Causal Diagrams For Empirical Research Paper

  • Angrist, J. and Imbens, G. (1991). Source of identifying information in evaluation models. Tech. Rep. Discussion Paper 1568, Department of Economics, Harvard University, Cambridge, MA.
  • Angrist, J., Imbens, G. and Rubin, D. (1996). Identification of causal effects using instrumental variables (with comments)., Journal of the American Statistical Association91 444–472.
  • Arah, O. (2008). The role of causal reasoning in understanding Simpson’s paradox, Lord’s paradox, and the suppression effect: Covariate selection in the analysis of observational studies., Emerging Themes in Epidemiology4 doi:10.1186/1742–7622–5–5. Online at http://www.ete-online.com/content/5/1/5.
  • Arjas, E. and Parner, J. (2004). Causal reasoning from longitudinal data., Scandinavian Journal of Statistics31 171–187.

    Mathematical Reviews (MathSciNet): MR2066247
    Digital Object Identifier: doi:10.1111/j.1467-9469.2004.02-134.x

  • Avin, C., Shpitser, I. and Pearl, J. (2005). Identifiability of path-specific effects. In, Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence IJCAI-05. Morgan-Kaufmann Publishers, Edinburgh, UK.

    Mathematical Reviews (MathSciNet): MR2192340

  • Balke, A. and Pearl, J. (1995). Counterfactuals and policy analysis in structural models. In, Uncertainty in Artificial Intelligence 11 (P. Besnard and S. Hanks, eds.). Morgan Kaufmann, San Francisco, 11–18.

    Mathematical Reviews (MathSciNet): MR1615008

  • Balke, A. and Pearl, J. (1997). Bounds on treatment effects from studies with imperfect compliance., Journal of the American Statistical Association92 1172–1176.
  • Berkson, J. (1946). Limitations of the application of fourfold table analysis to hospital data., Biometrics Bulletin2 47–53.
  • Bishop, Y., Fienberg, S. and Holland, P. (1975)., Discrete multivariate analysis: theory and practice. MIT Press, Cambridge, MA.

    Mathematical Reviews (MathSciNet): MR381130

  • Blyth, C. (1972). On Simpson’s paradox and the sure-thing principle., Journal of the American Statistical Association67 364–366.
  • Bollen, K. (1989)., Structural Equations with Latent Variables. John Wiley, New York.

    Mathematical Reviews (MathSciNet): MR996025
    Zentralblatt MATH: 0731.62159

  • Bonet, B. (2001). Instrumentality tests revisited. In, Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann, San Francisco, CA, 48–55.
  • Bowden, R. and Turkington, D. (1984)., Instrumental Variables. Cambridge University Press, Cambridge, England.

    Mathematical Reviews (MathSciNet): MR798790

  • Brent, R. and Lok, L. (2005). A fishing buddy for hypothesis generators., Science308 523–529.

    Zentralblatt MATH: 0683.00014

  • Cai, Z. and Kuroki, M. (2006). Variance estimators for three ‘probabilities of causation’., Risk Analysis25 1611–1620.

    Zentralblatt MATH: 1014.91056

  • Chalak, K. and White, H. (2006). An extended class of instrumental variables for the estimation of causal effects. Tech. Rep. Discussion Paper, UCSD, Department of, Economics.
  • Chen, A., Bengtsson, T. and Ho, T. (2009). A regression paradox for linear models: Sufficient conditions and relation to Simpson’s paradox., The American Statistician63 218–225.
  • Chickering, D. and Pearl, J. (1997). A clinician’s tool for analyzing non-compliance., Computing Science and Statistics29 424–431.

    Mathematical Reviews (MathSciNet): MR1601275
    Zentralblatt MATH: 0906.62052

  • Cole, P. (1997). Causality in epidemiology, health policy, and law., Journal of Marketing Research27 10279–10285.
  • Cole, S. and Hernán, M. (2002). Fallibility in estimating direct effects., International Journal of Epidemiology31 163–165.
  • Cox, D. (1958)., The Planning of Experiments. John Wiley and Sons, NY.

