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Chain graph models and their causal interpretations

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  • Steffen L. Lauritzen
  • Thomas S. Richardson

Abstract

Chain graphs are a natural generalization of directed acyclic graphs and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are many simple and apparently plausible, but ultimately fallacious, interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to flawed methods for applying background knowledge to model selection. We present a valid interpretation by showing how the distribution corresponding to a chain graph may be generated from the equilibrium distributions of dynamic models with feed‐back. These dynamic interpretations lead to a simple theory of intervention, extending the theory developed for directed acyclic graphs. Finally, we contrast chain graph models under this interpretation with simultaneous equation models which have traditionally been used to model feed‐back in econometrics.

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  • Steffen L. Lauritzen & Thomas S. Richardson, 2002. "Chain graph models and their causal interpretations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 321-348, August.
    • Handle: RePEc:bla:jorssb:v:64:y:2002:i:3:p:321-348
    DOI: 10.1111/1467-9868.00340
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    Cited by:

    1. Riccardo Borgoni & Ann Berrington & Peter Smith, 2012. "Selecting and fitting graphical chain models to longitudinal data," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(3), pages 715-738, April.
    2. Alberto Roverato, 2021. "On the interpretation of inflated correlation path weights in concentration graphs," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1485-1505, December.
    3. Hogun Chong & Mary Zey & David A. Bessler, 2010. "On corporate structure, strategy, and performance: a study with directed acyclic graphs and PC algorithm," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 31(1), pages 47-62.
    4. David Greasley & Les Oxley, 2010. "Cliometrics And Time Series Econometrics: Some Theory And Applications," Journal of Economic Surveys, Wiley Blackwell, vol. 24(5), pages 970-1042, December.
    5. Miljkovic, Dragan & Dalbec, Nathan & Zhang, Lei, 2016. "Estimating dynamics of US demand for major fossil fuels," Energy Economics, Elsevier, vol. 55(C), pages 284-291.
    6. Oxley, Les & Reale, Marco & Wilson, Granville Tunnicliffe, 2009. "Constructing structural VAR models with conditional independence graphs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2910-2916.
    7. Heckman, James & Pinto, Rodrigo, 2015. "Causal Analysis After Haavelmo," Econometric Theory, Cambridge University Press, vol. 31(1), pages 115-151, February.
    8. A. Charisse Farr & Kerrie Mengersen & Fabrizio Ruggeri & Daniel Simpson & Paul Wu & Prasad Yarlagadda, 2020. "Combining Opinions for Use in Bayesian Networks: A Measurement Error Approach," International Statistical Review, International Statistical Institute, vol. 88(2), pages 335-353, August.
    9. Zijun Wang, 2010. "Directed graphs, information structure and forecast combinations: an empirical examination of US unemployment rates," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(4), pages 353-366.
    10. Blom Tineke & Mooij Joris M., 2023. "Causality and independence in perfectly adapted dynamical systems," Journal of Causal Inference, De Gruyter, vol. 11(1), pages 1-35, January.
    11. Jonas Peters & Peter Bühlmann & Nicolai Meinshausen, 2016. "Causal inference by using invariant prediction: identification and confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 947-1012, November.
    12. Daniel O. Scharfstein & Jon Steingrimsson & Aidan McDermott & Chenguang Wang & Souvik Ray & Aimee Campbell & Edward Nunes & Abigail Matthews, 2022. "Global sensitivity analysis of randomized trials with nonmonotone missing binary outcomes: Application to studies of substance use disorders," Biometrics, The International Biometric Society, vol. 78(2), pages 649-659, June.
    13. Soraggi, Samuele & Wiuf, Carsten, 2019. "General theory for stochastic admixture graphs and F-statistics," Theoretical Population Biology, Elsevier, vol. 125(C), pages 56-66.
    14. Javier Pérez & A. Sánchez, 2011. "Is there a signalling role for public wages? Evidence for the euro area based on macro data," Empirical Economics, Springer, vol. 41(2), pages 421-445, October.
    15. Elizabeth L. Ogburn & Ilya Shpitser & Youjin Lee, 2020. "Causal inference, social networks and chain graphs," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1659-1676, October.
    16. Brathwaite, Timothy & Walker, Joan L., 2018. "Causal inference in travel demand modeling (and the lack thereof)," Journal of choice modelling, Elsevier, vol. 26(C), pages 1-18.
    17. Akyildirim, Erdinc & Cepni, Oguzhan & Pham, Linh & Uddin, Gazi Salah, 2022. "How connected is the agricultural commodity market to the news-based investor sentiment?," Energy Economics, Elsevier, vol. 113(C).
    18. Alessio Moneta, 2008. "Graphical causal models and VARs: an empirical assessment of the real business cycles hypothesis," Empirical Economics, Springer, vol. 35(2), pages 275-300, September.
    19. repec:jss:jstsof:15:i06 is not listed on IDEAS
    20. Geng, Zhi & Wang, Chi & Zhao, Qiang, 2005. "Decomposition of search for v-structures in DAGs," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 282-294, October.
    21. Tyler J. VanderWeele & James M. Robins, 2010. "Signed directed acyclic graphs for causal inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 111-127, January.
    22. Karim Chalak & Halbert White, 2008. "Causality, Conditional Independence, and Graphical Separation in Settable Systems," Boston College Working Papers in Economics 689, Boston College Department of Economics, revised 04 Jul 2010.
    23. Alessio Moneta, 2004. "Identification of Monetary Policy Shocks: A graphical causal approach," Notas Económicas, Faculty of Economics, University of Coimbra, issue 20, pages 39-62, December.

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