Sufficiency and Necessity Assumptions in Causal Structure Induction

Research on human causal induction has shown that people have general prior assumptions about causal strength and about how causes interact with the background. We propose that these prior assumptions about the parameters of causal systems do not only manifest themselves in estimations of causal strength or the selection of causes but also when deciding between alternative causal structures. In three experiments, we requested subjects to choose which of two observable variables was the cause and which the effect. We found strong evidence that learners have interindividually variable but intraindividually stable priors about causal parameters that express a preference for causal determinism (sufficiency or necessity; Experiment 1). These priors predict which structure subjects preferentially select. The priors can be manipulated experimentally (Experiment 2) and appear to be domain‐general (Experiment 3). Heuristic strategies of structure induction are suggested that can be viewed as simplified implementations of the priors.     

How two causes are different from one: The use of (un)conditional information in Simpson's paradox

In a causally complex world, two (or more) factors may simultaneously be potential causes of an effect. To evaluate the causal efficacy of a factor, the alternative factors must be controlled for (or conditionalized on). Subjects judged the causal strength of two potential causes of an effect that covaried with each other, thereby setting up a Simpson's paradox--a situation in which causal judgments should vary widely depending on whether or not they are conditionalized on the alternative potential cause. In Experiments 1 (table format) and 2 (trial-by-trial format), the subjects did conditionalize their judgments for one causal factor on a known alternative cause. The subjects also demonstrated that they knew what information was needed to properly make causal judgments when two potential causes are available. In Experiment 3 (trial-by-trial), those subjects who were not told about the causal mechanism by which the alternative cause operated were less likely to conditionalize on it. However, the more a subject recognized the covariation between the alternative cause and the effect, the more the subject conditionalized on it. Such behavior may arise from the interaction between bottom-up and top-down processing.     

Predictive versus diagnostic causal learning: Evidence from an overshadowing paradigm

Causal directionality belongs to one of the most fundamental aspects of causality that cannot be reduced to mere covariation. This paper is part of a debate between proponents of associative theories, which claim that learners are insensitive to the causal status of cues and outcomes, and proponents of causal-model theory, which postulates an interaction of assumptions about causal directionality and learning. Some researchers endorsing the associationist view have argued that evidence for the interaction between cue competition and causal directionality may be restricted to two-phase blocking designs. Furthermore, from the viewpoint of causal-model theory, blocking designs carry the potential problem that the predicted asymmetries of cue competition are partly dependent on asymmetries of retrospective inferences. The present experiments use a one-phase overshadowing paradigm that does not allow for retrospective inferences and therefore represents a more unambiguous test of sensitivity to causal directionality. The results strengthen causal-model theory by clearly demonstrating the influence of causal directionality on learning. However, they also provide evidence for boundary conditions for this effect by highlighting the role of the semantics of the learning task.     

Testing hypotheses on specific environmental causal effects on behavior

There have been strong critiques of the notion that environmental influences can have an important effect on psychological functioning. The substance of these criticisms is considered in order to infer the methodological challenges that have to be met. Concepts of cause and of the testing of causal effects are discussed with a particular focus on the need to consider sample selection and the value (and limitations) of longitudinal data. The designs that may be used to test hypotheses on specific environmental risk mechanisms for psychopathology are discussed in relation to a range of adoption strategies, twin designs, various types of "natural experiments," migration designs, the study of secular change, and intervention designs. In each case, consideration is given to the need for samples that "pull-apart" variables that ordinarily go together, specific hypotheses on possible causal processes, and the specification and testing of key assumptions. It is concluded that environmental risk hypotheses can be (and have been) put to the test but that it is usually necessary to use a combination of research strategies.     

Knowledge mediates the timeframe of covariation assessment in human causal induction

How do humans discover causal relations when the effect is not immediately observable? Previous experiments have uniformly demonstrated detrimental effects of outcome delays on causal induction. These findings seem to conflict with everyday causal cognition, where humans can apparently identify long-term causal relations with relative ease. Three experiments investigated whether the influence of delay on adult human causal judgements is mediated by experimentally induced assumptions about the timeframe of the causal relation in question, as suggested by Einhorn and Hogarth (1986). Causal judgements generally decreased when a delay separated cause and effect. This decrease was less pronounced when the thematic context of the causal relation induced participants to expect a delay. Experiment 3 ruled out an alternative explanation of the effect based on variations of cue and outcome saliencies, and showed that detrimental effects of delay are reduced even more when instructions explicitly mentioned the timeframe of the causal relation in question. Knowledge thus mediates the impact of delay on human causal judgement. Implications for contemporary theories of human causal induction are discussed.     

