Expectations and interpretations during causal learning

In existing models of causal induction, 4 types of covariation information (i.e., presence/absence of an event followed by presence/absence of another event) always exert identical influences on causal strength judgments (e.g., joint presence of events always suggests a generative causal relationship). In contrast, we suggest that, due to expectations developed during causal learning, learners give varied interpretations to covariation information as it is encountered and that these interpretations influence the resulting causal beliefs. In Experiments 1A-1C, participants' interpretations of observations during a causal learning task were dynamic, expectation based, and, furthermore, strongly tied to subsequent causal judgments. Experiment 2 demonstrated that adding trials of joint absence or joint presence of events, whose roles have been traditionally interpreted as increasing causal strengths, could result in decreased overall causal judgments and that adding trials where one event occurs in the absence of another, whose roles have been traditionally interpreted as decreasing causal strengths, could result in increased overall causal judgments. We discuss implications for traditional models of causal learning and how a more top-down approach (e.g., Bayesian) would be more compatible with the current findings.     

A Bayesian Theory of Sequential Causal Learning and Abstract Transfer

Two key research issues in the field of causal learning are how people acquire causal knowledge when observing data that are presented sequentially, and the level of abstraction at which learning takes place. Does sequential causal learning solely involve the acquisition of specific cause‐effect links, or do learners also acquire knowledge about abstract causal constraints? Recent empirical studies have revealed that experience with one set of causal cues can dramatically alter subsequent learning and performance with entirely different cues, suggesting that learning involves abstract transfer, and such transfer effects involve sequential presentation of distinct sets of causal cues. It has been demonstrated that pre‐training (or even post‐training) can modulate classic causal learning phenomena such as forward and backward blocking. To account for these effects, we propose a Bayesian theory of sequential causal learning. The theory assumes that humans are able to consider and use several alternative causal generative models, each instantiating a different causal integration rule. Model selection is used to decide which integration rule to use in a given learning environment in order to infer causal knowledge from sequential data. Detailed computer simulations demonstrate that humans rely on the abstract characteristics of outcome variables (e.g., binary vs. continuous) to select a causal integration rule, which in turn alters causal learning in a variety of blocking and overshadowing paradigms. When the nature of the outcome variable is ambiguous, humans select the model that yields the best fit with the recent environment, and then apply it to subsequent learning tasks. Based on sequential patterns of cue‐outcome co‐occurrence, the theory can account for a range of phenomena in sequential causal learning, including various blocking effects, primacy effects in some experimental conditions, and apparently abstract transfer of causal knowledge.     

Accessing causal relations in semantic memory

Most studies investigating semantic memory have focused on taxonomic or associative relations. Little is known about how other relations, such as causal relations, are represented and accessed. In three experiments, we presented participants with pairs of words one after another, describing events that referred to either a cause (e.g., spark) or an effect (e.g., fire). We manipulated the temporal order of word presentation and the question participants had to respond to. The results revealed that questions referring to the existence of a causal relation are answered faster when the first word refers to a cause and the second word refers to its effect than vice versa. However, no such asymmetry was observed with questions referring to the associative relation. People appear to distinguish the roles of cause and effect when queried specifically about a causal relation, but not when the same information is evaluated for the presence of an associative relation.     

Individual differences in causal learning and decision making

In judgment and decision making tasks, people tend to neglect the overall frequency of base-rates when they estimate the probability of an event; this is known as the base-rate fallacy. In causal learning, despite people's accuracy at judging causal strength according to one or other normative model (i.e., Power PC, DeltaP), they tend to misperceive base-rate information (e.g., the cause density effect). The present study investigates the relationship between causal learning and decision making by asking whether people weight base-rate information in the same way when estimating causal strength and when making judgments or inferences about the likelihood of an event. The results suggest that people differ according to the weight they place on base-rate information, but the way individuals do this is consistent across causal and decision making tasks. We interpret the results as reflecting a tendency to differentially weight base-rate information which generalizes to a variety of tasks. Additionally, this study provides evidence that causal learning and decision making share some component processes.     