    Mathematical Reviews (MathSciNet): MR95561

  • Cox, D. and Wermuth, N. (2003). A general condition for avoiding effect reversal after marginalization., Journal of the Royal Statistical Society, Series B (Statistical Methodology)65 937–941.

    Mathematical Reviews (MathSciNet): MR2017879
    Zentralblatt MATH: 1067.62017
    Digital Object Identifier: doi:10.1111/1467-9868.00424
    JSTOR: links.jstor.org

  • Cox, D. and Wermuth, N. (2004). Causality: A statistical view., International Statistical Review72 285–305.
  • Dawid, A. (1979). Conditional independence in statistical theory., Journal of the Royal Statistical Society, Series B41 1–31.

    Mathematical Reviews (MathSciNet): MR535541
    JSTOR: links.jstor.org

  • Dawid, A. (2000). Causal inference without counterfactuals (with comments and rejoinder)., Journal of the American Statistical Association95 407–448.

    Mathematical Reviews (MathSciNet): MR1803167
    Zentralblatt MATH: 0999.62003
    Digital Object Identifier: doi:10.2307/2669377
    JSTOR: links.jstor.org

  • Dawid, A. (2002). Influence diagrams for causal modelling and inference., International Statistical Review70 161–189.
  • DeFinetti, B. (1974)., Theory of Probability: A Critical Introductory Treatment. Wiley, London. 2 volumes. Translated by A. Machi and A. Smith.
  • Duncan, O. (1975)., Introduction to Structural Equation Models. Academic Press, New York.

    Mathematical Reviews (MathSciNet): MR398558
    Zentralblatt MATH: 0337.90019

  • Eells, E. (1991)., Probabilistic Causality. Cambridge University Press, Cambridge, MA.

    Mathematical Reviews (MathSciNet): MR1120269
    Zentralblatt MATH: 0785.60003

  • Frangakis, C. and Rubin, D. (2002). Principal stratification in causal inference., Biometrics1 21–29.

    Mathematical Reviews (MathSciNet): MR1891039
    Digital Object Identifier: doi:10.1111/j.0006-341X.2002.00021.x
    JSTOR: links.jstor.org

  • Glymour, M. and Greenland, S. (2008). Causal diagrams. In, Modern Epidemiology (K. Rothman, S. Greenland and T. Lash, eds.), 3rd ed. Lippincott Williams & Wilkins, Philadelphia, PA, 183–209.
  • Goldberger, A. (1972). Structural equation models in the social sciences., Econometrica: Journal of the Econometric Society40 979–1001.

    Mathematical Reviews (MathSciNet): MR327267
    Digital Object Identifier: doi:10.2307/1913851
    JSTOR: links.jstor.org

  • Goldberger, A. (1973). Structural equation models: An overview. In, Structural Equation Models in the Social Sciences (A. Goldberger and O. Duncan, eds.). Seminar Press, New York, NY, 1–18.
  • Good, I. and Mittal, Y. (1987). The amalgamation and geometry of two-by-two contingency tables., The Annals of Statistics15 694–711.

    Mathematical Reviews (MathSciNet): MR888434
    Zentralblatt MATH: 0665.62058
    Digital Object Identifier: doi:10.1214/aos/1176350369
    Project Euclid: euclid.aos/1176350369

  • Greenland, S. (1999). Relation of probability of causation, relative risk, and doubling dose: A methodologic error that has become a social problem., American Journal of Public Health89 1166–1169.
  • Greenland, S., Pearl, J. and Robins, J. (1999). Causal diagrams for epidemiologic research., Epidemiology10 37–48.
  • Greenland, S. and Robins, J. (1986). Identifiability, exchangeability, and epidemiological confounding., International Journal of Epidemiology15 413–419.
  • Haavelmo, T. (1943). The statistical implications of a system of simultaneous equations., Econometrica11 1–12. Reprinted in D.F. Hendry and M.S. Morgan (Eds.), The Foundations of Econometric Analysis, Cambridge University Press, 477–490, 1995.

