Simulating Casual Models: The Way to Structural Sensitivity

Simulating Causal Models: The Way to Structural Sensitivity York Hagmayer ( york.hagmayer@bio.uni-goettingen.de ) Department of Psychology, University of Gottingen, Gosslerstr. 14, 37073 Gottingen, Germany Michael R. Waldmann ( michael.waldmann@bio.uni-goettingen.de ) Department of Psychology, University of Gottingen, Gosslerstr. 14, 37073 Gottingen, Germany Abstract The majority of psychological studies on causality have fo- cused on simple cause-effect relations. Little is known about how people approach more realistic, complex causal networks. Two experiments are presented that investigate how participants integrate causal knowledge that was ac- quired in separate learning tasks into a coherent causal model. To accomplish this task it is necessary to bring to bear knowledge about the structural implications of causal models. For example, whereas common-cause models im- ply a covariation among the different effects of a common cause, no such covariation between the different causes of a joint effect is implied by a common-effect model. The ex- periments show that participants have virtually no explicit knowledge of these relations, and therefore tend to misrep- resent the structural implications of causal models in their explicit judgments. However, an implicit task that only re- quired predictions of singular events showed surprisingly accurate sensitivity to the structural implications of causal models. This dissociation supports the view that people’s sensitivity to structural implications is mediated by running simulations on mental analogs of the causal situations. Introduction In everyday life as well as in scientific research we rarely observe the behavior of complex causal networks at once. A more typical scenario is that we learn about single causal relations separately, and later try to inte- grate the different observed relations into a more com- plex interconnected causal model. For example, we might first learn that aspirin relieves headache. Later we may observe that aspirin unfortunately also creates stomach problems. Now we are in the position of put- ting these two pieces of knowledge together. The ques- tion is how? How are different fragments of causal knowledge integrated into coherent complex structures? Bayesian Causal Models One recent approach to this problem that has become increasingly popular in the past few years postulates Bayesian network models for representing causal knowl- edge (see Pearl, 1988, 2000; Glymour & Cooper, 1999). Bayesian network models provide compact, parsimonious representations of causal relations. For example, Figure 1 displays a causal model that connects five events, X 1 , X 2 , X 3 , X 4 , X 5 . One way to represent this domain is to list the 32 probabilities of the joint probability distribution, P(X 1 , X 2 , X 3 , X 4 , X 5 ), by considering every combination of present and absent events. Another possible strategy is to encode the base rates and all covariations that can be computed between five events. However, even with mod- estly complex structures the number of covariations be- comes very large, especially when more complex higher- order covariations between multiple events also are con- sidered. Bayesian network models reduce the complexity of representing causal knowledge by distinguishing be- tween direct causal relations (the arrows in Fig. 1), and covariations that can be derived by using information encoded in the structure of the causal models. The struc- ture of causal models primarily expresses information about conditional independence between events. For ex- ample, in Figure 1 event X 4 is coded as being independent of event X 5 conditional upon event X 3 . Conditional inde- pendence greatly simplifies computations by allowing the derivation of the indirect relations from products of the relevant components (see Pearl, 1988; Glymour & Coo- per, 1999). In Figure 1 the joint probability distribution can be factorized into the product of a small number of unconditional and conditional probabilities, P(X 1 ,X 2 ,X 3 ,X 4 ,X 5 ) = P(X 5 |X 3 )·P(X 4 |X 2 ,X 3 )· P(X 3 |X 1 )· P(X 2 )·P(X 1 ). X 1 Helicobacter Infection X 2 Stomach Problems Headaches X 3 X 4 Aspirin Consumption Pain Relief X 5 Figure 1: Example of a Bayesian Network The distinction between direct causal relations and indi- rect relations can also be used for the integration of sepa- rate pieces of causal knowledge. Combining the informa- tion that aspirin relieves headache with the information that it additionally causes stomach problems yields a