Causal discounting in the presence of a stronger cue is due to bias

People use information about the covariation between a putative cause and an outcome to determine whether a causal relationship obtains. When there are two candidate causes and one is more strongly related to the effect than is the other, the influence of the second is underestimated. This phenomenon is called causal discounting. In two experiments, we adapted paradigms for studying causal learning in order to apply signal detection analysis to this phenomenon. We investigated whether the presence of a stronger alternative makes the task more difficult (indexed by differences in d′) or whether people change the standard by which they assess causality (measured by β). Our results indicate that the effect is due to bias.     

Determining whether causal order affects cue selection in human contingency learning: Comments on Shanks and Lopez (1996)

Shanks and Lopez (1996) reported three experiments in which they attempted to test whether causal order affects cue selection, and concluded that it does not. Their study provides an opportunity to highlight some basic methodological criteria that must be met in order to test whether and how causal order influences learning. In particular, it is necessary to (1) ensure that participants consistently interpret the learning situation in terms of directed cause-effect relations; (2) measure the causal knowledge they acquire; (3) manipulate causal order; and (4) control the statistical relations between cause and effect. With respect to these criteria, each experiment reported by Shanks and Lopez fails on multiple counts. Moreover, several aspects of the results reported by Shanks and Lopez are explained by causal-model theory, but not by associative accounts. Their study thus adds to a growing body of evidence from different laboratories indicating that human contingency learning can be guided by causal interpretation.     

Inferences about unobserved causes in human contingency learning

Estimates of the causal efficacy of an event need to take into account the possible presence and influence of other unobserved causes that might have contributed to the occurrence of the effect. Current theoretical approaches deal differently with this problem. Associative theories assume that at least one unobserved cause is always present. In contrast, causal Bayes net theories (including Power PC theory) hypothesize that unobserved causes may be present or absent. These theories generally assume independence of different causes of the same event, which greatly simplifies modelling learning and inference. In two experiments participants were requested to learn about the causal relation between a single cause and an effect by observing their co-occurrence (Experiment 1) or by actively intervening in the cause (Experiment 2). Participants' assumptions about the presence of an unobserved cause were assessed either after each learning trial or at the end of the learning phase. The results show an interesting dissociation. Whereas there was a tendency to assume interdependence of the causes in the online judgements during learning, the final judgements tended to be more in the direction of an independence assumption. Possible explanations and implications of these findings are discussed.     

Causal judgement as evaluation of evidence: The use of confirmatory and disconfirrnatory information

There are four kinds of contingency information: occurrences and nonoccurrences of an effect in the presence and absence of a cause. In two experiments participants made judgements about sets of stimulus materials in which one of these four kinds had zero frequency. The experiments tested two kinds of predictions derived from the evidential evaluation model of causal judgement, which postulates that causal judgement depends on the proportion of instances evaluated as confirmatory for the cause being judged. The model predicts significant effects of manipulating the frequency of one kind of contingency information in the absence of changes in the objective contingency. The model also predicts that extra weight will be given to one kind of confirmatory information when the other kind has zero frequency, and to one kind of disconfirmatory information when the other kind has zero frequency. Results supported both sets of predictions, and also disconfirmed predictions of the power probabilistic contrast theory of causal judgement. This research therefore favours an account of causal judgement in which contingency information is transformed into evidence, and judgement is based on the net confirmatory or disconfirmatory value of the evidence.     

The influence of the number of relevant causes on the processing of covariation information in causal reasoning

Research on causal reasoning has focused on the influence of covariation between candidate causes and effects on causal judgments. We suggest that the type of covariation information to which people attend is affected by the task being performed. For this, we manipulated the test questions for the evaluation of contingency information and observed its influence on both contingency learning and subsequent causal selections. When people select one cause related to an effect, they focus on conditional contingencies assuming the absence of alternative causes. When people select two causes related to an effect, they focus on conditional contingencies assuming the presence of alternative causes. We demonstrated this use of contingency information in four experiments.     

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.     