    Mathematical Reviews (MathSciNet): MR7954
    Digital Object Identifier: doi:10.2307/1905714
    JSTOR: links.jstor.org

  • Hafeman, D. and Schwartz, S. (2009). Opening the black box: A motivation for the assessment of mediation., International Journal of Epidemiology3 838–845.
  • Heckman, J. (1992). Randomization and social policy evaluation. In, Evaluations: Welfare and Training Programs (C. Manski and I. Garfinkle, eds.). Harvard University Press, Cambridge, MA, 201–230.
  • Heckman, J. (2008). Econometric causality., International Statistical Review76 1–27.
  • Heckman, J. and Navarro-Lozano, S. (2004). Using matching, instrumental variables, and control functions to estimate economic choice models., The Review of Economics and Statistics86 30–57.
  • Heckman, J. and Vytlacil, E. (2005). Structural equations, treatment effects and econometric policy evaluation., Econometrica73 669–738.

    Mathematical Reviews (MathSciNet): MR2135141
    Digital Object Identifier: doi:10.1111/j.1468-0262.2005.00594.x
    JSTOR: links.jstor.org

  • Holland, P. (1988). Causal inference, path analysis, and recursive structural equations models. In, Sociological Methodology (C. Clogg, ed.). American Sociological Association, Washington, D.C., 449–484.
  • Hurwicz, L. (1950). Generalization of the concept of identification. In, Statistical Inference in Dynamic Economic Models (T. Koopmans, ed.). Cowles Commission, Monograph 10, Wiley, New York, 245–257.

    Mathematical Reviews (MathSciNet): MR38640

  • Imai, K., Keele, L. and Yamamoto, T. (2008). Identification, inference, and sensitivity analysis for causal mediation effects. Tech. rep., Department of Politics, Princton, University.
  • Imbens, G. and Wooldridge, J. (2009). Recent developments in the econometrics of program evaluation., Journal of Economic Literature47.
  • Kiiveri, H., Speed, T. and Carlin, J. (1984). Recursive causal models., Journal of Australian Math Society36 30–52.

    Mathematical Reviews (MathSciNet): MR719999
    Digital Object Identifier: doi:10.1017/S1446788700027312

  • Koopmans, T. (1953). Identification problems in econometric model construction. In, Studies in Econometric Method (W. Hood and T. Koopmans, eds.). Wiley, New York, 27–48.

    Mathematical Reviews (MathSciNet): MR61358
    Zentralblatt MATH: 0053.27905

  • Kuroki, M. and Miyakawa, M. (1999). Identifiability criteria for causal effects of joint interventions., Journal of the Royal Statistical Society29 105–117.

    Mathematical Reviews (MathSciNet): MR1765273

  • Lauritzen, S. (1996)., Graphical Models. Clarendon Press, Oxford.

    Mathematical Reviews (MathSciNet): MR1419991

  • Lauritzen, S. (2001). Causal inference from graphical models. In, Complex Stochastic Systems (D. Cox and C. Kluppelberg, eds.). Chapman and Hall/CRC Press, Boca Raton, FL, 63–107.

    Mathematical Reviews (MathSciNet): MR1893411
    Zentralblatt MATH: 1010.62004

  • Lindley, D. (2002). Seeing and doing: The concept of causation., International Statistical Review70 191–214.
  • Lindley, D. and Novick, M. (1981). The role of exchangeability in inference., The Annals of Statistics9 45–58.

