Models of covariation-based causal judgment: A review and synthesis

Abstract

Over the past 25 or so years, many researchers have sought to characterize the mechanisms by which people form causal beliefs from covariation information. This can be seen as a special case of the fundamental problem of associative learning (in a broad sense)-namely, the problem of describing how learned beliefs relate to the environmental contingencies on which they are based. Causal beliefs are influenced by a range of factors such as the temporal (Shanks, Pearson, & Dickinson, 1989; see also Buehner & May, 2003) and spatial (Glautier, 2002) distribution of events, as well as by more top-down factors such as causal expectations (Waldmann & Hagmayer, 2001). Yet within the total space defined by the attributes that influence causal learning, research has tended to occupy a rather restricted region: Specifically, numerous studies have held constant all other factors (e.g., spatial and temporal relationships) and varied only covariation information-that is, information about the frequencies of conjunctions and disjunctions between a target cause and effect. This research has thus been focused on a seemingly rather straightforward problem: to characterize the function that maps covariation information onto causal beliefs. Until an adequate description of this function emerges, we cannot be said to have even the beginnings of an understanding of causal knowledge or, since causal knowledge is central to cognition (Sloman, 2005), of cognition itself.This seemingly simple quest has proven to be a formidable challenge. However, there is no lack of candidate theories. The problem, rather, is that the core components of the theories are surrounded, in Kuhnian fashion, by a penumbra of additional assumptions that can often be manipulated to explain away awkward results. The end result is that we have not even been able to discriminate at the highest level of the theoretical hierarchy between associative and rule-based accounts, never mind to make finer discriminations between theories within each class. Moreover, research practice has exacerbated the problem. Researchers tend to design and run new experiments to distinguish between theories (often only between two theories), focusing on the parts of the experimental space where their favored theory is a priori likely to be most successful. There is little attempt to ensure that the favored theory adequately handles the historical record of prior experiments.In the present article, we take a new approach in an attempt to circumvent, at least partially, these difficulties. We report the results of a meta-analysis of historical causal learning studies that have manipulated contingency information, and we employ a cross-validation methodology, suitable for comparing models that make incommensurable assumptions, to try to find the model that provides the best overall account of the data. Although any given theory can argue away the results of a particular study by changing some of its peripheral assumptions or by arguing that some aspect of the experimental procedure violated ...

Accounting for occurrences: An explanation for some novel tendencies in causal judgment from contingency information

“…The usual finding is that A B C D (Anderson & Sheu, 1995;Levin, Wasserman, & Kao, 1993;Mandel & Lehman, 1998;Wasserman, Dorner, & Kao, 1990;Wasserman, Kao, Van Hamme, Katagiri, & Young, 1996;White, 2003a). White (2004) set weights in accordance with the findings of previous research and found that a model with those weights, termed wpCI (weighted proportion of confirming instances), was a better predictor of causal judgment than was the original pCI rule (see also Perales & Shanks, 2007).…”

“…To ameliorate predicted sample size effects, the predicted values in Tables 1-3 were generated by using a power transformation of the form j sign(support) abs(support) k , as recommended by Griffiths and Tenenbaum (2005). I followed the procedure used by Perales and Shanks (2007), searching k in intervals of 0.05 to find the maximum fit between support and judgments. Across the data sets used in Experiments 1 and 2, the best fit was found at k .35; those are the values reported herein.…”

“…Some studies have suggested that this might be so (e.g., Wasserman, Elek, Chatlosh, & Baker, 1993). However, a recent review and meta-analysis has confirmed that causal judgments tend to diverge from values of P in predictable ways (Perales & Shanks, 2007). The conclusion from that review was that observed tendencies in causal judgment are best accounted for by weighted averaging models of causal judgment (Busemeyer, 1991;Catena, Maldonado, & Cándido, 1998;White, 2003bWhite, , 2004).…”

Contrasting cue-density effects in causal and prediction judgments

“…Allan & Jenkins, 1983;Matute, Yarritu, & Vadillo, 2010;Perales, Catena, Shanks, & González, 2005;Wasserman et al, 1996). In spite of the formal parallelism between both density effects, the available evidence strongly suggests that the cue-density effect is smaller and less robust than the outcome-density effect (e.g., Hannah & Beneteau, 2009;Perales & Shanks, 2007).…”

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

“…By a recent count, over 40 algorithmic models of causal learning have been proposed in the literature (Hattori & Oaksford, 2007), almost all of which are nonnormative heuristics. Perales and Shanks (2007) compiled a metaanalysis of data from 114 conditions, taken from 17 experiments from 10 studies conducted in multiple labs, varying a variety of quantitative and qualitative parameters related to causal learning. Lu et al (2008) showed that the parameter-free Bayesian power PC model provides the best quantitative fit of any model that has been applied to the data in this meta-analysis (r ϭ .96).…”