Causal Inference when Observed and Unobserved Causes Interact

Causal Inference when Observed and Unobserved Causes Interact Benjamin M. Rottman (benjamin.rottman@yale.edu) Dept. of Psychology, Yale U. , 2 Hillhouse Ave. New Haven, CT 06520 Woo-kyoung Ahn (woo-kyoung.ahn@yale.edu) Dept. of Psychology, Yale U. , 2 Hillhouse Ave. New Haven, CT 06520 Abstract When a cause interacts with unobserved factors to produce an effect, the contingency between the observed cause and effect cannot be taken at face value to infer causality. Yet, it would be computationally intractable to consider all possible unobserved, interacting factors. Nonetheless, two experiments found that when an unobserved cause is assumed to be fairly stable over time, people can learn about such interactions and adjust their inferences about the causal efficacy of the observed cause. When they observed a period in which a cause and effect were associated followed by a period of the opposite association, rather than concluding a complete lack of causality, subjects inferred an unobserved, interacting cause. The interaction explains why the overall contingency between the cause and effect is low and allows people to still conclude that the cause is efficacious. Keywords: Causal Learning; Causal Inference Introduction People often use co-variation between two observed events to infer causal relationships. However, when inferring the causal efficacy of an observed cause, assumptions and beliefs about unobserved causes are critical. For example, if an observed cause is confounded with an unobserved cause, normative theories (e.g., Cheng, 1997; Pearl, 2000) demand withholding inferences about the observed cause. Furthermore, if an unobserved cause produces an effect such that it is difficult for an observed cause to further increase the probability of the effect (a ceiling effect), a learner should adjust his/her calculation of the efficacy of the cause to account for the unobserved cause (Cheng, 1997). Do people actually use beliefs about unobserved causes when making inferences about observed causes? Buehner and Cheng (1997; Buehner, Cheng & Clifford, 2003) found that people do adjust their causal efficacy estimates when unobserved causes produce floor or ceiling effects (but see Lober & Shanks, 2000; Vallee-Touragneau, et al., 1998, for alternative interpretations). Furthermore, recent studies have shown that people posit unobserved factors when an effect occurs in the absence of the observed cause (i.e., an unexplained effect; Luhmann & Ahn, 2007; Hagmayer & Waldmann, 2007). In summary, previous studies have shown that for floor/ceiling effects and unexplained events, peoples’ inferences about unobserved causes influence learning about observed causes (but see Luhmann, 2005, for alternative possibilities). The current study explores a third way that knowledge about unobserved causes can influence judgments of observed causes; observed and unobserved causes can interact to produce an effect. If a learner is unaware of such an interaction, he/she may incorrectly conclude that an observed variable has no causal relation with an effect. For example, consider a researcher studying if a new medicine reduces heart disease. Suppose that the medicine successfully reduced heart disease for half of the population, but the other half of the population had an undiscovered gene such that the medicine actually increased heart disease. In this scenario, even though the medicine is involved in a causal relationship with heart disease, there would be zero contingency between the two. This scenario poses a considerable challenge for causal learners; people cannot always look for interactions because there are simply too many possible interacting variables and there are always unobserved variables. When are people able to avoid overlooking real causal relationships that involve interactions with unobserved variables? We propose that people may overcome this challenge if an unobserved variable is fairly stable over time and people assume it to be fairly stable. Consider an interaction scenario when there are two light switches connected to one light; the light is on if both switches are up or down, but the light is off if one switch is up and the other is down (the biconditional logical function). For this scenario, even if a person only knows about one of the switches, one may be able to infer that the switch influences the light. For example, suppose you enter a room for the first time and discover that when you flip a switch up, a light goes on, and when you flip it down, the light goes off (gray cells, Steps 1-4 in Figure 1a). If you assume that other potential causes of the light are fairly stable (and did not happen to change every time you flipped your switch), you would infer that the switch influences the light. Later (Steps 4-5), the light turns off without anyone touching the switch (perhaps your daughter flipped the other switch unknown to you; U in Figure 1a). Afterwards, when the switch is down, the light is on, and off when up (Steps 5-8). From this scenario, you might be very confident that your switch influences the light; there were two long periods when the status of the switch correlated with the status of the light. Additionally, because the light mysteriously turned off, you might infer an unobserved factor (I in Figure 1a) that interacts with your