Pro-criminal attitudes,intervention, and recidivism

We review the recent research literature on pro-criminal attitudes (PCAs) as a causal factor of recidivism with a focus on studies on the effectiveness of offender treatment programs targeting PCAs to prevent recidivism. The main conclusions that can be derived from the literature are: (1) the evidence supports the hypothesis that PCAs are related to reoffending; (2) most investigated offender treatment programs tend to reduce PCAs, although the general lack of adequate control group designs does not rule out alternative explanations for this reduction; and (3) there is no conclusive empirical evidence that intervention programs designed to reduce PCAs are effective in reducing recidivism. Empirical research in this area lacks the theoretical and methodological rigor to test causal models of the influence of treatment on reducing PCAs, and effects of PCAs on recidivism. Limitations of the empirical evidence are related to inadequate research designs and/or suboptimal data analysis strategies. Recommendations concerning optimized research designs and data analysis strategies that are likely to provide more conclusive evidence on the relation of PCAs, PCA treatment, and recidivism are given.     

Effect Partitioning in Cross-Sectionally Clustered Data Without Multilevel Models

Abstract

Effect partitioning is almost exclusively performed with multilevel models (MLMs) – so much so that some have considered the two to be synonymous. MLMs are able to provide estimates with desirable statistical properties when data come from a hierarchical structure; but the random effects included in MLMs are not always integral to the analysis. As a result, other methods with relaxed assumptions are viable options in many cases. Through empirical examples and simulations, we show how generalized estimating equations (GEEs) can be used to effectively partition effects without random effects. We show that more onerous steps of MLMs such as determining the number of random effects and the structure for their covariance can be bypassed with GEEs while still obtaining identical or near-identical results. Additionally, violations of distributional assumptions adversely affect estimates with MLMs but have no effect on GEEs because no such assumptions are made. This makes GEEs a flexible alternative to MLMs with minimal assumptions that may warrant consideration. Limitations of GEEs for partitioning effects are also discussed.     

The meaning and computation of causal power: comment on Cheng (1997) and Novick and Cheng (2004)

D. Hume (1739/1987) argued that causality is not observable. P. W. Cheng (1997) claimed to present "a theoretical solution to the problem of causal induction first posed by Hume more than two and a half centuries ago" (p. 398) in the form of the power PC theory (L. R. Novick & P. W. Cheng, 2004). This theory claims that people's goal in causal induction is to estimate causal powers from observable covariation and outlines how this can be done in specific conditions. The authors first demonstrate that if the necessary assumptions were ever met, causal powers would be self-evident to a reasoner--they are either 0 or 1--making the theory unnecessary. The authors further argue that the assumptions the power PC theory requires to compute causal power are unobtainable in the real world and, furthermore, people are aware that requisite assumptions are violated. Therefore, the authors argue that people do not attempt to compute causal power.     

Estimating causal strength: the role of structural knowledge and processing effort.

The strength of causal relations typically must be inferred on the basis of statistical relations between observable events. This article focuses on the problem that there are multiple ways of extracting statistical information from a set of events. In causal structures involving a potential cause, an effect and a third related event, the assumed causal role of this third event crucially determines whether it is appropriate to control for this event when making causal assessments between the potential cause and the effect. Three experiments show that prior assumptions about the causal roles of the learning events affect the way contingencies are assessed with otherwise identical learning input. However, prior assumptions about causal roles is only one factor influencing contingency estimation. The experiments also demonstrate that processing effort affects the way statistical information is processed. These findings provide further evidence for the interaction between bottom-up and top-down influences in the acquisition of causal knowledge. They show that, apart from covariation information or knowledge about mechanisms, abstract assumptions about causal structures also may affect the learning process.     