Independence and dependence in human causal reasoning

Causal graphical models (CGMs) are a popular formalism used to model human causal reasoning and learning. The key property of CGMs is the causal Markov condition, which stipulates patterns of independence and dependence among causally related variables. Five experiments found that while adult’s causal inferences exhibited aspects of veridical causal reasoning, they also exhibited a small but tenacious tendency to violate the Markov condition. They also failed to exhibit robust discounting in which the presence of one cause as an explanation of an effect makes the presence of another less likely. Instead, subjects often reasoned “associatively,” that is, assumed that the presence of one variable implied the presence of other, causally related variables, even those that were (according to the Markov condition) conditionally independent. This tendency was unaffected by manipulations (e.g., response deadlines) known to influence fast and intuitive reasoning processes, suggesting that an associative response to a causal reasoning question is sometimes the product of careful and deliberate thinking. That about 60% of the erroneous associative inferences were made by about a quarter of the subjects suggests the presence of substantial individual differences in this tendency. There was also evidence that inferences were influenced by subjects’ assumptions about factors that disable causal relations and their use of a conjunctive reasoning strategy. Theories that strive to provide high fidelity accounts of human causal reasoning will need to relax the independence constraints imposed by CGMs.     

Structure and strength in causal induction

We present a framework for the rational analysis of elemental causal induction-learning about the existence of a relationship between a single cause and effect-based upon causal graphical models. This framework makes precise the distinction between causal structure and causal strength: the difference between asking whether a causal relationship exists and asking how strong that causal relationship might be. We show that two leading rational models of elemental causal induction, DeltaP and causal power, both estimate causal strength, and we introduce a new rational model, causal support, that assesses causal structure. Causal support predicts several key phenomena of causal induction that cannot be accounted for by other rational models, which we explore through a series of experiments. These phenomena include the complex interaction between DeltaP and the base-rate probability of the effect in the absence of the cause, sample size effects, inferences from incomplete contingency tables, and causal learning from rates. Causal support also provides a better account of a number of existing datasets than either DeltaP or causal power.     

A Bayesian view of covariation assessment

When participants assess the relationship between two variables, each with levels of presence and absence, the two most robust phenomena are that: (a) observing the joint presence of the variables has the largest impact on judgment and observing joint absence has the smallest impact, and (b) participants' prior beliefs about the variables' relationship influence judgment. Both phenomena represent departures from the traditional normative model (the phi coefficient or related measures) and have therefore been interpreted as systematic errors. However, both phenomena are consistent with a Bayesian approach to the task. From a Bayesian perspective: (a) joint presence is normatively more informative than joint absence if the presence of variables is rarer than their absence, and (b) failing to incorporate prior beliefs is a normative error. Empirical evidence is reported showing that joint absence is seen as more informative than joint presence when it is clear that absence of the variables, rather than their presence, is rare.     

Reply to Fairley and Manktelow’s comment on “Naive theories and causal deduction”

Fairley and Manktelow (1997) have mistaken an error of presentation for an error of substance. My causal theory remains the same: Causal reasoning scenarios that require the reasoner to decide whether or not an effect will occur in the presence of a viable cause trigger consideration of disabling conditions—that is, factors that could prevent the effect from occurring in the presence of a viable cause. Scenarios that require the reasoner to decide whether or not a particular cause has produced an observed effect trigger consideration of possible alternative causes. The data reported by Cummins (1995) and Cummins, Lubart, Alksnis, and Rist (1991) are consistent with this theoretical analysis.     

Causal learning from probabilistic events in 24‐month‐olds: an action measure

How do young children learn about causal structure in an uncertain and variable world? We tested whether they can use observed probabilistic information to solve causal learning problems. In two experiments, 24‐month‐olds observed an adult produce a probabilistic pattern of causal evidence. The toddlers then were given an opportunity to design their own intervention. In Experiment 1, toddlers saw one object bring about an effect with a higher probability than a second object. In Experiment 2, the frequency of the effect was held constant, though its probability differed. After observing the probabilistic evidence, toddlers in both experiments chose to act on the object that was more likely to produce the effect. The results demonstrate that toddlers can learn about cause and effect without trial‐and‐error or linguistic instruction on the task, simply by observing the probabilistic patterns of evidence resulting from the imperfect actions of other social agents. Such observational causal learning from probabilistic displays supports human children's rapid cultural learning.     

