this paper, I will argue that we can avoid a commitment to non-actual targets by sketching a framework where models are understood as having networks of possibilities as their targets. This raises a further question: what are the truthmakers for the modal claims that we can derive from models? I propose that we can find truthmakers for the modal claims derived from models in actuality, even in the case of supposedly non-actual targets. I then put this framework to use by examining a case study concerning the modelling of superheavy elements.

Equitable modelling of brain imaging by counterfactual augmentation with morphologically constrained 3D deep generative models

We describe CounterSynth, a conditional generative model of diffeomorphic deformations that induce label-driven, biologically plausible changes in volumetric brain images. The model is intended to synthesise counterfactual training data augmentations for downstream discriminative modelling tasks where fidelity is limited by data imbalance, distributional instability, confounding, or underspecification, and exhibits inequitable performance across distinct subpopulations. Focusing on demographic attributes, we evaluate the quality of synthesised counterfactuals with voxel-based morphometry, classification and regression of the conditioning attributes, and the Fréchet inception distance. Examining downstream discriminative performance in the context of engineered demographic imbalance and confounding, we use UK Biobank and OASIS magnetic resonance imaging data to benchmark CounterSynth augmentation against current solutions to these problems. We achieve state-of-the-art improvements, both in overall fidelity and equity. The source code for CounterSynth is available at https://github.com/guilherme-pombo/CounterSynth.

The pervasive impact of ignorance

Norm violations have been demonstrated to impact a wide range of seemingly non-normative judgments. Among other things, when agents' actions violate prescriptive norms they tend to be seen as having done those actions more freely, as having acted more intentionally, as being more of a cause of subsequent outcomes, and even as being less happy. The explanation of this effect continue to be debated, with some researchers appealing to features of actions that violate norms, and other researcher emphasizing the importance of agents' mental states when acting. Here, we report the results of two large-scale experiments that replicate and extend twelve of the studies that originally demonstrated the pervasive impact of norm violations. In each case, we build on the pre-existing experimental paradigms to additionally manipulate whether the agents knew that they were violating a norm while holding fixed the action done. We find evidence for a pervasive impact of ignorance: the impact of norm violations on non-normative judgments depends largely on the agent knowing that they were violating a norm when acting. Moreover, we find evidence that the reduction in the impact of normality is underpinned by people's counterfactual reasoning: people are less likely to consider an alternative to the agent's action if the agent is ignorant. We situate our findings in the wider debate around the role or normality in people's reasoning.

Contingentism for historians

In this paper, I will propose a formulation of the contingentism/inevitabilism (C/I) debate that does not require of alternatives to present-day scientific theories that they are equally successful, but rather asks whether they are historically possible. I argue that the debate has already, over the past decades, moved towards a more historical interpretation of the issue, and that it is worth exploring what it would entail to let go of normative considerations altogether. Different answers to inevitability questions still retain the philosophical relevance that originally led Ian Hacking to explore philosophical disagreement in terms of the contingentism/inevitabilism debate.¹.

Scientific counterfactuals as make-believe

Counterfactuals abound in science, especially when reasoning about and with models. This often requires entertaining counterfactual conditionals with nomologically or metaphysically impossible antecedents, namely, counternomics or counterpossibles. In this paper I defend the make-believe view of scientific counterfactuals, a naturalised fiction-based account of counterfactuals in science which provides a means to evaluate their meanings independently of the possibility of the states of affairs their antecedents describe, and under which they have non-trivial truth-values. Fiction is here understood as imagination (in contrast with its most typical association with falsity), characterised as a propositional attitude of pretense or 'make-believe' (Walton 1990). The application of this theory to scientific counterfactuals makes their evaluation a game of make-believe: a counterfactual is (fictionally) true iff its antecedent and the rules of the game prescribe the imagining of its consequent (Kimpton-Nye 2020). The result is a practice-based account of counterfactuals and counterfactual reasoning in science which incorporates insights from theoretical and experimental analytic philosophy as well as cognitive science. This way, the make-believe view of scientific counterfactuals shows that the evaluation of scientific counterfactuals is none other than a question of scientific representation in disguise.

