Effects of Causal Strength on Learning from Biased Sequences

Most research on step-by-step causal learning has focused on the various possible effects early correlations (in a sequence) can have on a learner’s causal beliefs. Recent work has suggested that more information about an individual’s learning strategy can be extracted by examining the slope of the learner’s causal belief trajectory over time after the world changes. We examined step-by-step causal learning from biased sequences with large probabilistic dependencies, using three analyses: testing for primacy vs. recency effects; classifying learning type based on learning curve slope; and a novel analysis based on the patterns of belief change found across multiple sequences. We found few standard order effects (and all of those were primacy effects), and people seemed to be reasoning in a more “model-based” manner than had previously been demonstrated. More generally, the effects of prior observations on subsequent learning appear to be substantially subtler than previous analyses revealed. Introduction and Related Research Causal beliefs play a central role in many areas of cognition (Sloman, 2005), and the psychological processes governing causal learning have been the focus of substantial research. The primary psychological work on causal learning has focused on causal inference “in the long run” (Cheng, 1997; Cheng & Novick, 1992; Gopnik, Glymour, Sobel, Schulz, Kushnir, & Danks, 2004; Griffiths & Tenenbaum, 2005; Perales & Shanks, 2003; White, 2003). The resulting theories aim to explain and predict how people’s causal beliefs depend on observed statistics and prior knowledge when presented with a sufficiently large number of cases. In contrast, we focus here on the stepwise learning problem, which has received much less attention (though see, e.g., Danks, Griffiths, & Tenenbaum, 2003; Shanks, 1995; Shanks & Dickinson, 1987; and papers discussed below). The goal in this setting is to characterize the ways in which people’s beliefs change upon the observation of one (or a few) cases. Thus, the resulting theories aim to predict and explain the step-by-step learning curves for sequences of cause-effect observations. A natural experimental technique for investigating caseby-case causal belief change is the use of biased sequences: ones in which the first and second halves of the sequence exhibit significantly different correlations between the putative cause and the effect. The contrast in the statistics for the first and second halves of the sequence enable us to focus on the ways in which prior observations effect the changes in an individual’s causal beliefs. To maximize the contrast between the sequence halves, we focus on conditions in which the correlation presented in the first half is exactly balanced out by the correlation of the second half. This combination results in zero correlation between the putative cause and the effect over the course of the entire sequence. Thus, any differences in final causal beliefs should be solely a result of order effects. For sequences with this type of internal structure, there are two obvious potential order effects. Primacy effects occur when the final causal beliefs are biased towards the initial correlation (as found in Dennis & Ahn, 2001). In contrast, recency effects occur when the final causal beliefs are biased towards the second half correlation (Catena, Maldonado, & Cándido, 1998; López, Shanks, Almaraz, & Fernández, 1998; Collins & Shanks, 2002). Two different types of theories of step-by-step causal learning have been proposed in order to account for such order effects. Associationist or error-correction models (e.g. Rescorla & Wagner, 1972; Pearce, 1994) predict that causal beliefs should change in response to the learner’s prediction errors. These models thus “track” the recent correlations in the sequence, and so are invariably thought to lead to recency effects. In contrast, theories based on explicit mental models (Dennis & Ahn, 2001) hold that the learner develops an explicit model of the underlying causal relationship during the course of observations. Subsequent observations are interpreted in light of that model and, when the model is sufficiently strong, contradictory evidence is discounted (Einhorn & Hogarth, 1978; Hogarth & Einhorn, 1992). Because of this discounting, evidence in the second half of the learning sequence has less impact on the learner’s causal beliefs, which is thought to result in primacy effects. Danks & Schwartz (2005) argued on theoretical grounds that one cannot simply infer that associationist theories always predict primacy effects, while model-based theories always predict recency effects. If an error-correction model has a time-varying learning rate (which is typically necessary for convergence in the long run; see Danks, 2003), then such a model has the potential to exhibit