{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T03:35:11Z","timestamp":1768620911764,"version":"3.49.0"},"publisher-location":"New York, NY, USA","edition-number":"1","reference-count":37,"publisher":"ACM","isbn-type":[{"value":"9781450395861","type":"print"}],"license":[{"start":{"date-parts":[[2022,2,28]],"date-time":"2022-02-28T00:00:00Z","timestamp":1646006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2022,2,28]]},"DOI":"10.1145\/3501714.3501742","type":"book-chapter","created":{"date-parts":[[2022,3,4]],"date-time":"2022-03-04T20:58:40Z","timestamp":1646427520000},"page":"483-506","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Detecting Latent Heterogeneity"],"prefix":"10.1145","author":[{"given":"Judea","family":"Pearl","sequence":"first","affiliation":[]}],"member":"320","published-online":{"date-parts":[[2022,3,4]]},"reference":[{"key":"e_1_3_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476902"},{"key":"e_1_3_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/2998558"},{"key":"e_1_3_2_1_4_1","volume-title":"Causality: Statistical Perspectives and Applications","author":"Angrist J. D.","year":"1999","unstructured":"Angrist , J. D. and A. B. Krueger . 1999 . \u201cHandbook of Labor Economics.\u201d Pp. 1277-366 in Causality: Statistical Perspectives and Applications , 1 st ed., vol. 3 , edited by O. Ashenfelter and D. Card. Amsterdam , the Netherlands : Elsevier . Angrist, J. D. and A. B. Krueger. 1999. \u201cHandbook of Labor Economics.\u201d Pp. 1277-366 in Causality: Statistical Perspectives and Applications, 1st ed., vol. 3, edited by O. Ashenfelter and D. Card. Amsterdam, the Netherlands: Elsevier.","edition":"1"},{"key":"e_1_3_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1257\/jep.24.2.3"},{"key":"e_1_3_2_1_6_1","volume-title":"Probabilities: Computational Methods, Bounds, and Applications.","author":"Balke A.","year":"1994","unstructured":"Balke , A. and J. Pearl . 1994 a. \u201cCounterfactual Probabilities: Computational Methods, Bounds, and Applications. \u201d Pp. 46-54 in Uncertainty in Artificial Intelligence 10, edited by R. L. de Mantaras and D. Poole . San Mateo, CA : Morgan Kaufmann . Balke, A. and J. Pearl. 1994a. \u201cCounterfactual Probabilities: Computational Methods, Bounds, and Applications.\u201d Pp. 46-54 in Uncertainty in Artificial Intelligence 10, edited by R. L. de Mantaras and D. Poole. San Mateo, CA: Morgan Kaufmann."},{"key":"e_1_3_2_1_7_1","volume-title":"Proceedings of the Twelfth National Conference on Artificial Intelligence","author":"Balke A.","unstructured":"Balke , A. and J. Pearl . 1994b. \u201cProbabilistic Evaluation of Counterfactual Queries.\u201d Pp. 230-37 in Proceedings of the Twelfth National Conference on Artificial Intelligence , vol. I , edited by B. Hayes-Roth and R. E. Korf. Menlo Park, CA: MIT Press. Balke, A. and J. Pearl. 1994b. \u201cProbabilistic Evaluation of Counterfactual Queries.\u201d Pp. 230-37 in Proceedings of the Twelfth National Conference on Artificial Intelligence, vol. I, edited by B. Hayes-Roth and R. E. Korf. Menlo Park, CA: MIT Press."},{"key":"e_1_3_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1972.10482387"},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ssresearch.2005.06.006"},{"key":"e_1_3_2_1_10_1","volume-title":"Netherlands: Springer.","author":"Brand J. E.","year":"2013","unstructured":"Brand , J. E. and J. S. Thomas . 2013 . \u201cCausal Effect Heterogeneity.\u201d Pp. 189-213 in Handbook of Causal Analysis for Social Research, chap. 11, edited by S. L. Morgan. Dordrecht , the Netherlands: Springer. Brand, J. E. and J. S. Thomas. 2013. \u201cCausal Effect Heterogeneity.\u201d Pp. 189-213 in Handbook of Causal Analysis for Social Research, chap. 11, edited by S. L. Morgan. Dordrecht, the Netherlands: Springer."},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1177\/0003122410363567"},{"key":"e_1_3_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1540-5982.2010.01622.x"},{"key":"e_1_3_2_1_13_1","first-page":"v3","article-title":"A Paradox from Randomization-based Causal Inference","volume":"1402","author":"Ding P.","year":"2014","unstructured":"Ding , P. 2014 . \u201c A Paradox from Randomization-based Causal Inference .\u201d Tech. rep., Harvard University, Cambridge, MA. arXiv : 1402 .0142 v3 . Ding, P. 2014. \u201cA Paradox from Randomization-based Causal Inference.