    Mathematical Reviews (MathSciNet): MR600531
    Zentralblatt MATH: 0473.62005
    Digital Object Identifier: doi:10.1214/aos/1176345331
    Project Euclid: euclid.aos/1176345331

  • MacKinnon, D., Fairchild, A. and Fritz, M. (2007). Mediation analysis., Annual Review of Psychology58 593–614.
  • Manski, C. (1990). Nonparametric bounds on treatment effects., American Economic Review, Papers and Proceedings80 319–323.
  • Marschak, J. (1950). Statistical inference in economics. In, Statistical Inference in Dynamic Economic Models (T. Koopmans, ed.). Wiley, New York, 1–50. Cowles Commission for Research in Economics, Monograph 10.
  • Meek, C. and Glymour, C. (1994). Conditioning and intervening., British Journal of Philosophy Science45 1001–1021.
  • Miettinen, O. (1974). Proportion of disease caused or prevented by a given exposure, trait, or intervention., Journal of Epidemiology99 325–332.
  • Morgan, S. and Winship, C. (2007)., Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research). Cambridge University Press, New York, NY.
  • Mortensen, L., Diderichsen, F., Smith, G. and Andersen, A. (2009). The social gradient in birthweight at term: quantification of the mediating role of maternal smoking and body mass index., Human Reproduction To appear, doi:10.1093/humrep/dep211.
  • Neyman, J. (1923). On the application of probability theory to agricultural experiments. Essay on principles. Section 9., Statistical Science5 465–480.

    Mathematical Reviews (MathSciNet): MR1092986
    Project Euclid: euclid.ss/1177012031

  • Pavlides, M. and Perlman, M. (2009). How likely is Simpson’s paradox?, The American Statistician63 226–233.
  • Pearl, J. (1988)., Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann, San Mateo, CA.

    Mathematical Reviews (MathSciNet): MR965765
    Zentralblatt MATH: 0746.68089

  • Pearl, J. (1993a). Comment: Graphical models, causality, and intervention., Statistical Science8 266–269.
  • Pearl, J. (1993b). Mediating instrumental variables. Tech. Rep. TR-210, http://ftp.cs.ucla.edu/pub/stat_ser/R210.pdf, Department of Computer Science, University of California, Los, Angeles.
  • Pearl, J. (1995a). Causal diagrams for empirical research., Biometrika82 669–710.

    Mathematical Reviews (MathSciNet): MR1380809
    Zentralblatt MATH: 0860.62045
    Digital Object Identifier: doi:10.1093/biomet/82.4.669
    JSTOR: links.jstor.org

  • Pearl, J. (1995b). On the testability of causal models with latent and instrumental variables. In, Uncertainty in Artificial Intelligence 11 (P. Besnard and S. Hanks, eds.). Morgan Kaufmann, San Francisco, CA, 435–443.

    Mathematical Reviews (MathSciNet): MR1615027

  • Pearl, J. (1998). Graphs, causality, and structural equation models., Sociological Methods and Research27 226–284.
  • Pearl, J. (2000a)., Causality: Models, Reasoning, and Inference. Cambridge University Press, New York. 2nd edition, 2009.

    Mathematical Reviews (MathSciNet): MR2548166

  • Pearl, J. (2000b). Comment on A.P. Dawid’s, Causal inference without counterfactuals., Journal of the American Statistical Association95 428–431.
  • Pearl, J. (2001). Direct and indirect effects. In, Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence. Morgan Kaufmann, San Francisco, CA, 411–420.
  • Pearl, J. (2003). Statistics and causal inference: A review., Test Journal12 281–345.

    Mathematical Reviews (MathSciNet): MR2044313
    Zentralblatt MATH: 1044.62003
    Digital Object Identifier: doi:10.1007/BF02595718

  • Pearl, J. (2005). Direct and indirect effects. In, Proceedings of the American Statistical Association, Joint Statistical Meetings. MIRA Digital Publishing, Minn., MN, 1572–1581.
  • Pearl, J. (2009a)., Causality: Models, Reasoning, and Inference. 2nd ed. Cambridge University Press, New York.