Individual differences methods for randomized experiments

Experiments allow researchers to randomly vary the key manipulation, the instruments of measurement, and the sequences of the measurements and manipulations across participants. To date, however, the advantages of randomized experiments to manipulate both the aspects of interest and the aspects that threaten internal validity have been primarily used to make inferences about the average causal effect of the experimental manipulation. This article introduces a general framework for analyzing experimental data to make inferences about individual differences in causal effects. Approaches to analyzing the data produced by a number of classical designs and 2 more novel designs are discussed. Simulations highlight the strengths and weaknesses of the data produced by each design with respect to internal validity. Results indicate that, although the data produced by standard designs can be used to produce accurate estimates of average causal effects of experimental manipulations, more elaborate designs are often necessary for accurate inferences with respect to individual differences in causal effects. The methods described here can be diversely applied by researchers interested in determining the extent to which individuals respond differentially to an experimental manipulation or treatment and how differential responsiveness relates to individual participant characteristics.     

Randomization tests as alternative analysis methods for behavior‐analytic data

Randomization statistics offer alternatives to many of the statistical methods commonly used in behavior analysis and the psychological sciences, more generally. These methods are more flexible than conventional parametric and nonparametric statistical techniques in that they make no assumptions about the underlying distribution of outcome variables, are relatively robust when applied to small‐n data sets, and are generally applicable to between‐groups, within‐subjects, mixed, and single‐case research designs. In the present article, we first will provide a historical overview of randomization methods. Next, we will discuss the properties of randomization statistics that may make them particularly well suited for analysis of behavior‐analytic data. We will introduce readers to the major assumptions that undergird randomization methods, as well as some practical and computational considerations for their application. Finally, we will demonstrate how randomization statistics may be calculated for mixed and single‐case research designs. Throughout, we will direct readers toward resources that they may find useful in developing randomization tests for their own data.     

An Error Concerning Noses

We identify a strategy for getting beliefs from fiction via three assumptions: (1) a certain causal generality holds in the fiction and does so because (2) causal generalities in fiction are (with noted exceptions) carried over from what the author takes to be fact; (3) the author is reliable on this topic, so what the author takes to be fact is fact. We do not question (2). While (3) will, in particular cases, be doubtful, the strategy is vulnerable more generally to the worry that what looks like a causal generality may be instead an authorial intervention of a kind from which no causal connection can be inferred; in such cases (1) turns out to be false though it may seem at first sight to be true. In consequence we have extra reason for being careful in forming beliefs based on fictions.     

The intervention selection bias: an underrecognized confound in intervention research

Selection bias can be the most important threat to internal validity in intervention research, but is often insufficiently recognized and controlled. The bias is illustrated in research on parental interventions (punishment, homework assistance); medical interventions (hospitalization); and psychological interventions for suicide risk, sex offending, and juvenile delinquency. The intervention selection bias is most adequately controlled in randomized studies or strong quasi-experimental designs, although recent statistical innovations can enhance weaker designs. The most important points are to increase awareness of the intervention selection bias and to systematically evaluate plausible alternative explanations of data before making causal conclusions.     

Marginal mean weighting through stratification: a generalized method for evaluating multivalued and multiple treatments with nonexperimental data

Propensity score matching and stratification enable researchers to make statistical adjustment for a large number of observed covariates in nonexperimental data. These methods have recently become popular in psychological research. Yet their applications to evaluations of multi-valued and multiple treatments are limited. The inverse-probability-of-treatment weighting method, though suitable for evaluating multi-valued and multiple treatments, often generates results that are not robust when only a portion of the population provides support for causal inference or when the functional form of the propensity score model is misspecified. The marginal mean weighting through stratification (MMW-S) method promises a viable nonparametric solution to these problems. By computing weights on the basis of stratified propensity scores, MMW-S adjustment equates the pretreatment composition of multiple treatment groups under the assumption that unmeasured covariates do not confound the treatment effects given the observed covariates. Analyzing data from a weighted sample, researchers can estimate a causal effect by computing the difference between the estimated average potential outcomes associated with alternative treatments within the analysis of variance framework. After providing an intuitive illustration of the theoretical rationale underlying the weighting method for causal inferences, the article demonstrates how to apply the MMW-S method to evaluations of treatments measured on a binary, ordinal, or nominal scale approximating a completely randomized experiment; to studies of multiple concurrent treatments approximating factorial randomized designs; and to moderated treatment effects approximating randomized block designs. The analytic procedure is illustrated with an evaluation of educational services for English language learners attending kindergarten in the United States.     