\u201d Tech. rep., Harvard University, Cambridge, MA. arXiv:1402.0142v3.","journal-title":"Tech. rep., Harvard University, Cambridge, MA. arXiv"},{"key":"e_1_3_2_1_14_1","volume-title":"Milton Keynes, U.K.: College Publications.","author":"Elwert F.","year":"2010","unstructured":"Elwert , F. and C. Winship . 2010 . \u201cEffect Heterogeneity and Bias in Main-effects-only Regression Models.\u201d Pp. 327-36 in Heuristics, Probability and Causality: A Tribute to Judea Pearl, edited by R. Dechter, H. Geffner, and J. Halpern . Milton Keynes, U.K.: College Publications. Elwert, F. and C. Winship. 2010. \u201cEffect Heterogeneity and Bias in Main-effects-only Regression Models.\u201d Pp. 327-36 in Heuristics, Probability and Causality: A Tribute to Judea Pearl, edited by R. Dechter, H. Geffner, and J. Halpern. Milton Keynes, U.K.: College Publications."},{"key":"e_1_3_2_1_15_1","first-page":"151","article-title":"An Axiomatic Characterization of Causal Counterfactuals","volume":"3","author":"Galles D.","year":"1998","unstructured":"Galles , D. and J. Pearl . 1998 . \u201c An Axiomatic Characterization of Causal Counterfactuals .\u201d Foundation of Science 3 : 151 - 182 . Galles, D. and J. Pearl. 1998. \u201cAn Axiomatic Characterization of Causal Counterfactuals.\u201d Foundation of Science 3:151-82.","journal-title":"Foundation of Science"},{"key":"e_1_3_2_1_16_1","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1080\/00031305.1991.10475813","article-title":"On the Logical Justification of Conditional Tests for Two-by-two Contingency Tables","volume":"45","author":"Greenland S.","year":"1991","unstructured":"Greenland , S. 1991 . \u201c On the Logical Justification of Conditional Tests for Two-by-two Contingency Tables .\u201d The American Statistician 45 : 248 - 251 . Greenland, S. 1991. \u201cOn the Logical Justification of Conditional Tests for Two-by-two Contingency Tables.\u201d The American Statistician 45:248-51.","journal-title":"The American Statistician"},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1613\/jair.648"},{"key":"e_1_3_2_1_18_1","volume-title":"Pp. 201-30 in Evaluations: Welfare and Training Programs","author":"Heckman J.","unstructured":"Heckman , J. 1992. \u201c Randomization and Social Policy Evaluation .\u201d Pp. 201-30 in Evaluations: Welfare and Training Programs , edited by C. Manski and I. Garfinkle. Cambridge, MA : Harvard University Press . Heckman, J. 1992. \u201cRandomization and Social Policy Evaluation.\u201d Pp. 201-30 in Evaluations: Welfare and Training Programs, edited by C. Manski and I. Garfinkle. Cambridge, MA: Harvard University Press."},{"key":"e_1_3_2_1_19_1","volume-title":"New York: Cambridge University Press.","author":"Heckman J.","year":"1985","unstructured":"Heckman , J. and R. Robb . 1985 . \u201cAlternative Methods for Evaluating the Impact of Interventions.\u201d Pp. 156-245 in Longitudinal Analysis of Labor Market Data, edited by J. Heckman and B. Singer . New York: Cambridge University Press. Heckman, J. and R. Robb. 1985. \u201cAlternative Methods for Evaluating the Impact of Interventions.\u201d Pp. 156-245 in Longitudinal Analysis of Labor Market Data, edited by J. Heckman and B. Singer. New York: Cambridge University Press."},{"key":"e_1_3_2_1_20_1","volume-title":"New York: Springer-Verlag.","author":"Heckman J.","year":"1986","unstructured":"Heckman , J. and R. Robb . 1986 . \u201cAlternative Methods for Solving the Problem of Selection Bias in Evaluating the Impact of Treatments on Outcomes.\u201d Pp. 63-107 in Drawing Inference from Self Selected Samples, edited by H. Wainer . New York: Springer-Verlag. Heckman, J. and R. Robb. 1986. \u201cAlternative Methods for Solving the Problem of Selection Bias in Evaluating the Impact of Treatments on Outcomes.\u201d Pp. 63-107 in Drawing Inference from Self Selected Samples, edited by H. Wainer. New York: Springer-Verlag."},{"key":"e_1_3_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1162\/rest.88.3.389"},{"key":"e_1_3_2_1_22_1","volume-title":"New York: Cambridge University Press.","author":"Morgan S. L.","year":"2007","unstructured":"Morgan , S. L. and C. Winship . 2007 . Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research) . New York: Cambridge University Press.\u2009\u2009 Morgan, S. L. and C. Winship. 2007. Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research). New York: Cambridge University Press."