It's not what you did, it's what you could have done

We are more likely to judge agents as morally culpable after we learn they acted freely rather than under duress or coercion. Interestingly, the reverse is also true: Individuals are more likely to be judged to have acted freely after we learn that they committed a moral violation. Researchers have argued that morality affects judgments of force by making the alternative actions the agent could have done instead appear comparatively normal, which then increases the perceived availability of relevant alternative actions. Across five studies, we test the novel predictions of this account. We find that the degree to which participants view possible alternative actions as normal strongly predicts their perceptions that an agent acted freely. This pattern holds both for perceptions of the prescriptive normality of the alternatives (whether the actions are good) and descriptive normality of the alternatives (whether the actions are unusual). We also find that manipulating the prudential value of alternative actions or the degree to which alternatives adhere to social norms, has a similar effect to manipulating whether the actions or their alternatives violate moral norms. This pattern persists even when what is actually done is held constant, and these effects are explained by changes in the perceived normality of the alternatives. Together, these results suggest that across contexts, participants' force judgments depend not on the morality of the actual action taken, but on the normality of possible alternatives. More broadly, our results build on prior work that suggests a unifying role of normality and counterfactuals across many areas of high-level human cognition.

An interaction effect of norm violations on causal judgment

Existing research has shown that norm violations influence causal judg- ments, and a number of different models have been developed to explain these effects. One such model, the necessity/sufficiency model, predicts an interac- tion pattern in people's judgments. Specifically, it predicts that when people are judging the degree to which a particular factor is a cause, there should be an interaction between (a) the degree to which that factor violates a norm and (b) the degree to which another factor in the situation violates norms. A study of moral norms (N=1000) and norms of proper functioning (N=3000) revealed robust evidence for the predicted interaction effect. The implications of these patterns for existing theories of causal judgments is discussed.

Better I than He: Personal perspective modulates counterfactual processing

First-person narratives are more attentively and emotionally engaging than third-person narratives. This study examined whether and how personal perspective modulates counterfactual processing. Participants read counterfactual and causal conditionals written from the first-person or third-person perspective (e.g., If/Because I/he had read enough literature before, I/he would have finished my/his thesis easily.), followed by factual consequences that contained a critical word either consistent or inconsistent with preceding contexts (e.g., Therefore, when I/he was about to defend the thesis I/he felt panicked/confident). In both perspectives, inconsistent words showed a prolonged N400 vs. consistent words in the counterfactual condition, but a larger P600 in the causal condition. The critical word showed a larger P600 in the first- than the third-person condition in counterfactual scenarios, but not in causal scenarios. These findings suggest that personal perspective exerts different influences on counterfactual processing, presumably by modulating the amount of attentional resources involved.

Learning analytics dashboard: a tool for providing actionable insights to learners

This study investigates current approaches to learning analytics (LA) dashboarding while highlighting challenges faced by education providers in their operationalization. We analyze recent dashboards for their ability to provide actionable insights which promote informed responses by learners in making adjustments to their learning habits. Our study finds that most LA dashboards merely employ surface-level descriptive analytics, while only few go beyond and use predictive analytics. In response to the identified gaps in recently published dashboards, we propose a state-of-the-art dashboard that not only leverages descriptive analytics components, but also integrates machine learning in a way that enables both predictive and prescriptive analytics. We demonstrate how emerging analytics tools can be used in order to enable learners to adequately interpret the predictive model behavior, and more specifically to understand how a predictive model arrives at a given prediction. We highlight how these capabilities build trust and satisfy emerging regulatory requirements surrounding predictive analytics. Additionally, we show how data-driven prescriptive analytics can be deployed within dashboards in order to provide concrete advice to the learners, and thereby increase the likelihood of triggering behavioral changes. Our proposed dashboard is the first of its kind in terms of breadth of analytics that it integrates, and is currently deployed for trials at a higher education institution.

Causal Judgment in the Wild: Evidence from the 2020 U.S. Presidential Election

When explaining why an event occurred, people intuitively highlight some causes while ignoring others. How do people decide which causes to select? Models of causal judgment have been evaluated in simple and controlled laboratory experiments, but they have yet to be tested in a complex real-world setting. Here, we provide such a test, in the context of the 2020 U.S. presidential election. Across tens of thousands of simulations of possible election outcomes, we computed, for each state, an adjusted measure of the correlation between a Biden victory in that state and a Biden election victory. These effect size measures accurately predicted the extent to which U.S. participants (N = 207, preregistered) viewed victory in a given state as having caused Biden to win the presidency. Our findings support the theory that people intuitively select as causes of an outcome the factors with the largest standardized causal effect on that outcome across possible counterfactual worlds.

Mediation analysis methods used in observational research: a scoping review and recommendations

Background

Mediation analysis methodology underwent many advancements throughout the years, with the most recent and important advancement being the development of causal mediation analysis based on the counterfactual framework. However, a previous review showed that for experimental studies the uptake of causal mediation analysis remains low. The aim of this paper is to review the methodological characteristics of mediation analyses performed in observational epidemiologic studies published between 2015 and 2019 and to provide recommendations for the application of mediation analysis in future studies.