    Mathematical Reviews (MathSciNet): MR1744773

  • Pearl, J. (2009b). Letter to the editor: Remarks on the method of propensity scores., Statistics in Medicine28 1415–1416. http://ftp.cs.ucla.edu/pub/statser/r345-sim.pdf.
  • Pearl, J. (2009c). Myth, confusion, and science in causal analysis. Tech. Rep. R-348, University of California, Los Angeles, CA., http://ftp.cs.ucla.edu/pub/statser/r348.pdf.
  • Pearl, J. and Paz, A. (2009). Confounding equivalence in observational studies. Tech. Rep. TR-343, University of California, Los Angeles, CA., http://ftp.cs.ucla.edu/pub/stat_ser/r343.pdf.
  • Pearl, J. and Robins, J. (1995). Probabilistic evaluation of sequential plans from causal models with hidden variables. In, Uncertainty in Artificial Intelligence 11 (P. Besnard and S. Hanks, eds.). Morgan Kaufmann, San Francisco, 444–453.

    Mathematical Reviews (MathSciNet): MR1615006

  • Pearl, J. and Verma, T. (1991). A theory of inferred causation. In, Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference (J. Allen, R. Fikes and E. Sandewall, eds.). Morgan Kaufmann, San Mateo, CA, 441–452.

    Mathematical Reviews (MathSciNet): MR1142134

  • Pearson, K., Lee, A. and Bramley-Moore, L. (1899). Genetic (reproductive) selection: Inheritance of fertility in man., Philosophical Transactions of the Royal Society A73 534–539.
  • Petersen, M., Sinisi, S. and van der Laan, M. (2006). Estimation of direct causal effects., Epidemiology17 276–284.
  • Robertson, D. (1997). The common sense of cause in fact., Texas Law Review75 1765–1800.
  • Robins, J. (1986). A new approach to causal inference in mortality studies with a sustained exposure period – applications to control of the healthy workers survivor effect., Mathematical Modeling7 1393–1512.

    Mathematical Reviews (MathSciNet): MR877758
    Zentralblatt MATH: 0614.62136
    Digital Object Identifier: doi:10.1016/0270-0255(86)90088-6

  • Robins, J. (1987). A graphical approach to the identification and estimation of causal parameters in mortality studies with sustained exposure periods., Journal of Chronic Diseases40 139S–161S.
  • Robins, J. (1989). The analysis of randomized and non-randomized aids treatment trials using a new approach to causal inference in longitudinal studies. In, Health Service Research Methodology: A Focus on AIDS (L. Sechrest, H. Freeman and A. Mulley, eds.). NCHSR, U.S. Public Health Service, Washington, D.C., 113–159.
  • Robins, J. (1999). Testing and estimation of directed effects by reparameterizing directed acyclic with structural nested models. In, Computation, Causation, and Discovery (C. Glymour and G. Cooper, eds.). AAAI/MIT Press, Cambridge, MA, 349–405.

    Mathematical Reviews (MathSciNet): MR1689948

  • Robins, J. (2001). Data, design, and background knowledge in etiologic inference., Epidemiology12 313–320.

    Zentralblatt MATH: 0647.62093

  • Robins, J. and Greenland, S. (1989a). The probability of causation under a stochastic model for individual risk., Biometrics45 1125–1138.

    Mathematical Reviews (MathSciNet): MR1040629
    Digital Object Identifier: doi:10.2307/2531765
    JSTOR: links.jstor.org

  • Robins, J. and Greenland, S. (1989b). Estimability and estimation of excess and etiologic fractions., Statistics in Medicine8 845–859.
  • Robins, J. and Greenland, S. (1992). Identifiability and exchangeability for direct and indirect effects., Epidemiology3 143–155.

