The influence of temporal distributions on causal induction from tabular data

Two experiments investigated the joint influence of statistical and temporal information on causal inference from tabular data. Participants were presented with unambiguous data sets containing information about relative effect frequencies in cause-present and cause-absent situations. In addition to contingency information, the stimuli also revealed information about the temporal distribution of effects. The participants took this information into account when making causal judgments, so that the mere advancing or postponing of the effect in time was attached with causal significance, even when the cause did not increase the overall probability of the effect. These results cannot be reconciled with standard contingency accounts of causal induction.     

Causal attribution from covariation information: the evidential evaluation model

It is hypothesized that causal attributions are made by transforming covariation information into evidence according to notions of evidential value, and that causal judgement is a function of the proportion of instances that are evaluated as confirmatory for the causal hypothesis under test: this is called the evidential evaluation model. An experiment was designed to test the judgemental rule in this model by setting up problems presenting consensus, distinctiveness, and consistency information in which the proportion of confirmatory instances varied but the objective contingency did not. It was found that judgements tended to vary with the proportion of confirmatory instances. Several other current models of causal judgement or causal attribution fail to account for this result. Similar findings have been obtained in studies of causal judgement from contingency information, so the present findings support an argument that the evidential evaluation model provides a unified account of judgement in both domains. Copyright © 2002 John Wiley & Sons, Ltd.     

Causal judgement from information about outcome magnitude

Information was presented in which a candidate cause was either present or absent, and the outcome variable (number of spots on a patient's skin) could take any of four nonzero values. It was found that cause-absent information carried greater weight than cause-present information. This is contrary to the usual finding for contingency information about binary outcome variables. Judgement was influenced more by extreme values of the outcome variable, and larger outcome values tended to have more effect on judgements than smaller outcome values. The hypothesis that participants compute linear correlation is disconfirmed by these results. Instead, the results show that participants focus disproportionate attention on some kinds of events and neglect others.     

Causal competition based on generic priors

Although we live in a complex and multi-causal world, learners often lack sufficient data and/or cognitive resources to acquire a fully veridical causal model. The general goal of making precise predictions with energy-efficient representations suggests a generic prior favoring causal models that include a relatively small number of strong causes. Such “sparse and strong” priors make it possible to quickly identify the most potent individual causes, relegating weaker causes to secondary status or eliminating them from consideration altogether. Sparse-and-strong priors predict that competition will be observed between candidate causes of the same polarity (i.e., generative or else preventive) even if they occur independently. For instance, the strength of a moderately strong cause should be underestimated when an uncorrelated strong cause also occurs in the general learning environment, relative to when a weaker cause also occurs. We report three experiments investigating whether independently-occurring causes (either generative or preventive) compete when people make judgments of causal strength. Cue competition was indeed observed for both generative and preventive causes. The data were used to assess alternative computational models of human learning in complex multi-causal situations.     

Are preventive and generative causal reasoning symmetrical? Extinction and competition

We tested whether preventive and generative reasoning processes are symmetrical by keeping the training and testing of preventive (inhibitory) and generative (excitatory) causal cues as similar as possible. In Experiment 1, we extinguished excitors and inhibitors in a blocking design, in which each extinguished cause was presented in compound with a novel cause, with the same outcome occurring following the compound and following the novel cause alone. With this novel extinction procedure, the inhibitory cues seemed more likely to lose their properties than the excitatory cues. In Experiment 2, we investigated blocking of excitatory and inhibitory causes and found similar blocking effects. Taken together, these results suggest that acquisition of excitation and inhibition is similar, but that inhibition is more liable to extinguish with our extinction procedure. In addition, we used a variable outcome, and this enabled us to test the predictions of an inferential reasoning account about what happens when the outcome level is at its minimum or maximum (De Houwer, Beckers, & Glautier, 2002). We discuss the predictions of this inferential account, Rescorla and Wagner's (1972) model, and a connectionist model-the auto-associator.     

Contingency bias in probability judgement may arise from ambiguity regarding additional causes

We tested whether preventive and generative reasoning processes are symmetrical by keeping the training and testing of preventive (inhibitory) and generative (excitatory) causal cues as similar as possible. In Experiment 1, we extinguished excitors and inhibitors in a blocking design, in which each extinguished cause was presented in compound with a novel cause, with the same outcome occurring following the compound and following the novel cause alone. With this novel extinction procedure, the inhibitory cues seemed more likely to lose their properties than the excitatory cues. In Experiment 2, we investigated blocking of excitatory and inhibitory causes and found similar blocking effects. Taken together, these results suggest that acquisition of excitation and inhibition is similar, but that inhibition is more liable to extinguish with our extinction procedure. In addition, we used a variable outcome, and this enabled us to test the predictions of an inferential reasoning account about what happens when the outcome level is at its minimum or maximum (De Houwer, Beckers, & Glautier, 2002). We discuss the predictions of this inferential account, Rescorla and Wagner's (1972) model, and a connectionist model—the auto-associator.     