Methods

We searched the MEDLINE and EMBASE databases for observational epidemiologic studies published between 2015 and 2019 in which mediation analysis was applied as one of the primary analysis methods. Information was extracted on the characteristics of the mediation model and the applied mediation analysis method.

Results

We included 174 studies, most of which applied traditional mediation analysis methods (n = 123, 70.7%). Causal mediation analysis was not often used to analyze more complicated mediation models, such as multiple mediator models. Most studies adjusted their analyses for measured confounders, but did not perform sensitivity analyses for unmeasured confounders and did not assess the presence of an exposure-mediator interaction.

Conclusions

To ensure a causal interpretation of the effect estimates in the mediation model, we recommend that researchers use causal mediation analysis and assess the plausibility of the causal assumptions. The uptake of causal mediation analysis can be enhanced through tutorial papers that demonstrate the application of causal mediation analysis, and through the development of software packages that facilitate the causal mediation analysis of relatively complicated mediation models.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-021-01426-3.

Similarities and differences in understanding negative and affirmative counterfactuals and causal assertions: Evidence from eye-tracking

Two eye-tracking experiments compared affirmative and negative counterfactuals, "if she had (not) arrived early, she would (not) have bought roses" and affirmative and negative causal assertions, "Because she arrived (did not arrive) early, she bought (did not buy) roses." When participants heard a counterfactual, they looked on screen at words corresponding to its conjecture ("roses"), and its presupposed facts ("no roses"), whereas for a causal assertion, they looked only at words corresponding to the facts. For counterfactuals, they looked at the conjecture first, and later the presupposed facts, and at the latter more than the former. The effect was more pronounced for negative counterfactuals than affirmative ones because the negative counterfactual's presupposed facts identify a specific item ("she bought roses"), whereas the affirmative counterfactual's presupposed facts do not ("she did not buy roses"). Hence, when participants were given a binary context, "she did not know whether to buy roses or carnations," they looked primarily at the presupposed facts for both sorts of counterfactuals. We discuss the implications for theories of negation, the dual meaning of counterfactuals, and their relation to causal assertions.

Local causation

The counterfactual and regularity theories are universal accounts of causation. I argue that these should be generalized to produce local accounts of causation. A hallmark of universal accounts of causation is the assumption that apparent variation in causation between locations must be explained by differences in background causal conditions, by features of the causal-nexus or causing-complex. The local account of causation presented here rejects this assumption, allowing for genuine variation in causation to be explained by differences in location. I argue that local accounts of causation are plausible, and have pragmatic, empirical and theoretical advantages over universal accounts. I then report on the use of presheaves as models of local causation. The use of presheaves as models of local variation has precedents in algebraic geometry, category theory and physics; they are here used as models of local causal variation. The paper presents this idea as stemming from an approach using presheaves as models of local truth. Finally, I argue that a proper balance between universal and local causation can be assuaged by moving from presheaves to fully-fledged sheaf models.

Predicting responsibility judgments from dispositional inferences and causal attributions

The question of how people hold others responsible has motivated decades of theorizing and empirical work. In this paper, we develop and test a computational model that bridges the gap between broad but qualitative framework theories, and quantitative but narrow models. In our model, responsibility judgments are the result of two cognitive processes: a dispositional inference about a person's character from their action, and a causal attribution about the person's role in bringing about the outcome. We test the model in a group setting in which political committee members vote on whether or not a policy should be passed. We assessed participants' dispositional inferences and causal attributions by asking how surprising and important a committee member's vote was. Participants' answers to these questions in Experiment 1 accurately predicted responsibility judgments in Experiment 2. In Experiments 3 and 4, we show that the model also predicts moral responsibility judgments, and that importance matters more for responsibility, while surprise matters more for judgments of wrongfulness.

A counterfactual simulation model of causation by omission

When do people say that an event that did not happen was a cause? We extend the counterfactual simulation model (CSM) of causal judgment (Gerstenberg, Goodman, Lagnado, & Tenenbaum, 2021) and test it in a series of three experiments that look at people's causal judgments about omissions in dynamic physical interactions. The problem of omissive causation highlights a series of questions that need to be answered in order to give an adequate causal explanation of why something happened: what are the relevant variables, what are their possible values, how are putative causal relationships evaluated, and how is the causal responsibility for an outcome attributed to multiple causes? The CSM predicts that people make causal judgments about omissions in physical interactions by using their intuitive understanding of physics to mentally simulate what would have happened in relevant counterfactual situations. Prior work has argued that normative expectations affect judgments of omissive causation. Here we suggest a concrete mechanism of how this happens: expectations affect what counterfactuals people consider, and the more certain people are that the counterfactual outcome would have been different from what actually happened, the more causal they judge the omission to be. Our experiments show that both the structure of the physical situation as well as expectations about what will happen affect people's judgments.