    Zentralblatt MATH: 0647.62093

  • Rosenbaum, P. (2002)., Observational Studies. 2nd ed. Springer-Verlag, New York.

    Mathematical Reviews (MathSciNet): MR1899138

  • Rosenbaum, P. and Rubin, D. (1983). The central role of propensity score in observational studies for causal effects., Biometrika70 41–55.

    Mathematical Reviews (MathSciNet): MR742974
    Zentralblatt MATH: 0522.62091
    Digital Object Identifier: doi:10.1093/biomet/70.1.41
    JSTOR: links.jstor.org

  • Rothman, K. (1976). Causes., American Journal of Epidemiology104 587–592.
  • Rubin, D. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies., Journal of Educational Psychology66 688–701.
  • Rubin, D. (2004). Direct and indirect causal effects via potential outcomes., Scandinavian Journal of Statistics31 161–170.

    Mathematical Reviews (MathSciNet): MR2066246
    Digital Object Identifier: doi:10.1111/j.1467-9469.2004.02-123.x

  • Rubin, D. (2005). Causal inference using potential outcomes: Design, modeling, decisions., Journal of the American Statistical Association100 322–331.

    Mathematical Reviews (MathSciNet): MR2166071
    Zentralblatt MATH: 1117.62418
    Digital Object Identifier: doi:10.1198/016214504000001880

  • Rubin, D. (2007). The design, versus the analysis of observational studies for causal effects: Parallels with the design of randomized trials. Statistics in Medicine26 20–36.

    Mathematical Reviews (MathSciNet): MR2312697
    Digital Object Identifier: doi:10.1002/sim.2739

  • Rubin, D. (2009). Author’s reply: Should observational studies be designed to allow lack of balance in covariate distributions across treatment group?, Statistics in Medicine28 1420–1423.
  • Shpitser, I. and Pearl, J. (2006). Identification of conditional interventional distributions. In, Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (R. Dechter and T. Richardson, eds.). AUAI Press, Corvallis, OR, 437–444.
  • Shpitser, I. and Pearl, J. (2007). What counterfactuals can be tested. In, Proceedings of the Twenty-Third Conference on Uncertainty in Artificial Intelligence. AUAI Press, Vancouver, BC, Canada, 352–359. Also, Journal of Machine Learning Research, 9:1941–1979, 2008.

    Mathematical Reviews (MathSciNet): MR2447308

  • Shpitser, I. and Pearl, J. (2008). Dormant independence. In, Proceedings of the Twenty-Third Conference on Artificial Intelligence. AAAI Press, Menlo Park, CA, 1081–1087.
  • Shpitser, I. and Pearl, J. (2009). Effects of treatment on the treated: Identification and generalization. In, Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence. AUAI Press, Montreal, Quebec.
  • Shrier, I. (2009). Letter to the editor: Propensity scores., Statistics in Medicine28 1317–1318. See also Pearl 2009 http://ftp.cs.ucla.edu/pub/stat_ser/r348.pdf.
  • Shrout, P. and Bolger, N. (2002). Mediation in experimental and nonexperimental studies: New procedures and recommendations., Psychological Methods7 422–445.
  • Simon, H. (1953). Causal ordering and identifiability. In, Studies in Econometric Method (W. C. Hood and T. Koopmans, eds.). Wiley and Sons, Inc., New York, NY, 49–74.

    Mathematical Reviews (MathSciNet): MR61358

  • Simon, H. and Rescher, N. (1966). Cause and counterfactual., Philosophy and Science33 323–340.
  • Simpson, E. (1951). The interpretation of interaction in contingency tables., Journal of the Royal Statistical Society, Series B13 238–241.

    Mathematical Reviews (MathSciNet): MR51472
    JSTOR: links.jstor.org

  • Sobel, M. (1998). Causal inference in statistical models of the process of socioeconomic achievement., Sociological Methods & Research27 318–348.
  • Sobel, M. (2008). Identification of causal parameters in randomized studies with mediating variables., Journal of Educational and Behavioral Statistics33 230–231.
  • Spirtes, P., Glymour, C. and Scheines, R. (1993)., Causation, Prediction, and Search. Springer-Verlag, New York.