},{"key":"e_1_3_2_1_23_1","volume-title":"New York: Cambridge University Press.","author":"Morgan S. L.","year":"2015","unstructured":"Morgan , S. L. and C. Winship . 2015 . Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research) . 2 nd ed. New York: Cambridge University Press.\u2009\u2009 Morgan, S. L. and C. Winship. 2015. Counterfactuals and Causal Inference: Methods and Principles for Social Research (Analytical Methods for Social Research). 2nd ed. New York: Cambridge University Press.","edition":"2"},{"key":"e_1_3_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9531.2008.00204.x"},{"key":"e_1_3_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177010894"},{"key":"e_1_3_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/82.4.669"},{"key":"e_1_3_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511803161"},{"key":"e_1_3_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1515\/jci-2013-0027"},{"key":"e_1_3_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1080\/00031305.2014.876829"},{"key":"e_1_3_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0266466614000231"},{"key":"e_1_3_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/70.1.41"},{"key":"e_1_3_2_1_32_1","volume-title":"Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence, edited by R. Dechter and T. Richardson. Corvallis, OR: AUAI Press.","author":"Shpitser I.","unstructured":"Shpitser , I. and J. Pearl . 2006. \u201cIdentification of Conditional Interventional Distributions.\u201d Pp. 437-44 in Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence, edited by R. Dechter and T. Richardson. Corvallis, OR: AUAI Press.\u2009\u2009 Shpitser, I. and J. Pearl. 2006. \u201cIdentification of Conditional Interventional Distributions.\u201d Pp. 437-44 in Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence, edited by R. Dechter and T. Richardson. Corvallis, OR: AUAI Press."},{"key":"e_1_3_2_1_33_1","volume-title":"Proceedings of the Twenty-fifth Conference on Uncertainty in Artificial Intelligence, edited by J. Bilmes and A. Ng. Corvallis, OR: AUAI Press.","author":"Shpitser I.","unstructured":"Shpitser , I. and J. Pearl . 2009. \u201cEffects of Treatment on the Treated: Identification and Generalization.\u201d Pp. 514-21 in Proceedings of the Twenty-fifth Conference on Uncertainty in Artificial Intelligence, edited by J. Bilmes and A. Ng. Corvallis, OR: AUAI Press.\u2009\u2009 Shpitser, I. and J. Pearl. 2009. \u201cEffects of Treatment on the Treated: Identification and Generalization.\u201d Pp. 514-21 in Proceedings of the Twenty-fifth Conference on Uncertainty in Artificial Intelligence, edited by J. Bilmes and A. Ng. Corvallis, OR: AUAI Press."},{"key":"e_1_3_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1086\/288105"},{"key":"e_1_3_2_1_35_1","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1111\/j.2517-6161.1951.tb00088.x","article-title":"The Interpretation of Interaction in Contingency Tables","volume":"13","author":"Simpson E.","year":"1951","unstructured":"Simpson , E. 1951 . \u201c The Interpretation of Interaction in Contingency Tables .\u201d Journal of the Royal Statistical Society, Series B 13 : 238 - 241 .\u2009\u2009 Simpson, E. 1951. \u201cThe Interpretation of Interaction in Contingency Tables.\u201d Journal of the Royal Statistical Society, Series B 13:238-41.","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"e_1_3_2_1_36_1","doi-asserted-by":"publisher","DOI":"10.1097\/EDE.0b013e318127181b"},{"key":"e_1_3_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.soc.25.1.659"},{"key":"e_1_3_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1177\/0081175012452652"}],"container-title":["Probabilistic and Causal Inference"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3501714.3501742","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3501714.3501742","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T20:11:45Z","timestamp":1750191105000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3501714.3501742"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,28]]},"ISBN":["9781450395861"],"references-count":37,"alternative-id":["10.1145\/3501714.3501742","10.1145\/3501714"],"URL":"https:\/\/doi.org\/10.1145\/3501714.3501742","relation":{},"subject":[],"published":{"date-parts":[[2022,2,28]]},"assertion":[{"value":"2022-03-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"2022-03-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}