Signed directed acyclic graphs for causal inference

Summary.  Formal rules governing signed edges on causal directed acyclic graphs are described and it is shown how these rules can be useful in reasoning about causality. Specifically, the notions of a monotonic effect, a weak monotonic effect and a signed edge are introduced. Results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an intervention in the presence of intermediate variables. The incorporation of signed edges in the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables. It is shown that when certain assumptions about monotonic effects can be made then these results can be used to draw conclusions about the presence of causal effects even when data are missing on confounding variables.

[1]  James M. Robins,et al.  Discussion of Causal Diagrams for Empirical Research by J. Pearl , 1995 .

[2]  T. Haavelmo.  The Statistical Implications of a System of Simultaneous Equations , 1943 .

[3]  James M. Robins,et al.  Causal Inference from Complex Longitudinal Data , 1997 .

[4]  A. Tsybakov,et al.  Wavelets, approximation, and statistical applications , 1998 .

[5]  D. Francis.  An introduction to structural equation models. , 1988, Journal of clinical and experimental neuropsychology.

[6]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[7]  Nanny Wermuth,et al.  A general condition for avoiding effect reversal after marginalization , 2003 .

[8]  G. Shaw,et al.  Maternal pesticide exposure from multiple sources and selected congenital anomalies. , 1999 .

[9]  R. Kronmal,et al.  Assessing the sensitivity of regression results to unmeasured confounders in observational studies. , 1998, Biometrics.

[10]  Manabu Kuroki,et al.  IDENTIFIABILITY CRITERIA FOR CAUSAL EFFECTS OF JOINT INTERVENTIONS , 1999 .

[11]  D. Walkup,et al.  Association of Random Variables, with Applications , 1967 .

[12]  J. Robins.  A new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect , 1986 .

[13]  A. P. Dawid,et al.  Independence properties of directed Markov fields. Networks, 20, 491-505 , 1990 .

[14]  James M. Robins,et al.  Properties of Monotonic Effects on Directed Acyclic Graphs , 2009, J. Mach. Learn. Res..

[15]  D. Rubin,et al.  Discussion of: 'Causal Diagrams for Empirical Research' by J. Pearl , 1995 .

[16]  Marek J. Druzdzel,et al.  Efficient Reasoning in Qualitative Probabilistic Networks , 1993, AAAI.

[17]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[18]  A. Dawid.  Influence Diagrams for Causal Modelling and Inference , 2002 .

[19]  J. Robins.  Addendum to “a new approach to causal inference in mortality studies with a sustained exposure period—application to control of the healthy worker survivor effect” , 1987 .

[20]  J. Pearl.  Causal diagrams for empirical research , 1995 .

[21]  C. Manski.  Monotone Treatment Response , 2009, Identification for Prediction and Decision.

[22]  A. Dawid,et al.  Causal Inference without Counterfactuals , 2000 .

[23]  D. Rubin,et al.  Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary Outcome , 1983 .

[24]  J. Pearl,et al.  Causal diagrams for epidemiologic research. , 1999, Epidemiology.

[25]  S. Lauritzen,et al.  Chain graph models and their causal interpretations , 2002 .

[26]  Shouhong Wang,et al.  Application of the Back Propagation Neural Network Algorithm with Monotonicity Constraints for Two‐Group Classification Problems* , 1993 .

[27]  Dan Geiger,et al.  Identifying independence in bayesian networks , 1990, Networks.

[28]  A. J. Feelders,et al.  Classification trees for problems with monotonicity constraints , 2002, SKDD.

[29]  Judea Pearl,et al.  Testing Identifiability of Causal Effects , 1995, UAI.

[30]  James M. Robins,et al.  Probabilistic evaluation of sequential plans from causal models with hidden variables , 1995, UAI.

[31]  J. Pearl.  [Bayesian Analysis in Expert Systems]: Comment: Graphical Models, Causality and Intervention , 1993 .

[32]  J. Robins,et al.  Minimal sufficient causation and directed acyclic graphs , 2009, 0906.1720.

[33]  A. P. Dawid,et al.  Corrigenda: Influence Diagrams for Causal Modelling and Inference , 2002 .

[34]  James M Robins,et al.  Directed acyclic graphs, sufficient causes, and the properties of conditioning on a common effect. , 2007, American journal of epidemiology.

[35]  J. Robins,et al.  Causal Directed Acyclic Graphs and the Direction of Unmeasured Confounding Bias , 2008, Epidemiology.

[36]  Manabu Kuroki,et al.  Covariate selection for estimating the causal effect of control plans by using causal diagrams , 2003 .

[37]  Z. Geng,et al.  Criteria for confounders in epidemiological studies , 2002 .

[38]  Michael P. Wellman.  Fundamental Concepts of Qualitative Probabilistic Networks , 1990, Artif. Intell..

[39]  Judea Pearl,et al.  Causal networks: semantics and expressiveness , 2013, UAI.

[40]  D. A. Kenny,et al.  Correlation and Causation , 1937, Wilmott.

[41]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[42]  Steffen L. Lauritzen,et al.  Independence properties of directed markov fields , 1990, Networks.

[43]  J. Robins,et al.  Sensitivity Analyses for Unmeasured Confounding Assuming a Marginal Structural Model for Repeated Measures , 2022 .

[44]  Jan C. Bioch.  Dualization, decision lists and identification of monotone discrete functions , 2004, Annals of Mathematics and Artificial Intelligence.

[45]  Linda C. van der Gaag,et al.  Monotonicity in Bayesian Networks , 2004, UAI.