用不同外部表征方式集中呈现信息条件下的因果力判断

在分别用文字陈述、表格和图形三种外部表征方式集中呈现因果信息的条件下,用直接估计因果力大小的实验范式考察单一因果关系因果力估计的特点,检验概率对比模型,效力PC理论和pCI规则。让287名大学生被试估计不同化学药物影响动物基因变异的能力。结果发现,对单一因果关系因果力估计具有以下4个特点：⑴不对称性：在预防原因条件下的因果力估计较多符合效力PC理论,而在产生原因条件下的因果力估计一般符合概率对比模型;⑵文字陈述、表格和图形三种信息外部表征方式,不影响产生原因条件下的因果力估计,但影响预防原因条件下的因果力估计。在预防原因条件下,与文字陈述和表格表征相比,图形表征会促使更多被试按效力PC理论来做因果力估计;⑶没有被试使用pCI规则;⑷被试估计因果力所使用的规则存在明显的个体差异。     

Tests of the power PC theory of causal induction with negative contingencies

The power PC theory of causal induction (Cheng, 1997) proposes that causal estimates are based on the power p of a potential cause, where p is the contingency between the cause and effect normalized by the base rate of the effect. Previous tests of this theory have concentrated on generative causes that have positive contingencies with their associated outcomes. Here we empirically test this theory in two experiments using preventive causes that have negative contingencies for their outcomes. Contrary to the power PC theory, the results show that causal judgments vary with contingency across conditions of constant power p. This pattern is consistent, however, with several alternative accounts of causal judgment.     

Visual impressions of generative transmission

ABSTRACT

Previous research has shown that stimuli in which a moving object (A) contacts a stationary one (B) and stops, and object B then moves off in the same direction, give rise to a causal impression: object A is perceived as producing the motion of object B. This impression is weakened or does not occur if there is a delay between A contacting B and B moving, or if there is a spatial gap between B and the location at which A stops. It is shown that a strong causal impression can occur despite the presence of both gap and delay if there are cues to generative transmission of causal influence from A to B. The cues investigated were successive colour change of a series of objects filling the gap between A and B. Reported causal impressions were stronger with the colour change stimuli than with stimuli in which the objects were present but did not change colour, and stronger if the colour change proceeded from A to B than if it proceeded in the opposite direction. Reported causal impressions increased in strength as the number of objects involved in the colour change increased, consistent with the hypothesis that the colour change is a cue to a process of transmission, and inconsistent with the hypothesis that it is perceived or inferred as involving a chain of causal relations. Other kinds of changes to object properties—a small upward motion, shrinkage without moving, and disappearance—yielded similar results. It appears that any rapid sequential change in object properties in the direction of causal influence can function to give rise to the visual impression of generative transmission. The possible role of apparent motion is discussed.     

因果力比较范式下对效力PC理论的检验

在用图形方式集中呈现信息的条件下,用因果力大小比较的实验范式检验效力PC理论。233名大学生被试对不同化学药物影响动物基因变异的能力做大小比较判断。结果发现,对单一因果关系因果力大小的比较判断具有以下3个特点：（1）不对称性：在预防原因条件下的因果力判断一般符合效力PC理论,而在产生原因条件下的因果力判断一般不符合效力PC理论;（2）在同时变化协变值DP和结果基率P(E|~C)的产生原因条件下,多数被试使用DP规则。这与概率对比模型的预测相一致,而不支持效力PC理论;（3）在固定协变值DP而只变化结果基率P(E|~C)的产生原因条件下,多数被试使用变异比RP规则。这是目前所有的因果推理理论都不能解释的现象。     

Transitive inference by pigeons: Does the geometric presentation of the stimuli make a difference?