Face masks, public policies and slowing the spread of COVID-19: Evidence from Canada

We estimate the impact of indoor face mask mandates and other non-pharmaceutical interventions (NPI) on COVID-19 case growth in Canada. Mask mandate introduction was staggered from mid-June to mid-August 2020 in the 34 public health regions in Ontario, Canada's largest province by population. Using this variation, we find that mask mandates are associated with a 22 percent weekly reduction in new COVID-19 cases, relative to the trend in absence of mandate. Province-level data provide corroborating evidence. We control for mobility behaviour using Google geo-location data and for lagged case totals and case growth as information variables. Our analysis of additional survey data shows that mask mandates led to an increase of about 27 percentage points in self-reported mask wearing in public. Counterfactual policy simulations suggest that adopting a nationwide mask mandate in June could have reduced the total number of diagnosed COVID-19 cases in Canada by over 50,000 over the period July-November 2020. Jointly, our results indicate that mandating mask wearing in indoor public places can be a powerful policy tool to slow the spread of COVID-19.

Autistic Adults are Not Impaired at Maintaining or Switching Between Counterfactual and Factual Worlds: An ERP Study

We report an event-related brain potential (ERP) experiment that tests whether autistic adults are able to maintain and switch between counterfactual and factual worlds. Participants (N = 48) read scenarios that set up a factual or counterfactual scenario, then either maintained the counterfactual world or switched back to the factual world. When the context maintained the world, participants showed appropriate detection of the inconsistent critical word. In contrast, when participants had to switch from a counterfactual to factual world, they initially experienced interference from the counterfactual context, then favoured the factual interpretation of events. None of these effects were modulated by group, despite group-level impairments in Theory of Mind and cognitive flexibility among the autistic adults. These results demonstrate that autistic adults can appropriately use complex contextual cues to maintain and/or update mental representations of counterfactual and factual events.

The specter of irreparable ignorance: counterfactuals and causality in economics

Those economists who have emphasized true uncertainty have tended to draw an epistemic distinction between an ascertainable past and an unknowable future. But in one critical respect-in extracting causal relationships-that epistemic distinction is not warranted. Whether they are situated in the past or future, causal arguments in economics depend equally on counterfactual reasoning. Counterfactualizing entails the construction of fictitious narratives-narratives about worlds that do not exist. Unfortunately, there is no dependable method for ascertaining the uniquely correct counterfactual. This implies that causal claims in economics, too, are irreducibly fictitious. The chief value of counterfactuals, then, is not to prove causation but to help scholars and practitioners confront an inscrutable world-to imagine and prepare for unknowable possible futures. In this endeavor, economic pluralism, which expands the range of plausible counterfactuals, is to be taken as a virtue rather than a curse.

Immoral Professors and Malfunctioning Tools: Counterfactual Relevance Accounts Explain the Effect of Norm Violations on Causal Selection

Causal judgments are widely known to be sensitive to violations of both prescriptive norms (e.g., immoral events) and statistical norms (e.g., improbable events). There is ongoing discussion as to whether both effects are best explained in a unified way through changes in the relevance of counterfactual possibilities, or whether these two effects arise from unrelated cognitive mechanisms. Recent work has shown that moral norm violations affect causal judgments of agents, but not inanimate artifacts used by those agents. These results have been interpreted as showing that prescriptive norm violations only affect causal reasoning about intentional agents, but not the use of inanimate artifacts, thereby providing evidence that the effect of prescriptive norm violations arises from mechanisms specific to reasoning about intentional agents, and thus casting doubt on a unified counterfactual analysis of causal reasoning. Four experiments explore this recent finding and provide clear support for a unified counterfactual analysis. Experiment 1 demonstrates that these newly observed patterns in causal judgments are closely mirrored by judgments of counterfactual relevance. Experiment 2 shows that the relationship between causal and counterfactual judgments is moderated by causal structure, as uniquely predicted by counterfactual accounts. Experiment 3 directly manipulates the relevance of counterfactual alternatives and finds that causal judgments of intentional agents and inanimate artifacts are similarly affected. Finally, Experiment 4 shows that prescriptive norm violations (in which artifacts malfunction) affect causal judgments of inanimate artifacts in much the same way that prescriptive norm violations (in which agents act immorally) affect causal judgments of intentional agents.

