Graphical Causal Models Research Articles

Bayes nets and babies: infants’ developing statistical reasoning abilities and their representation of causal knowledge

A fundamental assumption of the causal graphical model framework is the Markov assumption, which posits that learners can discriminate between two events that are dependent because of a direct causal relation between them and two events that are independent conditional on the value of another event(s). Sobel and Kirkham (2006) demonstrated that 8-month-old infants registered conditional independence information among a sequence of events; infants responded according to the Markov assumption in such a way that was inconsistent with models that rely on simple calculations of associative strength. The present experiment extends these findings to younger infants, and demonstrates that such responses potentially develop during the second half of the first year of life. These data are discussed in terms of a developmental trajectory between associative mechanisms and causal graphical models as representations of infants' causal and statistical learning.

Revisiting the omitted variables argument: Substantive vs. statistical adequacy

The problem of omitted variables is commonly viewed as a statistical misspecification issue which renders the inference concerning the influence of X t on yt unreliable, due to the exclusion of certain relevant factors W t . That is, omitting certain potentially important factors W t may confound the influence of X t on yt . The textbook omitted variables argument attempts to assess the seriousness of this unreliability using the sensitivity of the estimator to the inclusion/exclusion of W t , by tracing that effect to the potential bias/inconsistency of . It is argued that the confounding problem is one of substantive inadequacy in so far as the potential error concerns subject‐matter, not statistical, information. Moreover, the textbook argument in terms of the sensitivity of point estimates provides a poor basis for addressing the confounding problem. The paper reframes the omitted variables question into a hypothesis testing problem, supplemented with a post‐data evaluation of inference based on severe testing. It is shown that this testing perspective can deal effectively with assessing the problem of confounding raised by the omitted variables argument. The assessment of the confouding effect using hypothesis testing is related to the conditional independence and faithfulness assumptions of graphical causal modeling.

Structure and strength in causal induction

We present a framework for the rational analysis of elemental causal induction—learning about the existence of a relationship between a single cause and effect—based upon causal graphical models. This framework makes precise the distinction between causal structure and causal strength: the difference between asking whether a causal relationship exists and asking how strong that causal relationship might be. We show that two leading rational models of elemental causal induction, Δ P and causal power, both estimate causal strength, and we introduce a new rational model, causal support, that assesses causal structure. Causal support predicts several key phenomena of causal induction that cannot be accounted for by other rational models, which we explore through a series of experiments. These phenomena include the complex interaction between Δ P and the base-rate probability of the effect in the absence of the cause, sample size effects, inferences from incomplete contingency tables, and causal learning from rates. Causal support also provides a better account of a number of existing datasets than either Δ P or causal power.

A theory of causal learning in children: causal maps and Bayes nets.

The authors outline a cognitive and computational account of causal learning in children. They propose that children use specialized cognitive systems that allow them to recover an accurate "causal map" of the world: an abstract, coherent, learned representation of the causal relations among events. This kind of knowledge can be perspicuously understood in terms of the formalism of directed graphical causal models, or Bayes nets. Children's causal learning and inference may involve computations similar to those for learning causal Bayes nets and for predicting with them. Experimental results suggest that 2- to 4-year-old children construct new causal maps and that their learning is consistent with the Bayes net formalism.

Book Reviews

Book reviewed in this article:Contrasts and effect sizes in behavioral research. A correlational approach: By R. Rosenthal, R. L. Rosnow, & D. R. RubinMultilevel modeling: Methodological advances, issues and applications: Edited by S. P. Reise & N. DuanThe mind's arrows—Bayes nets and graphical causal models in psychology: By C. GlymourPsychological research: The ideas behind the methods: By Douglas G. MookOrdinal measurement in the behavioral sciences: By Norman Cliff and John A. KeatsIntroduction to nonparametric item response theory: By K. Sijtsma and I. W. MolenaarThe analysis and interpretation of multivariate data for social scientists: By D. J. Bartholomew, F. Steele, I. Moustaki, & J. I. Galbraith

Inferring causal networks from observations and interventions

AbstractInformation about the structure of a causal system can come in the form of observational data—random samples of the system's autonomous behavior—or interventional data—samples conditioned on the particular values of one or more variables that have been experimentally manipulated. Here we study people's ability to infer causal structure from both observation and intervention, and to choose informative interventions on the basis of observational data. In three causal inference tasks, participants were to some degree capable of distinguishing between competing causal hypotheses on the basis of purely observational data. Performance improved substantially when participants were allowed to observe the effects of interventions that they performed on the systems. We develop computational models of how people infer causal structure from data and how they plan intervention experiments, based on the representational framework of causal graphical models and the inferential principles of optimal Bayesian decision‐making and maximizing expected information gain. These analyses suggest that people can make rational causal inferences, subject to psychologically reasonable representational assumptions and computationally reasonable processing constraints.

Inferring causal networks from observations and interventions

Information about the structure of a causal system can come in the form of observational data—random samples of the system’s autonomous behavior—or interventional data—samples conditioned on the particular values of one or more variables that have been experimentally manipulated. Here we study people’s ability to infer causal structure from both observation and intervention, and to choose informative interventions on the basis of observational data. In three causal inference tasks, participants were to some degree capable of distinguishing between competing causal hypotheses on the basis of purely observational data. Performance improved substantially when participants were allowed to observe the effects of interventions that they performed on the systems. We develop computational models of how people infer causal structure from data and how they plan intervention experiments, based on the representational framework of causal graphical models and the inferential principles of optimal Bayesian decision-making and maximizing expected information gain. These analyses suggest that people can make rational causal inferences, subject to psychologically reasonable representational assumptions and computationally reasonable processing constraints.

Review: The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology

1Division of Humanities and Social Sciences, California Institute of Technology, Pasadena, CA 91125, USA The Mind's Arrows: Bayes Nets and Graphical Causal Models in Psychology Clark Glymour Cambridge, MA MIT Press 2001 xv + 222 Hardback$30.00

Causal learning mechanisms in very young children: Two-, three-, and four-year-olds infer causal relations from patterns of variation and covariation.

Three studies investigated whether young children make accurate causal inferences on the basis of patterns of variation and covariation. Children were presented with a new causal relation by means of a machine called the "blicket detector." Some objects, but not others, made the machine light up and play music. In the first 2 experiments, children were told that "blickets make the machine go" and were then asked to identify which objects were "blickets." Two-, 3-, and 4-year-old children were shown various patterns of variation and covariation between two different objects and the activation of the machine. All 3 age groups took this information into account in their causal judgments about which objects were blickets. In a 3rd experiment, 3- and 4-year-old children used the information when they were asked to make the machine stop. These results are related to Bayes-net causal graphical models of causal learning.

Causal learning mechanisms in very young children: Two-, three-, and four-year-olds infer causal relations from patterns of variation and covariation.

Three studies investigated whether young children make accurate causal inferences on the basis of patterns of variation and covariation. Children were presented with a new causal relation by means of a machine called the "blicket detector." Some objects, but not others, made the machine light up and play music. In the first 2 experiments, children were told that "blickets make the machine go" and were then asked to identify which objects were "blickets." Two-, 3-, and 4-year-old children were shown various patterns of variation and covariation between two different objects and the activation of the machine. All 3 age groups took this information into account in their causal judgments about which objects were blickets. In a 3rd experiment, 3- and 4-year-old children used the information when they were asked to make the machine stop. These results are related to Bayes-net causal graphical models of causal learning.