In studies of transitive inference (TI), nonhuman animals are typically trained with the following 5-term task: A+B?, B+C?, C+D?, D+E? where the letters stand for arbitrary stimuli and [+] indicates that choice is reinforced and [?] indicates that choice is not reinforced. A TI effect is found when, given the untrained test pair BD, subjects choose B. TI effects have been found in many nonhuman species. Although reinforcement history has been posited as an account of the TI effect, it has failed to account for a variety of conditions under which TI effects have been found. A more cognitive account of TI is that organisms are able to form a representation of the series (A > B > C > D > E). In support of this hypothesis, Roberts and Phelps (Psychol Sci 5:368–374, 1994) found that presentation of the pairs of stimuli in a linear arrangement facilitated TI performance by rats, whereas presentation of the pairs of stimuli in a circular arrangement did not. Using methods adapted from Roberts and Phelps, we trained pigeons on either a linear or a circular arrangement of stimuli with the 5-term task. Results indicated that on the BD test pair, pigeons trained with a circular arrangement did not differ from those trained with a linear arrangement. Furthermore, we found that memory for training pairs was variable and was highly correlated with degree of TI. The results suggest that regardless of how pigeons are able to represent the stimuli, choice was not affected by the spatial arrangement of the stimuli during training.     

Choosing optimal causal backgrounds for causal discovery

In two experiments, we studied the strategies that people use to discover causal relationships. According to inferential approaches to causal discovery, if people attempt to discover the power of a cause, then they should naturally select the most informative and unambiguous context. For generative causes this would be a context with a low base rate of effects generated by other causes and for preventive causes a context with a high base rate. In the following experiments, we used probabilistic and/or deterministic target causes and contexts. In each experiment, participants observed several contexts in which the effect occurred with different probabilities. After this training, the participants were presented with different target causes whose causal status was unknown. In order to discover the influence of each cause, participants were allowed, on each trial, to choose the context in which the cause would be tested. As expected by inferential theories, the participants preferred to test generative causes in low base rate contexts and preventative causes in high base rate contexts. The participants, however, persisted in choosing the less informative contexts on a substantial minority of trials long after they had discovered the power of the cause. We discuss the matching law from operant conditioning as an alternative explanation of the findings.     

How causal knowledge affects classification: A generative theory of categorization

Several theories have been proposed regarding how causal relations among features of objects affect how those objects are classified. The assumptions of these theories were tested in 3 experiments that manipulated the causal knowledge associated with novel categories. There were 3 results. The 1st was a multiple cause effect in which a feature's importance increases with its number of causes. The 2nd was a coherence effect in which good category members are those whose features jointly corroborate the category's causal knowledge. These 2 effects can be accounted for by assuming that good category members are those likely to be generated by a category's causal laws. The 3rd result was a primary cause effect, in which primary causes are more important to category membership. This effect can also be explained by a generative account with an additional assumption: that categories often are perceived to have hidden generative causes.     

Constructing Relational Sentences: Establishing Arbitrarily AppliCable Comparative Relations with the Relational Completion Procedure

The present study examined the effectiveness of the Relational Completion Procedure (RCP) in establishing arbitrarily applicable comparative relations after training with either linear (Experiment 1) or non-linear (Experiment 2) arbitrary relations. Linear relations were those presented in a sequential order (i.e., A-B, B-C, C-D, etc.), while nonlinear relations were presented in a nonsequential order (i.e., C-D, B-C, A-B, etc.). After nonarbitrary relational training and testing to establish the contextual functions of MORE THAN and LESS THAN, adults underwent constructed-response nonarbitrary relational training and testing with physically dissimilar stimuli in which they were required to “complete” relational sentences in the presence of the cues. Next, during arbitrary relational training with abstract stimuli, participants were randomly assigned to 1 of 3 training groups: All-More (E > D, D > C., C > B, and B > A), All-Less (A < B, B < C., C < D, and D < E), and Less-More (A < B, B < C., D > C., and E > D). Finally, during arbitrary relational testing, probes for mutually entailed relations were followed by probes for 1-and 2-node combinatorially entailed relations. The yield, or percentage of participants passing, was 83% in Experiment 1 and 91.6% in Experiment 2. Our findings demonstrate that the RCP was successful in establishing arbitrarily applicable comparative relations with adults regardless of the order in which the arbitrary relational training trials were presented.

     

Judgement of two causal candidates from contingency information: II. Effects of information about one cause on judgements of the other cause

When judgements are being made about two causes there are eight possible kinds of contingency information: occurrences and nonoccurrences of the outcome when both causes are present, when Cause 1 alone is present, when Cause 2 alone is present, and when neither cause is present. It is proposed that contingency information is used to some extent to judge proportionate strength, which is the proportion of occurrences of the outcome that each cause can account for. This leads to a prediction that judgements of one cause will be influenced by information about occurrences, but not nonoccurrences, of the outcome when only the other cause is present. In six experiments consistent support was found for this prediction when the cause being judged had a positive relation with the outcome, but no consistent tendency was found when the cause being judged had a negative relation with the outcome. The effects found for causes with positive contingency cannot be explained by the Rescorla-Wagner model of causal judgement nor by the hypothesis that causal judgements are based on conditional contingencies.     