IDENTIFICATION AND INFERENCE FOR MARGINAL AVERAGE TREATMENT EFFECT ON THE TREATED WITH AN INSTRUMENTAL VARIABLE

In observational studies, treatments are typically not randomized and therefore estimated treatment effects may be subject to confounding bias. The instrumental variable (IV) design plays the role of a quasi-experimental handle since the IV is associated with the treatment and only affects the outcome through the treatment. In this paper, we present a novel framework for identification and inference using an IV for the marginal average treatment effect amongst the treated (ETT) in the presence of unmeasured confounding. For inference, we propose three different semiparametric approaches: (i) inverse probability weighting (IPW), (ii) outcome regression (OR), and (iii) doubly robust (DR) estimation, which is consistent if either (i) or (ii) is consistent, but not necessarily both. A closed-form locally semiparametric efficient estimator is obtained in the simple case of binary IV and outcome and the efficiency bound is derived for the more general case.

Possibilities and the parallel meanings of factual and counterfactual conditionals

The mental model theory postulates that the meanings of conditionals are based on possibilities. Indicative conditionals-such as "If he is injured tomorrow, then he will take some leave"-have a factual interpretation that can be paraphrased as It is possible, and remains so, that he is injured tomorrow, and in that case certain that he takes some leave. Subjunctive conditionals, such as, "If he were injured tomorrow, then he would take some leave," have a prefactual interpretation that has the same paraphrase. But when context makes clear that his injury will not occur, the subjunctive has a counterfactual paraphrase, with the first clause: It was once possible, but does not remain so, that he will be injured tomorrow. Three experiments corroborated these predictions for participants' selections of paraphrases in their native Spanish, for epistemic and deontic conditionals, for those referring to past and to future events, and for those with then clauses referring to what may or must happen. These results are contrary to normal modal logics. They are also contrary to theories based on probabilities, which are inapplicable to deontic conditionals, such as, "If you have a ticket, then you must enter the show."

The Suppression of Inferences From Counterfactual Conditionals

We examine two competing effects of beliefs on conditional inferences. The suppression effect occurs for conditionals, for example, "if she watered the plants they bloomed," when beliefs about additional background conditions, for example, "if the sun shone they bloomed" decrease the frequency of inferences such as modus tollens (from "the plants did not bloom" to "therefore she did not water them"). In contrast, the counterfactual elevation effect occurs for counterfactual conditionals, for example, "if she had watered the plants they would have bloomed," when beliefs about the known or presupposed facts, "she did not water the plants and they did not bloom" increase the frequency of inferences such as modus tollens. We report six experiments that show that beliefs about additional conditions take precedence over beliefs about presupposed facts for counterfactuals. The modus tollens inference is suppressed for counterfactuals that contain additional conditions (Experiments 1a and 1b). The denial of the antecedent inference (from "she did not water the plants" to "therefore they did not bloom") is suppressed for counterfactuals that contain alternatives (Experiments 2a and 2b). We report a new "switched-suppression" effect for conditionals with negated components, for example, "if she had not watered the plants they would not have bloomed": modus tollens is suppressed by alternatives and denial of the antecedent by additional conditions, rather than vice versa (Experiments 3a and 3b). We discuss the implications of the results for alternative theories of conditional reasoning.

Estimation of marginal causal effects in the presence of confounding by cluster

A popular way to control for unmeasured confounders is to utilize clusters (e.g. sets of siblings), in which a potentially large set of confounders are constant. By estimating the exposure-outcome association within clusters, rather than between unrelated subjects, all cluster-constant confounders are implicitly controlled for. To analyze such clustered data, it is common to use fixed effects models, which absorb all cluster-constant confounders into a cluster-specific intercept. In this article, we show how linear and log-linear fixed effects models can be used to estimate marginal counterfactual means. These counterfactual means can be estimated and presented for each exposure level separately, or contrasted to form a wide range of marginal causal effects. For binary outcomes, we propose to estimate marginal causal effects with marginal logistic between-within models. These models include a constant intercept common for all clusters, and control for unmeasured cluster-constant confounders by adding the mean exposure level in each cluster to the model. We illustrate the proposed methods by re-analyzing data from a co-twin control study on birth weight and Attention-Deficit/Hyperactivity Disorder.