Testing mediational models with longitudinal data: questions and tips in the use of structural equation modeling

R. M. Baron and D. A. Kenny (1986; see record 1987-13085-001) provided clarion conceptual and methodological guidelines for testing mediational models with cross-sectional data. Graduating from cross-sectional to longitudinal designs enables researchers to make more rigorous inferences about the causal relations implied by such models. In this transition, misconceptions and erroneous assumptions are the norm. First, we describe some of the questions that arise (and misconceptions that sometimes emerge) in longitudinal tests of mediational models. We also provide a collection of tips for structural equation modeling (SEM) of mediational processes. Finally, we suggest a series of 5 steps when using SEM to test mediational processes in longitudinal designs: testing the measurement model, testing for added components, testing for omitted paths, testing the stationarity assumption, and estimating the mediational effects.     

Proceeding From Observed Correlation to Causal Inference: The Use of Natural Experiments

ABSTRACT— This article notes five reasons why a correlation between a risk (or protective) factor and some specified outcome might not reflect environmental causation. In keeping with numerous other writers, it is noted that a causal effect is usually composed of a constellation of components acting in concert. The study of causation, therefore, will necessarily be informative on only one or more subsets of such components. There is no such thing as a single basic necessary and sufficient cause. Attention is drawn to the need (albeit unobservable) to consider the counterfactual (i.e., what would have happened if the individual had not had the supposed risk experience). Fifteen possible types of natural experiments that may be used to test causal inferences with respect to naturally occurring prior causes (rather than planned interventions) are described. These comprise five types of genetically sensitive designs intended to control for possible genetic mediation (as well as dealing with other issues), six uses of twin or adoptee strategies to deal with other issues such as selection bias or the contrasts between different environmental risks, two designs to deal with selection bias, regression discontinuity designs to take into account unmeasured confounders, and the study of contextual effects. It is concluded that, taken in conjunction, natural experiments can be very helpful in both strengthening and weakening causal inferences.     

A Gricean approach to the use of consensus and distinctiveness in causal attributions of verbally described interpersonal events

Various causal attribution theories, starting with the covariation model, argue that people use consensus, distinctiveness, and consistency information to causally explain events and behaviors. Yet, the visual presentation of the covariation model in the form of a cube is based on the assumptions that these dimensions generally affect attributions independently, symmetrically, and equally. A Gricean analysis suggests that these assumptions may not generally hold in the case of causal judgments for verbally communicated interpersonal events. We had participants judge the causal role of an actor and a patient in interpersonal events that were described through actor‐verb‐patient sentences under high versus low consensus and distinctiveness (Studies 1, 2, and 3) or without such information (Studies 2 and 3). As predicted by Gricean logic, consensus and distinctiveness effects on causality ratings depended on the target whose causal role participants assessed, on the information about the alternative dimension, and, most consistently, on consensus and distinctiveness being high versus low. Copyright © 2013 John Wiley & Sons, Ltd.     

Error probabilities for inference of causal directions

A main message from the causal modelling literature in the last several decades is that under some plausible assumptions, there can be statistically consistent procedures for inferring (features of) the causal structure of a set of random variables from observational data. But whether we can control the error probabilities with a finite sample size depends on the kind of consistency the procedures can achieve. It has been shown that in general, under the standard causal Markov and Faithfulness assumptions, the procedures can only be pointwise but not uniformly consistent without substantial background knowledge. This implies the impossibility of choosing a finite sample size to control the worst case error probabilities. In this paper, I consider the simpler task of inferring causal directions when the skeleton of the causal structure is known, and establish a similarly negative result concerning the possibility of controlling error probabilities. Although the result is negative in form, it has an interesting positive implication for causal discovery methods.     

Inferring causal networks from observations and interventions

Information about the structure of a causal system can come in the form of observational data—random samples of the system's autonomous behavior—or interventional data—samples conditioned on the particular values of one or more variables that have been experimentally manipulated. Here we study people's ability to infer causal structure from both observation and intervention, and to choose informative interventions on the basis of observational data. In three causal inference tasks, participants were to some degree capable of distinguishing between competing causal hypotheses on the basis of purely observational data. Performance improved substantially when participants were allowed to observe the effects of interventions that they performed on the systems. We develop computational models of how people infer causal structure from data and how they plan intervention experiments, based on the representational framework of causal graphical models and the inferential principles of optimal Bayesian decision‐making and maximizing expected information gain. These analyses suggest that people can make rational causal inferences, subject to psychologically reasonable representational assumptions and computationally reasonable processing constraints.