    Mathematical Reviews (MathSciNet): MR1227558

  • Spirtes, P., Glymour, C. and Scheines, R. (2000)., Causation, Prediction, and Search. 2nd ed. MIT Press, Cambridge, MA.

    Mathematical Reviews (MathSciNet): MR1815675

  • Stock, J. and Watson, M. (2003)., Introduction to Econometrics. Addison Wesley, New York.
  • Strotz, R. and Wold, H. (1960). Recursive versus nonrecursive systems: An attempt at synthesis., Econometrica28 417–427.

    Mathematical Reviews (MathSciNet): MR120034
    Digital Object Identifier: doi:10.2307/1907731
    JSTOR: links.jstor.org

  • Suppes, P. (1970)., A Probabilistic Theory of Causality. North-Holland Publishing Co., Amsterdam.

    Mathematical Reviews (MathSciNet): MR465774

  • Tian, J., Paz, A. and Pearl, J. (1998). Finding minimal separating sets. Tech. Rep. R-254, University of California, Los Angeles, CA.
  • Tian, J. and Pearl, J. (2000). Probabilities of causation: Bounds and identification., Annals of Mathematics and Artificial Intelligence28 287–313.

    Mathematical Reviews (MathSciNet): MR1797625
    Zentralblatt MATH: 1048.03502
    Digital Object Identifier: doi:10.1023/A:1018912507879

  • Tian, J. and Pearl, J. (2002). A general identification condition for causal effects. In, Proceedings of the Eighteenth National Conference on Artificial Intelligence. AAAI Press/The MIT Press, Menlo Park, CA, 567–573.
  • VanderWeele, T. (2009). Marginal structural models for the estimation of direct and indirect effects., Epidemiology20 18–26.
  • VanderWeele, T. and Robins, J. (2007). Four types of effect modification: A classification based on directed acyclic graphs., Epidemiology18 561–568.
  • Wasserman, L. (2004)., All of Statistics: A Concise Course in Statistical Inference. Springer Science+Business Media, Inc., New York, NY.

    Mathematical Reviews (MathSciNet): MR2055670

  • Wermuth, N. (1992). On block-recursive regression equations., Brazilian Journal of Probability and Statistics (with discussion) 6 1–56.

    Mathematical Reviews (MathSciNet): MR1220428

  • Wermuth, N. and Cox, D. (1993). Linear dependencies represented by chain graphs., Statistical Science8 204–218.

    Mathematical Reviews (MathSciNet): MR1243593
    Digital Object Identifier: doi:10.1214/ss/1177010887
    Project Euclid: euclid.ss/1177010887

  • Whittaker, J. (1990)., Graphical Models in Applied Multivariate Statistics. John Wiley, Chichester, England.

    Mathematical Reviews (MathSciNet): MR1112133

  • Woodward, J. (2003)., Making Things Happen. Oxford University Press, New York, NY.
  • Wooldridge, J. (2002)., Econometric Analysis of Cross Section and Panel Data. MIT Press, Cambridge and London.
  • Wooldridge, J. (2009). Should instrumental variables be used as matching variables? Tech. Rep. https://www.msu.edu/ ec/faculty/wooldridge/current%20research/treat1r6.pdf, Michigan State University, MI.
  • Wright, S. (1921). Correlation and causation., Journal of Agricultural Research20 557–585.
  • Yule, G. (1903). Notes on the theory of association of attributes in statistics., Biometrika2 121–134.
  • Канадец. - Да. Он вызвал «скорую». Мы решили уйти.

    One thought on “Causal Diagrams For Empirical Research Paper

    Leave a Reply

    Your email address will not be published. Required fields are marked *