Synthesizing dam-induced land system change

Dam construction and operation modify land systems. We synthesized 178 observations of dam-induced land system changes from 54 peer-reviewed case studies. Changing extents of forests (23%), agricultural land (21%), and built-up areas (11%) were reported frequently, alongside alterations in land use intensity (23%). Land cover changes were mostly related to hydropower and multi-purpose dams, while irrigation dams dominantly caused land use intensity changes. While a significant share of the changes was caused by reservoir flooding (29%), indirect effects which interact with societal and environmental systems (42%) were of utmost importance. We suggested the distance to the dam and the time since commissioning as potential controls for the direction of land system changes. Our insights provide opportunities for future inductive investigations across large populations of dams at regional to global scales and highlight that multi-disciplinary research perspectives are imperative for the production of generalizable knowledge.

Mediation analysis with a time-to-event outcome: a review of use and reporting in healthcare research

BACKGROUND

Mediation analysis tests whether the relationship between two variables is explained by a third intermediate variable. We sought to describe the usage and reporting of mediation analysis with time-to-event outcomes in published healthcare research.

METHODS

A systematic search of Medline, Embase, and Web of Science was executed in December 2016 to identify applications of mediation analysis to healthcare research involving a clinically relevant time-to-event outcome. We summarized usage over time and reporting of important methodological characteristics.

RESULTS

We included 149 primary studies, published from 1997 to 2016. Most studies were published after 2011 (n = 110, 74%), and the annual number of studies nearly doubled in the last year (from n = 21 to n = 40). A traditional approach (causal steps or change in coefficient) was most commonly taken (n = 87, 58%), and the majority of studies (n = 114, 77%) used a Cox Proportional Hazards regression for the outcome. Few studies (n = 52, 35%) mentioned any of the assumptions or limitations fundamental to a causal interpretation of mediation analysis.

CONCLUSION

There is increasing use of mediation analysis with time-to-event outcomes. Current usage is limited by reliance on traditional methods and the Cox Proportional Hazards model, as well as low rates of reporting of underlying assumptions. There is a need for formal criteria to aid authors, reviewers, and readers reporting or appraising such studies.

Thinking About the Opposite of What Is Said: Counterfactual Conditionals and Symbolic or Alternate Simulations of Negation

When people understand a counterfactual such as "if the flowers had been roses, the trees would have been orange trees," they think about the conjecture, "there were roses and orange trees," and they also think about its opposite, the presupposed facts. We test whether people think about the opposite by representing alternates, for example, "poppies and apple trees," or whether models can contain symbols, for example, "no roses and no orange trees." We report the discovery of an inference-to-alternates effect-a tendency to make an affirmative inference that refers to an alternate even from a negative minor premise, for example, "there were no orange trees, therefore there were poppies." Nine experiments show the inference-to-alternates effect occurs in a binary context, but not a multiple context, and for direct and indirect reference; it can be induced and reduced by prior experience with similar inferences, and it also occurs for indicative conditionals. The results have implications for theories of counterfactual conditionals, and of negation.

Pragmatic skills predict online counterfactual comprehension: Evidence from the N400

Counterfactual thought allows people to consider alternative worlds they know to be false. Communicating these thoughts through language poses a social-communicative challenge because listeners typically expect a speaker to produce true utterances, but counterfactuals per definition convey information that is false. Listeners must therefore incorporate overt linguistic cues (subjunctive mood, such as in If I loved you then) in a rapid way to infer the intended counterfactual meaning. The present EEG study focused on the comprehension of such counterfactual antecedents and investigated if pragmatic ability—the ability to apply knowledge of the social-communicative use of language in daily life—predicts the online generation of counterfactual worlds. This yielded two novel findings: (1) Words that are consistent with factual knowledge incur a semantic processing cost, as reflected in larger N400 amplitude, in counterfactual antecedents compared to hypothetical antecedents (If sweets were/are made of sugar). We take this to suggest that counterfactuality is quickly incorporated during language comprehension and reduces online expectations based on factual knowledge. (2) Individual scores on the Autism Quotient Communication subscale modulated this effect, suggesting that individuals who are better at understanding the communicative intentions of other people are more likely to reduce knowledge-based expectations in counterfactuals. These results are the first demonstration of the real-time pragmatic processes involved in creating possible worlds.