Preschool children learn about causal structure from conditional interventions

The conditional intervention principle is a formal principle that relates patterns of interventions and outcomes to causal structure. It is a central assumption of experimental design and the causal Bayes net formalism. Two studies suggest that preschoolers can use the conditional intervention principle to distinguish causal chains, common cause and interactive causal structures even in the absence of differential spatiotemporal cues and specific mechanism knowledge. Children were also able to use knowledge of causal structure to predict the patterns of evidence that would result from interventions. A third study suggests that children's spontaneous play can generate evidence that would support such accurate causal learning.     

Perceiving a strong causal relation in a weak contingency: Further investigation of the evidential evaluation model of causal judgement

Contingency information is information about the occurrence or nonoccurrence of a certain effect in the presence or absence of a candidate cause. An objective measure of contingency is the δP rule, which involves subtracting the probability of occurrence of an effect when a causal candidate is absent from the probability of occurrence of the effect when the candidate is present. Causal judgements conform closely to δP but deviate from it under certain circumstances. Three experiments show that such deviations can be predicted by a model of causal judgement that has two components: a rule of evidence, that causal judgement is a function of the proportion of relevant instances that are judged to be confirmatory for the causal candidate, and a tendency for information about instances in which the candidate is present to have greater effect on judgement than instances in which the candidate is absent. Two experiments demonstrate how this model accounts for some recently published findings. A third experiment shows that it is possible to use the model to predict the occurrence of high causal judgements when the objective contingency is close to zero.     

Order effects in contingency learning: The role of task complexity

Dennis and Ahn (2001) found that during contingency learning, initial evidence influences causal judgments more than does later evidence (a primacy effect), whereas López, Shanks, Almaraz, and Fernández (1998) found the opposite (a recency effect). We propose that in contingency learning, people use initial evidence to develop an anchoring hypothesis that tends to be underadjusted by later evidence, resulting in a primacy effect. Thus, factors interfering with initial hypothesis development, such as simultaneously learning too many contingencies, as in López et al., would reduce the primacy effect. Experiment 1 showed a primacy effect with learning contingencies involving only one outcome but no primacy effect with two outcomes. Experiment 2 demonstrated that the magnitude of the primacy effect correlated with participants' verbal working memory capacity. It is concluded that a critical moderator for exhibition of the primacy effect is task complexity, presumably because it interferes with initial hypothesis development.     

Non-bayesian inference: causal structure trumps correlation

The study tests the hypothesis that conditional probability judgments can be influenced by causal links between the target event and the evidence even when the statistical relations among variables are held constant. Three experiments varied the causal structure relating three variables and found that (a) the target event was perceived as more probable when it was linked to evidence by a causal chain than when both variables shared a common cause; (b) predictive chains in which evidence is a cause of the hypothesis gave rise to higher judgments than diagnostic chains in which evidence is an effect of the hypothesis; and (c) direct chains gave rise to higher judgments than indirect chains. A Bayesian learning model was applied to our data but failed to explain them. An explanation-based hypothesis stating that statistical information will affect judgments only to the extent that it changes beliefs about causal structure is consistent with the results.     

Categories and causality: the neglected direction

The standard approach guiding research on the relationship between categories and causality views categories as reflecting causal relations in the world. We provide evidence that the opposite direction also holds: categories that have been acquired in previous learning contexts may influence subsequent causal learning. In three experiments we show that identical causal learning input yields different attributions of causal capacity depending on the pre-existing categories to which the learning exemplars are assigned. There is a strong tendency to continue to use old conceptual schemes rather than switch to new ones even when the old categories are not optimal for predicting the new effect, and when they were motivated by goals that differed from the present context of causal discovery. However, we also found that the use of prior categories is dependent on the match between categories and causal effect. Whenever the category labels suggest natural kinds which can be plausibly related to the causal effects, transfer was observed. When the categories were arbitrary, or could not be plausibly related to the causal effect learners abandoned the categories, and used different categories to predict the causal effect.