Causal judgements about two causal candidates: Accounting for occurrences,estimating strength,and the importance of interaction judgements

When two possible causes of an outcome are under consideration, contingency information concerns each possible combination of presence and absence of the two causes with occurrences and nonoccurrences of the outcome. White (2008) proposed that such judgements could be predicted by a weighted averaging model integrating these kinds of contingency information. The weights in the model are derived from the hypothesis that causal judgements seek to meet two main aims, accounting for occurrences of the outcome and estimating the strengths of the causes. Here it is shown that the model can explain many but not all relevant published findings. The remainder can be explained by reasoning about interactions between the two causes, by scenario-specific effects, and by variations in cell weight depending on quantity of available information. An experiment is reported that supports this argument. The review and experimental results support the case for a cognitive model of causal judgement in which different kinds of contingency information are utilised to satisfy particular aims of the judgement process.     

Causal imprinting in causal structure learning

Suppose one observes a correlation between two events, B and C, and infers that B causes C. Later one discovers that event A explains away the correlation between B and C. Normatively, one should now dismiss or weaken the belief that B causes C. Nonetheless, participants in the current study who observed a positive contingency between B and C followed by evidence that B and C were independent given A, persisted in believing that B causes C. The authors term this difficulty in revising initially learned causal structures "causal imprinting." Throughout four experiments, causal imprinting was obtained using multiple dependent measures and control conditions. A Bayesian analysis showed that causal imprinting may be normative under some conditions, but causal imprinting also occurred in the current study when it was clearly non-normative. It is suggested that causal imprinting occurs due to the influence of prior knowledge on how reasoners interpret later evidence. Consistent with this view, when participants first viewed the evidence showing that B and C are independent given A, later evidence with only B and C did not lead to the belief that B causes C.     

Accounting for occurrences: a new view of the use of contingency information in causal judgment

When people make causal judgments from contingency information, a principal aim is to account for occurrences of the outcome. When 2 causes are under consideration, the capacity of either to account for occurrences is judged from how likely the cause is to be present when the outcome occurs and from the rate at which the outcome occurs when that cause alone is present, which gives an estimate of the strength of the cause. These propositions are formalized in a weighted averaging model, which successfully predicted several judgmental phenomena not predicted by other models of causal judgment. These include a tendency for judgment of one cause (A) to be reduced as the number of occurrences of when only the other one (B) increases and a tendency for A to receive higher judgments than B if A is better able to account for occurrences than B is even if B has a higher contingency with the outcome than A does. Overshadowing, a tendency for judgments of B to be depressed if A has a higher contingency, is weak or absent when B is better able to account for occurrences than A. Results of several experiments support these and related predictions derived from the accounting for occurrences hypothesis.     

Analogical and category-based inference: a theoretical integration with Bayesian causal models

A fundamental issue for theories of human induction is to specify constraints on potential inferences. For inferences based on shared category membership, an analogy, and/or a relational schema, it appears that the basic goal of induction is to make accurate and goal-relevant inferences that are sensitive to uncertainty. People can use source information at various levels of abstraction (including both specific instances and more general categories), coupled with prior causal knowledge, to build a causal model for a target situation, which in turn constrains inferences about the target. We propose a computational theory in the framework of Bayesian inference and test its predictions (parameter-free for the cases we consider) in a series of experiments in which people were asked to assess the probabilities of various causal predictions and attributions about a target on the basis of source knowledge about generative and preventive causes. The theory proved successful in accounting for systematic patterns of judgments about interrelated types of causal inferences, including evidence that analogical inferences are partially dissociable from overall mapping quality.     

A causal model theory of the meaning of cause, enable, and prevent

The verbs cause , enable , and prevent express beliefs about the way the world works. We offer a theory of their meaning in terms of the structure of those beliefs expressed using qualitative properties of causal models, a graphical framework for representing causal structure. We propose that these verbs refer to a causal model relevant to a discourse and that "A causes B" expresses the belief that the causal model includes a link from A to B. "A enables/allows B" entails that the model includes a link from A to B, that A represents a category of events necessary for B, and that an alternative cause of B exists. "A prevents B" entails that the model includes a link from A to B and that A reduces the likelihood of B. This theory is able to account for the results of four experiments as well as a variety of existing data on human reasoning.