How Children with Autism Reason about Other's Intentions: False-Belief and Counterfactual Inferences

We examine false belief and counterfactual reasoning in children with autism with a new change-of-intentions task. Children listened to stories, for example, Anne is picking up toys and John hears her say she wants to find her ball. John goes away and the reason for Anne's action changes-Anne's mother tells her to tidy her bedroom. We asked, 'What will John believe is the reason that Anne is picking up toys?' which requires a false-belief inference, and 'If Anne's mother hadn't asked Anne to tidy her room, what would have been the reason she was picking up toys?' which requires a counterfactual inference. We tested children aged 6, 8 and 10 years. Children with autism made fewer correct inferences than typically developing children at 8 years, but by 10 years there was no difference. Children with autism made fewer correct false-belief than counterfactual inferences, just like typically developing children.

For and Against Methodologies: Some Perspectives on Recent Causal and Statistical Inference Debates

I present an overview of two methods controversies that are central to analysis and inference: That surrounding causal modeling as reflected in the "causal inference" movement, and that surrounding null bias in statistical methods as applied to causal questions. Human factors have expanded what might otherwise have been narrow technical discussions into broad philosophical debates. There seem to be misconceptions about the requirements and capabilities of formal methods, especially in notions that certain assumptions or models (such as potential-outcome models) are necessary or sufficient for valid inference. I argue that, once these misconceptions are removed, most elements of the opposing views can be reconciled. The chief problem of causal inference then becomes one of how to teach sound use of formal methods (such as causal modeling, statistical inference, and sensitivity analysis), and how to apply them without generating the overconfidence and misinterpretations that have ruined so many statistical practices.

Does water kill? A call for less casual causal inferences

"Can this number be interpreted as a causal effect?" is a key question for scientists and decision makers. The potential outcomes approach, a quantitative counterfactual theory, describes conditions under which the question can be answered affirmatively. This article reviews one of those conditions, known as consistency, and its implications for real world decisions.

Causal identification: a charge of epidemiology in danger of marginalization

The requirement for framing all causal questions as well-defined interventions is being promoted in the causal inference literature within epidemiology. One can consider this perspective as an intervention on the field which requires a refocusing of epidemiologic questions and retooling of epidemiologic methods. Although this intervention has produced many positive results, we think that its underlying assumptions and the possibilities of unintended consequences warrant examination. In so doing, we argue that this approach can lead to the neglect of causal identification as a useful link between associations and the estimation of intervention effects.

Second-Guessing Scientists and Engineers: Post Hoc Criticism and the Reform of Practice in Green Chemistry and Engineering

The article examines and extends work bringing together engineering ethics and Science and Technology Studies, which had built upon Diane Vaughan's analysis of the Challenger shuttle accident as a test case. Reconsidering the use of her term "normalization of deviance," the article argues for a middle path between moralizing against and excusing away engineering practices contributing to engineering disaster. To explore an illustrative pedagogical case and to suggest avenues for constructive research developing this middle path, it examines the emergence of green chemistry and green engineering. Green chemistry began when Paul Anastas and John Warner developed a set of new rules for chemical synthesis that sought to learn from missed opportunities to avoid environmental damage in the twentieth century, an approach that was soon extended to engineering as well. Examination of tacit assumptions about historical counterfactuals in recent, interdisciplinary discussions of green chemistry illuminate competing views about the field's prospects. An integrated perspective is sought, addressing how both technical practice within chemistry and engineering and the influence of a wider "social movement" can play a role in remedying environmental problems.

Basic Conditional Reasoning: How Children Mimic Counterfactual Reasoning

Children approach counterfactual questions about stories with a reasoning strategy that falls short of adults' Counterfactual Reasoning (CFR). It was dubbed "Basic Conditional Reasoning" (BCR) in Rafetseder et al. (Child Dev 81(1):376-389, 2010). In this paper we provide a characterisation of the differences between BCR and CFR using a distinction between permanent and nonpermanent features of stories and Lewis/Stalnaker counterfactual logic. The critical difference pertains to how consistency between a story and a conditional antecedent incompatible with a nonpermanent feature of the story is achieved. Basic conditional reasoners simply drop all nonpermanent features of the story. Counterfactual reasoners preserve as much of the story as possible while accommodating the antecedent.

Counterfactuals and causal models: introduction to the special issue

Judea Pearl won the 2010 Rumelhart Prize in computational cognitive science due to his seminal contributions to the development of Bayes nets and causal Bayes nets, frameworks that are central to multiple domains of the computational study of mind. At the heart of the causal Bayes nets formalism is the notion of a counterfactual, a representation of something false or nonexistent. Pearl refers to Bayes nets as oracles for intervention, and interventions can tell us what the effect of action will be or what the effect of counterfactual possibilities would be. Counterfactuals turn out to be necessary to understand thought, perception, and language. This selection of papers tells us why, sometimes in ways that support the Bayes net framework and sometimes in ways that challenge it.

A predictive processing theory of sensorimotor contingencies: Explaining the puzzle of perceptual presence and its absence in synesthesia

Normal perception involves experiencing objects within perceptual scenes as real, as existing in the world. This property of "perceptual presence" has motivated "sensorimotor theories" which understand perception to involve the mastery of sensorimotor contingencies. However, the mechanistic basis of sensorimotor contingencies and their mastery has remained unclear. Sensorimotor theory also struggles to explain instances of perception, such as synesthesia, that appear to lack perceptual presence and for which relevant sensorimotor contingencies are difficult to identify. On alternative "predictive processing" theories, perceptual content emerges from probabilistic inference on the external causes of sensory signals, however, this view has addressed neither the problem of perceptual presence nor synesthesia. Here, I describe a theory of predictive perception of sensorimotor contingencies which (1) accounts for perceptual presence in normal perception, as well as its absence in synesthesia, and (2) operationalizes the notion of sensorimotor contingencies and their mastery. The core idea is that generative models underlying perception incorporate explicitly counterfactual elements related to how sensory inputs would change on the basis of a broad repertoire of possible actions, even if those actions are not performed. These "counterfactually-rich" generative models encode sensorimotor contingencies related to repertoires of sensorimotor dependencies, with counterfactual richness determining the degree of perceptual presence associated with a stimulus. While the generative models underlying normal perception are typically counterfactually rich (reflecting a large repertoire of possible sensorimotor dependencies), those underlying synesthetic concurrents are hypothesized to be counterfactually poor. In addition to accounting for the phenomenology of synesthesia, the theory naturally accommodates phenomenological differences between a range of experiential states including dreaming, hallucination, and the like. It may also lead to a new view of the (in)determinacy of normal perception.

Causal premise semantics

The rise of causality and the attendant graph-theoretic modeling tools in the study of counterfactual reasoning has had resounding effects in many areas of cognitive science, but it has thus far not permeated the mainstream in linguistic theory to a comparable degree. In this study I show that a version of the predominant framework for the formal semantic analysis of conditionals, Kratzer-style premise semantics, allows for a straightforward implementation of the crucial ideas and insights of Pearl-style causal networks. I spell out the details of such an implementation, focusing especially on the notions of intervention on a network and backtracking interpretations of counterfactuals.

Counterfactual graphical models for longitudinal mediation analysis with unobserved confounding

Questions concerning mediated causal effects are of great interest in psychology, cognitive science, medicine, social science, public health, and many other disciplines. For instance, about 60% of recent papers published in leading journals in social psychology contain at least one mediation test (Rucker, Preacher, Tormala, & Petty, 2011). Standard parametric approaches to mediation analysis employ regression models, and either the "difference method" (Judd & Kenny, 1981), more common in epidemiology, or the "product method" (Baron & Kenny, 1986), more common in the social sciences. In this article, we first discuss a known, but perhaps often unappreciated, fact that these parametric approaches are a special case of a general counterfactual framework for reasoning about causality first described by Neyman (1923) and Rubin (1924) and linked to causal graphical models by Robins (1986) and Pearl (2006). We then show a number of advantages of this framework. First, it makes the strong assumptions underlying mediation analysis explicit. Second, it avoids a number of problems present in the product and difference methods, such as biased estimates of effects in certain cases. Finally, we show the generality of this framework by proving a novel result which allows mediation analysis to be applied to longitudinal settings with unobserved confounders.

Causal responsibility and counterfactuals

How do people attribute responsibility in situations where the contributions of multiple agents combine to produce a joint outcome? The prevalence of over-determination in such cases makes this a difficult problem for counterfactual theories of causal responsibility. In this article, we explore a general framework for assigning responsibility in multiple agent contexts. We draw on the structural model account of actual causation (e.g., Halpern & Pearl, 2005) and its extension to responsibility judgments (Chockler & Halpern, 2004). We review the main theoretical and empirical issues that arise from this literature and propose a novel model of intuitive judgments of responsibility. This model is a function of both pivotality (whether an agent made a difference to the outcome) and criticality (how important the agent is perceived to be for the outcome, before any actions are taken). The model explains empirical results from previous studies and is supported by a new experiment that manipulates both pivotality and criticality. We also discuss possible extensions of this model to deal with a broader range of causal situations. Overall, our approach emphasizes the close interrelations between causality, counterfactuals, and responsibility attributions.